Predicting the Next Move
Grade
Title
Teacher
Student
G10 Physics: Predicting the Next Move AB Assessment
You will one assessment of AB, entitled The Physics of Road Safety. When admiring a new car, no one ever asks the owner how well its stops....just how well it goes. One of the most significant factors to consider when buying a new car is the vehicle braking capability. The laws of Physics will determine the braking distance and therefore whether you will crash or not. When vehicles do collide, what happens is again determined by the law of Physics. The concept of momentum is critical here in order to understand what happens to the car and the passengers inside it. Your task is to research one or more factors that affect the physics of road safety. You could; •
Look at the factors that affect the braking capability of a vehicle. This would involve looking at the way that the braking force and initial kinetic energy affects the total stopping distance of the car.
•
Consider the important role of momentum in car collisions. The law of conservation of momentum is very important and applies to situations where one vehicle hits another (or hits a tree…).
Your report should; •
Contain a mixture of text and graphical sources and it should be persuasively written.
•
Use correct scientific terminology.
•
Make good use of worked examples using appropriate equations.
•
Be no more than 1200 words long and should contain a full bibliography with references in the MLA style.
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G10 Physics: Predicting the Next Move DEF Assessment
You will have one assessment of criteria DEF, entitled The Ballistic Pendulum. In this experiment you will use a simple pendulum to move an object. Your task is to investigate one factor that affects the average distance moved by the object.
You should; •
Conduct trial runs for the various possible factors that could affect the average speed.
•
Based upon the conclusion from your trail runs, choose one factor to investigate in more detail.
•
Decide on a suitable number and range of values for this factor (the independent variable)
•
Decide on a suitable number of repeats.
•
Consider how to make your measurements precise and accurate.
Thread
Pendulum bob
Object
Surface
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G10 Physics: Predicting the Next Move Speed, Distance & Time
You may be familiar with the most common equation of motion to calculate the speed (or velocity) of an object;
Usually the distance (or displacement) is measured in metres and the time is measured in seconds, so the speed would then be in units of metres per second. Other units are also possible, such as kilometres per hour, millimetres per second and so on. Example 1. A car travels 18 km in a time of 30 minutes. What is the speed of the car in metres per second?
18 18 000
30 30 60 1800
18 000 1800
10
Example 2. What would be the speed of the car in Example 1 measured in kilometres per hour?
18
30 0.5
18 0.5
36
In the S.I. system of measurements then the unit is metres per second and this is the unit that will be used throughout this topic.
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G10 Physics: Predicting the Next Move Speed, Distance & Time
The same equation can be used to calculate either the distance travelled (if the speed and time taken are known) or the time taken (if the speed and distance travelled are known). Example 3. Pavlina runs 6.0 km at a constant speed of 3.0 ms-1. What is the time taken?
6.0 6 000 ! 3.0 "
6 000 3.0
2 000
Example 4. Pavlina then runs for 90 minutes at a constant speed of 5.0 ms-1. How far did she run? Express the answer in standard form.
! 5.0
" 90 60 5 400
5.0 5 400 27 000
2.7 10' In Physics, measurements reflect with the often extreme scales in the Universe. So measurements are often either very large or very small. For this reason standard form is most often used to express numbers.
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G10 Physics: Predicting the Next Move Speed, Distance & Time
In the exercise below calculate the missing quantity. Distance
Time
Average speed
In metres (m)
In seconds (s)
In metres per second (ms-1)
100
5.0
Journey
A
B
12
C
4.0 x 104
D
6.0 x 103
200
1 200
E
F
30
2.0 x 106
8.0 x 10-6
2.0
3.6 x 103
7 200
I
J
15
5.0 x 102
G
H
25
600
5.0 Ă— 10-6
5 x 10-2
25 x 10-9
K
[1 year]
3.0 x 108
L
500
3.0 x 108
Note: the distance travelled in K is called the light year and the distance in L is the separation between the Earth and the Sun and is called the astronomical unit.
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G10 Physics: Predicting the Next Move More Difficult Questions
1. Tommy and Anna plan to go to see their friend Estelle, who is staying at her house. Anna pops out to get a present for Estelle. Impatient to leave, Tommy decides to make the journey on his own from their house to Estelle’s House, a distance of 15.0 km. He decides to walk and travels at a constant speed of 3.0 ms-1 and leaves at mid-day. Anna returns home to find that Tommy has gone… …In an effort to catch up, she leaves at 12.45 p.m. and uses her roller skates, travelling at a constant speed of 6.0 ms-1 all the way to Estelle. Who gets to see Estelle first? What is the arrival time difference between Tommy and Anna?
2. Rohan decides to see his friend Hugh. He leaves his house at mid-day and sets off on his donkey, travelling the distance of 10km at a constant speed of 2.5ms-1. At 12.30 pm Hugh decides that Rohan must have forgotten to come and see him. Hugh sets off along a different route, travelling the distance of 12.6 km at a constant speed of 3.0 ms-1. When Rohan gets to Hugh’s he finds a note on his door telling him that Hugh has made the journey to Rohan’s house… …Rohan immediately travels back to his own house, using his original route, at a constant speed of 5.0 ms-1. Who gets to Rohan’s house first?
3. Ioannis starts at point A and runs due East with a constant speed of 4.0 ms-1. At the same time, Momo starts from point B, 14 km East of point A. Momo runs with a constant speed of 3.0 ms-1 directly towards point A (i.e. due West). How far from point A do Ioannis and Momo meet?
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G10 Physics: Predicting the Next Move Distance– Time Graphs
A journey can be represented on a graph. The most common types in Physics are the distance (displacement)-time graph and the speed (velocity)-time graph. Each graph gives important information about the journey. One important point is that, since the journeys have a particular direction, then they can be thought of as journeys that happen along one long straight line.
Exercise Represent the following descriptions on the graph below. a) Klesta: a constant distance of 10m. b) Anna: a distance that increases at a steady rate so that after 14 s it is 10m. c) Moritz: a distance of 10m at 0 s that decreases at a steady rate so that after 14 s the distance is zero. 12 11 10 9
Distance / m
8 7 6 5 4 3 2 1 0 0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Time / s
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G10 Physics: Predicting the Next Move Distance – Time Graphs
Look at the Journey Lana’s journey below.
Lana's Journey 6.0 5.5 5.0 4.5
Displacement / m
4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0
1
2
3
4
5
6
7
8
9
10
11
12
Time / s
a) Draw an appropriate line of best fit through Lana’s data. b) Calculate the gradient of the line of best fit. c) Give the unit of the gradient. What physical quantity does this represent?
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G10 Physics: Predicting the Next Move Distance – Time Graphs
Look at the Patrick’s Journey below.
Patrick's Journey 14.0 13.0 12.0 11.0 10.0
Displacement / m
9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0 0
1
2
3
4
5
6
7
8
9
10
11
12
Time / s
a) Draw an appropriate line of best fit through the data. b) Calculate the gradient of the line of best fit. c) What is the Patrick’s velocity in this journey? d) Describe in one or two sentences what is happening in Patrick’s journey.
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G10 Physics: Predicting the Next Move Distance – Time Graphs
Look at the Aira’s Journey below.
Aira's Journey 10.0
9.0
8.0
Displacement / m
7.0
6.0
5.0
4.0
3.0
2.0
1.0
0.0 0
1
2
3
4
5
6
7
8
9
10
11
12
Time / s
a) Draw two straight lines of best fit through the data. b) Calculate the gradient of the line of best fit between 2 and 12 seconds. Give the unit. c) Describe what is happening in Aira’s journey in one or two sentences.
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G10 Physics: Predicting the Next Move Distance – Time Graphs
Look at the Jonathan’s Journey below.
Jonathan' s Journey 6.0 5.5 5.0 4.5
Displacement / m
4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0
1
2
3
4
5
6
7
8
9
10
11
12
Time / s
a) Draw two straight lines of best fit through the data. b) Calculate Jonathan’s velocity between zero and 6 s and between 6 and 12 s. c) What is Jonathan’s displacement for the entire journey? d) What is Jonathan’s average velocity for the Jonathan’s journey?
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G10 Physics: Predicting the Next Move Curved Data
Look at the Jeffrey’s Journey below – it is an example of a situation where the displacement does not increase steadily.
Jeffrey's Journey 150 140 130 120 110
Displacement / m
100 90 80 70 60 50 40 30 20 10 0 0
1
2
3
4
5
6
7
8
9
10
11
12
Time / s
a) Draw an appropriate line of best fit through the data. b) Estimate Jeff’s instantaneous velocity at a time of 8.0 s – you will do this by drawing a tangent to your curve and finding the gradient of your tangent (you may have done something similar in your Grade 9 Chemistry unit on rates of reaction).
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G10 Physics: Predicting the Next Move Curved Data
a) Start by drawing a smooth line of best fit through the data. b) Then, at a time of 8.0s, estimate the slope of your curve – extend this to the edges of the graph. c) Make a triangle by drawing the vertical and horizontal parts as shown. d) Calculate the gradient of the triangle.
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G10 Physics: Predicting the Next Move Curved Data
From the tangent‌
∆)
124 * + ,
∆-
8.1 * ,
)
∆ ∆
124 8.1
16 * 2 . .. , Key Points This method can be used on any curved line. It gives an estimate of the slope at a point on a curve Remember that, as usual, the gradient has a unit.
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G10 Physics: Predicting the Next Move Speed – Time Graphs
Instead of plotting the displacement against the time, we can plot the speed (velocity) against the time directly. Look at Courtney’s car journey. This journey shows a constant velocity – of 25 ms-1 – over a time of 12 seconds. What is the total distance that Courtney has travelled?
Courtney's Journey 30.0 28.0 26.0 24.0 22.0
Velocity / ms-1
20.0 18.0 16.0 14.0 12.0 10.0 8.0 6.0 4.0 2.0 0.0 0
1
2
3
4
5
6
7
8
9
10
11
12
Time / s
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G10 Physics: Predicting the Next Move Speed – Time Graphs
We can calculate this as;
∆ ∆
40 12 480
a) Now draw a straight line of best fit through the data. b) Calculate the area under the line. c) Notice that the area is identical to the calculation above. d) For a velocity time graph the area under the graph gives the total distance travelled. This is true for all velocity time graphs. e) What does the gradient of the graph tell us about the journey? The graph shows a constant (steady) velocity of 25 ms-1, so it is not accelerating or decelerating. f)
We can say that the average acceleration is zero - the gradient of the line of best fit is equal to the acceleration.
/ . 0
1 1
2 ) 2
3
Notice that the unit for acceleration is “metre per second squared� or “metre per second per second�. You may also see this written as “m/s/s�. You can also calculate acceleration directly from a formula as;
2 ) ∆ 2 ∆
0
The last formula is commonly used in textbooks where “v� is the final velocity, “u� is the initial velocity and “t� is the change in time.
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G10 Physics: Predicting the Next Move Calculating Acceleration
Examples a) Teddy starts from rest and accelerates uniformly. After 5.0 seconds he has a velocity of 10 ms-1. Calculate the acceleration of the runner.
∆ ∆
*410 0 0, 5.0
410 5.0
42.0 3
b) Neha is travelling in a car that has an initial velocity of 30 ms-1. It decelerates uniformly to a velocity of 10 ms-1 in a time of 4.0 s. Calculate Neha’s deceleration. (note: a deceleration is a “negative acceleration�)
∆ ∆
*410 0 30, 4.0
020 4.0
05.0 3 i.e. a deceleration of +5.0 ms-2
The answer of “minus 5.0 metres per second squaredâ€? means that, in each second, the car loses 5.0 ms-1 of velocity. The velocity of the car would change as (in ms-1) 30 (at the start), 25 (after 1 second), 20 (after 2 seconds), ‌ and so on.
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G10 Physics: Predicting the Next Move Speed – Time Graphs
Mathy’s journey below shows a changing velocity – the velocity is decreasing at a steady rate from 12.0 ms-1 at the start to 4.8 ms-1 at the end, 12 seconds later.
Mathy's Journey 14.0 13.0 12.0 11.0 10.0
Velocity / ms-1
9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0 0
1
2
3
4
5
6
7
8
9
10
11
12
Time / s
a) What is Mathy’s total distance travelled for this journey? (Draw an appropriate line of best fit and find the area under the line). b) What is Mathy’s average acceleration for this journey?
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G10 Physics: Predicting the Next Move Speed – Time Graphs
For the acceleration you will need to calculate the gradient of your line of best fit.
/
∆ ∆
*4.8 0 12, 12
00.60 3 Notice that;
a) The answer can be read as “an acceleration of minus 0.60 metres per second squared�. b) The minus sign indicates that the object is slowing down (decelerating). c) We could also correctly say that the journey shows “a deceleration of +0.60 metres per second squared�. d) The unit for the gradient is the unit for velocity (metres per second) divided by the unit for time (seconds). This gives a unit for acceleration of “metres per second per second� or “metres per second squared�. e) The deceleration (negative acceleration) can be interpreted as “each second, the velocity of the object decreases by 0.60 metres per second.� f)
The velocity decreases, each second, by 0.60 metres per second so it decreases as 12.0, 11.4, 10.8, 10.2, ‌ and so on.
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G10 Physics: Predicting the Next Move Speed – Time Graphs
Look at the Min Jae’s journey below. It represents a car accelerating at a constant (steady) rate.
Min Jae's Journey 30.0 28.0 26.0 24.0 22.0
Velocity / ms-1
20.0 18.0 16.0 14.0 12.0 10.0 8.0 6.0 4.0 2.0 0.0 0
1
2
3
4
5
6
7
8
9
10
11
12
Time / s
a) Calculate the total distance travelled by Min Jae. b) Calculate Min Jae’s acceleration for the journey.
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G10 Physics: Predicting the Next Move Velocity – Time Graphs
The graph below represents the Nick’s journey on a motorbike as it first accelerates and then decelerates.
Nick's Journey 14.0 13.0 12.0 11.0 10.0
Velocity / ms-1
9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0 0
1
2
3
4
5
6
7
8
9
10
11
12
Time / s
a) Calculate Nick’s acceleration on the motorbike in the first 6 seconds and the last 6 seconds. b) Calculate the total distance travelled by Nick.
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G10 Physics: Predicting the Next Move Speed – Time Graphs
The graph below represents Vera’s journey in a car travelling between traffic lights – the car accelerates, then travels at a steady velocity before decelerating.
Vera's Journey 32.0 30.0 28.0 26.0 24.0 22.0
Velocity / ms-1
20.0 18.0 16.0 14.0 12.0 10.0 8.0 6.0 4.0 2.0 0.0 0
1
2
3
4
5
6
7
8
9
10
11
12
Time / s
a) Calculate Vera’s acceleration in each of the 3 stages of the journey. b) Calculate the total distance travelled by Vera.
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G10 Physics: Predicting the Next Move Adding Forces
Forces are another example of a vector quantity – they have both a size and a direction. Add these combinations of forces together - you need to give the resultant (overall or combined) force and the direction. If forces are in – line then you can add them together. It is conventional to think of forces that go to the right and upwards as positive and forces that go to the left and downwards are negative (just like the axes on a graph). Adding forces is easy. First add up the forces that are in the same line. Then to add forces that are perpendicular to each other you need to use Pythagoras.
a) 5N
12N
b)
3N
3N
6N
6N
c) 15N
12N
4N
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G10 Physics: Predicting the Next Move Adding Forces
You can also add forces together by making a scale drawing. •
First you need to choose a scale for your drawing such as “1cm represents 10N”.
•
Add up all forces in the same line (for example, horizontally and vertically).
•
Mark a point on your graph paper to represent the start.
•
Draw your resulting forces to scale on graph paper. Add them tip to tail – one force followed by another.
•
Draw an arrow from the start to the tip of the final arrow– this represents the resultant force.
•
The length of the resultant arrow and its direction can then be easily measured.
Example. •
Add forces of; 5.0N West 12N North 14N East and 6.0N South East by scale drawing.
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G10 Physics: Predicting the Next Move Adding Forces
The dashed arrow on the diagram shows the resultant force. This method can be used for any combination of forces – or any combination of any other vector such as displacement, velocity and so forth.
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G10 Physics: Predicting the Next Move Force, Mass and Acceleration
In these experiments you will look at the effect of; a) In experiment 1, changing the size of a force acting on a constant mass. The force in the experiment will be provided by some weights that hang over the side of the bench. b) In experiment 2, changing the size of a mass that being acted on by a constant force. The mass in the experiment will be a trolley. Weights can be added to the trolley to increase its mass. The basic arrangement looks like the picture below.
acceleration
heavy trolley
pulley
weight
You will need to time the movement of the trolley over a fixed distance across the bench. You can use this formula to calculate the acceleration of the trolley.
2
3
3
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G10 Physics: Predicting the Next Move Newton’s First and Second Laws
The conclusions of the trolley experiment Newton’s second law is usually written as;
5
We can say; If there is a resultant force F acting on a mass m, then it will accelerate with an acceleration a where;
5
If there is no resultant force (F = 0) acting on a mass m, then there is no acceleration (a = 0). Where there is no resultant force we usually say the forces are balanced. In this case the object must be either; •
Stationary. or
•
Moving at a constant velocity (a constant speed in a straight line).
These statements are often referred to as Newton’s First Law. Watch these links; http://www.brainpop.com/science/motionsforcesandtime/acceleration/
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G10 Physics: Predicting the Next Move Equal and Opposite!
Think of a ball striking a wall – shown above. a) How can we be sure that there are forces involved here? b) Does the ball exert a force on the wall? c) Does the wall exert a force on the ball?
Now think about a baseball player. d) How can we be sure that there are forces involved here? e) Does the ball exert a force on the baseball bat? f)
Does the baseball bat exert a force on the ball?
Newton realised that all forces come in pairs – the force of the ball on the wall (the action) is the same as the force of the wall on the ball (the re-action). In the same way, the action of the baseball bat on the ball is equal and opposite to the re-action of the ball on the baseball bat.
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G10 Physics: Predicting the Next Move Equal and Opposite!
Newton’s third law can be written as; •
For every action, there is an equal and opposite reaction. Or
•
If body A exerts a force on body B, then body B exerts an equal and opposite force on body A.
We can apply this law to a whole range of everyday situations. As an example, look at the runner above. a) For the runner to move forwards, in what direction is the force of the runner (the action) on the ground? b) According to Newton’s third law, in what direction is the force of the ground (the reaction) on the runner? c) Why does the runner move forwards? d) Suppose the force of the runner on the ground was 250 N backwards and the mass of the runner was 50kg. What would be the acceleration of the runner? e) Once the runner starts moving, the force of the air acting against him is 150N. What is the acceleration of the runner now? f)
Eventually the force of the air acting against the runner is 250N. What can we say about the motion of the runner in this case?
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G10 Physics: Predicting the Next Move Gravitational Field Strength
Let’s look back at Newton’s second law;
F ma
This equation means “if there is a resultant force acting on a mass, then it must accelerate�. Suppose that we have an object that is falling towards the Earth, and we ignore any effects of air resistance so that the force of gravity is the only force that we need to consider.
What would the acceleration of the object be? This can be calculated and it can also be measured. The figure for the “acceleration due to gravity� near the surface of the Earth is;
10 3 Now let us put this value into Newton’s formula for the second law;
5
This equation gives us the force on a mass falling towards the Earth because of the force of gravity. We usually call this force the weight of an object.
5 . / ) 9
How strong is our gravitational field? The gravitational field strength – the number of newtons of force for each kilogram of mass – can be obtained easily;
5 :
5 * ; , * ,
So the number of “newtons per kilogram� is equal to g - around 10 Nkg-1 here on the surface of the Earth. It is no accident that the numbers for “acceleration due to gravity� and “gravitational field strength� are identical.
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G10 Physics: Predicting the Next Move Equal and Opposite!
Mass 60 kg
Mass 6.0 x 1024 kg
Now we will look at the situation of a skydiver falling to Earth. Igor the skydiver is accelerating downwards because there is a resultant force acting downwards on him. On or near the surface of the Earth we know that each 1kg of mass is pulled downward with a force of about 10N;
/ 5 ! 10 < Calculate the force of gravity pulling Igor downwards. We usually call this the weight â&#x20AC;&#x201C; notice that weight is a force and is measured in newtons (N). According to Newtonâ&#x20AC;&#x2122;s third law â&#x20AC;&#x201C; Igor must be pulling the Earth upwards with the same force! Use Newtonâ&#x20AC;&#x2122;s third law to state the upward force of Igor acting on the Earth. Use Newtonâ&#x20AC;&#x2122;s second law, and the figure for the mass of the Earth, to calculate the acceleration of the Earth upwards (towards Igor). Explain why we do not, in practise, see the Earth accelerating towards falling objects like sky divers.
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G10 Physics: Predicting the Next Move Sky Diving
Now we will continue to use Newton’s laws to explain the motion of a Igor the sky-diver as he falls to Earth. In your answers indicate clearly which of Newton’s three laws you are using. For example, if you wanted to use Newton’s second law in your explanation you could begin an explanation with; “Using Newton’s second law, if there is a force acting on a mass then….” a) Suppose that Igor has just jumped out of a plane so that he has not yet started to fall. Describe the forces acting on Igor. b) Explain why Igor will start to accelerate downwards. As Igor accelerates, the force of the air reacting upwards will increase. c) Explain what effect this will have on Igor’s motion. Eventually, the force of the air upwards will be equal and opposite to the weight force pulling Igor downwards. d) Explain why Igor has now reached her Terminal Velocity. Igor opens his parachute! e) What effect will this have on the forces acting on Igor? f)
What effect will it have on his motion?
g) Explain why, once the parachute is opened, the forces on Igor will eventually become balanced. h) Explain why Igor will eventually fall at a steady rate that is much less than before.
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G10 Physics: Predicting the Next Move Into Space!
Emma the astronaut is taking a trip to the Moon. Before taking off in her space ship, Emma checks her mass and his weight; Mass = 45 kg Weight = 450 N a) Use the information above to calculate the gravitational field strength g, in Nkg-1 (newtons per kilogram) for the surface of the Earth. In space, far away from any planets and moons, Emma measures the gravitational field strength. Gravitational field strength in space = 0 N kg-1 b) Calculate or state Emma’s mass and weight in space from this information. Emma makes a successful landing on the Moon. She decides to re-measure her mass and gravitational field strength. Mass = 45 kg Gravitational field strength on the Moon’s surface = 1.6 Nkg-1. c) Use this information to calculate Emma’s weight on the surface of the Moon. d) On the Moon, would Emma be able to jump less high, the same height or higher than on Earth? Explain your answer.
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G10 Physics: Predicting the Next Move Work Against Gravity
5.0m
Jakub is going to dive off one of the diving boards. Jakub has to do work in order to climb to one of the ladders â&#x20AC;&#x201C; the higher Jakub climbs, the more work he has to do. Jakub has to work against the force of gravity in order to climb up. He does this by providing a force of his own â&#x20AC;&#x201C; using his muscles. Jakubâ&#x20AC;&#x2122;s muscles provide enough upward force to counteract out the downward force of gravity and move up the ladder at a steady speed. The amount of energy that Jakub has to use is called the work done. The formula for the amount of work done by Jakub is;
9 5 . . â&#x2C6;&#x2020;= 5 â&#x2C6;&#x2020;
In this case Jakubâ&#x20AC;&#x2122;s muscle force is equal to his weight force and the change in displacement is how far he moves vertically, in other words his change in height;
9 ) ;
/>= â&#x2C6;&#x2020;
We call this work done against the force of gravity his Gravitational Potential Energy (GPE)
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G10 Physics: Predicting the Next Move Working Against Gravity
Example Jakub has a mass of 60kg. How much GPE does he have when; a) He climbs up to the lowest diving board? b) He climbs directly to the highest diving board? c) He climbs from the lowest to the highest diving board? d) Does it matter how fast Jakub climbs the ladder?
Answer a)
? ; + : â&#x2C6;&#x2020;= â&#x2C6;&#x2020;
60 10 1.25 750 A
Answer b)
B + : â&#x2C6;&#x2020;= â&#x2C6;&#x2020;
60 10 5.0 3000 A
Answer c)
C ; + : â&#x2C6;&#x2020;= â&#x2C6;&#x2020;
60 10 3.75 2250 A
Answer d) No â&#x20AC;&#x201C; the amount of energy that he needs to do the useful work in climbing the ladder is the same. He might of course waste more energy (for example as heat) by climbing at different speeds and this would change his efficiency. The rate at which work is done is called the power and so climbing the ladder faster would require more power but not more energy.
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G10 Physics: Predicting the Next Move A Question of Work
1. How much work is done in these situations : a) Alwin pushes a van against a friction force of 300 N for 10 m. b) Chiara pushes a shopping trolley with a force of 30 N for a distance of 100 m. c) Rifkat lifts a weight of 500 N through a height of 2.0 m. 2. Umberto pushes a barrow at a steady speed of 2.0 ms-1 for 10 s, using a force of 100 N. a) How far did Umberto travel? b) How much work has Umberto done? c) Where does the energy come from? (What is the energy transfer involved?) 3. Edward with a mass of 60 kg climbs 10 m vertically up a ladder. a) What is his weight? (assume that g = 10 Nkg-1) b) How much work has been done by Edward? c) What are the energy changes here? 4. Annie the archer pulls back the arrow in her bow a distance of 0.50 m against an average force of 200 N. a) How much work has Annie done? b) What are the energy changes here? c) What would be the initial kinetic energy of Annieâ&#x20AC;&#x2122;s arrow (assuming that the energy transfer has 100% efficiency).
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G10 Physics: Predicting the Next Move Moving Energy
The car in the picture above is braking. The brakes have to do work so that the car stops after some distance. The size of the braking force is F Newtons and the car comes to a stop in a displacement of â&#x2C6;&#x2020;s metres. We can say that the work done â&#x2C6;&#x2020;E on the car by the brakes is;
â&#x2C6;&#x2020;= 5 â&#x2C6;&#x2020;
Suppose that the car has a mass m, an initial velocity of u ms-1 and a final velocity of v ms-1. Then we can use Newtonâ&#x20AC;&#x2122;s law to say;
5
* 0 , 0 â&#x2C6;&#x2020;
â&#x2C6;&#x2020;
Then final velocity of the car is zero since it comes to a stop so the change in velocity is just the initial velocity of the car. The minus sign is indicating that the car is decelerating â&#x20AC;&#x201C; the braking force is in the opposite direction to the carâ&#x20AC;&#x2122;s movement. Now we can work out the displacement by using the formula;
) â&#x2C6;&#x2020;
* 4 , â&#x2C6;&#x2020;
2
Here again this formula simplifies since the final velocity v is zero; â&#x2C6;&#x2020;
4 â&#x2C6;&#x2020;
2
Now we can put the expressions for the force F and the change in displacement â&#x2C6;&#x2020;s into the formula for the work done.
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G10 Physics: Predicting the Next Move Moving Energy 9 5 â&#x2C6;&#x2020; â&#x2C6;&#x2020;= 0 0
â&#x2C6;&#x2020;
â&#x2C6;&#x2020;
2
1 3 2
What this formula means is; â&#x20AC;˘
The brakes have done work to decelerate and stop the car (hence the minus sign).
â&#x20AC;˘
The brakes have transferred the original movement energy of the car to heat energy (try touching the brake pads on a bicycle after stopping!).
â&#x20AC;˘
Since energy is conserved, we can say that the original amount of movement energy equal in size to the final amount of heat energy;
D ) 4 â&#x20AC;˘
1 3 2
We call this energy due to movement the kinetic energy (KE).
E = ) E= 4
1 3 2
â&#x20AC;˘
Note: you will usually see this formula with a â&#x20AC;&#x153;vâ&#x20AC;? used instead of a â&#x20AC;&#x153;uâ&#x20AC;? to indicate the velocity of the object).
â&#x20AC;˘
Note also that the kinetic energy, like all forms of energy, is a scalar quantity â&#x20AC;&#x201C; it has a size only.
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G10 Physics: Predicting the Next Move Moving Energy
Examples Consider the flight of a 747 jet aircraft. The aircraft (plus passengers) has a mass of 4.0 x 105 kg. The velocity (or speed) of the jet at take-off is 80 ms-1 and its average cruising velocity (speed) is 240 ms-1. Calculate the kinetic energy of the jet at take-off and when cruising.
0 .. : E=
1 3 2
0.5 4.0 10F *80,3
1.3 10G A
2 : E=
1 3 2
0.5 4.0 10F *240,3
1.2 10 H A
Notice that the formula for kinetic energy has a term for the mass of the object and a term for the velocity (speed); If the mass of the object is doubled, then the kinetic energy is doubled â&#x20AC;&#x201C; the kinetic energy will increase in proportion to the mass. If the velocity (speed) is doubled, the kinetic energy will increase by four times and if the velocity is three times greater then the kinetic energy will be nine times more. This is because the velocity is squared in the formula.
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G10 Physics: Predicting the Next Move From Kinetic to Potential Energy
2
1 Mass = 0.50kg Initial Velocity = 10 ms-1
3
Suppose that a ball is kicked vertically straight up into the air. The mass of the ball and its initial velocity are known â&#x20AC;&#x201C; 0.50kg and 10 ms-1. How high will the ball go? To solve this problem we will use a significant concept â&#x20AC;&#x201C; the conservation of energy. This means that the total energy of the ball in position 1 is the same as position 2 (highest point) and also in position 3 (just before it hits the ground). The total energy is a combination of potential energy (because it is changing height) and kinetic energy (because it is moving). In position 1 the ball has kinetic energy â&#x20AC;&#x201C; it has just been kicked- but it has not yet left the ground. In this case we can say that the potential energy is zero so;
> 1 :
E = )
1 3 2
> = ) 0
In this case we can calculate the total energy because we already know the mass and initial velocity of the ball.
> 1 " = ) 0.5 0.5 *10,3 25 A
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G10 Physics: Predicting the Next Move From Kinetic to Potential Energy
2
1 Mass = 0.50kg Initial Velocity = 10 ms-1
3
So how high will the ball go? In position 2 the ball has reached its highest point â&#x20AC;&#x201C; its velocity is zero. So the kinetic energy of the ball is also zero. On the other hand, the ball has gained height and so it has gained gravitational potential energy. Remember that the total energy â&#x20AC;&#x201C; kinetic plus potential â&#x20AC;&#x201C; is constant.
> 2 :
E = ) 0
> = ) â&#x2C6;&#x2020;
" = ) 25 A
So now we can calculate the change in height for the ball;
> = ) â&#x2C6;&#x2020; 0.5 10 â&#x2C6;&#x2020; 5.0 â&#x2C6;&#x2020; 5.0 â&#x2C6;&#x2020; 25 â&#x2C6;&#x2020;
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25 5.0 5.0
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G10 Physics: Predicting the Next Move From Potential to Kinetic Energy
The ball in the last example reached a maximum height of 5.0 metres. What will be the velocity of the ball (downwards) just before it hits the ground? To calculate this we can just use the same ideas as before. In position 2 the ball has no kinetic energy but it does have gravitational potential energy. From the last example we know that the total energy of the ball (kinetic plus potential) is 25 Joules. Finally, in position 3, the ball has kinetic energy but (just before it hits the ground) no potential energy.
3 :
E = )
1 3 2
> = ) 0
" = ) 25 A
Proceeding as before we get;
1 3 25 A 2 3
2 25 0.5
100
â&#x2C6;&#x161;100
10
So the ball returns back to the ground with exactly the same velocity as its initial velocity when it was first kicked.
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G10 Physics: Predicting the Next Move GPE and KE Questions
5.0 m
Fred is going diving. He has two options â&#x20AC;&#x201C; a diving board at a height of 1.25 m above the water and a diving board at a height of 5.0 m above the water. Fred has a mass of 60 kg and the gravitational field strength g = 10 N kg-1. Fred takes the 1.25 m option first. a) Calculate the gain in gravitational potential energy of Fred. b) Calculate the kinetic energy of Fred just before he hits the water.
Fred now decides to dive from the 5.0 m board. a) How much more gravitational potential energy has Fred gained compared to the 1.25 m board? b) Just before Fred hits the water, how much more kinetic energy has he gained? c) How high would the diving board have to be for Fred to have a velocity of 20 ms-1 just before he hit the water?
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G10 Physics: Predicting the Next Move Combining GPE and KE Equations
Quite often we do not know the mass of an object or person, like Ernie in the picture. So how do we proceed with our calculations? Suppose that the only information that we had was the height of each diving board, as shown on the diagram. What will be Ernieâ&#x20AC;&#x2122;s velocity just before he hits the water? In this case we can just use the two equations for GPE and KE at the same time. Once again the concept of the conservation of energy is used â&#x20AC;&#x201C; we will use the idea that Ernieâ&#x20AC;&#x2122;s total energy on the diving board (which is only GPE with no KE) is equal to his total energy just before he hits the water (which is only KE with no GPE). So; 1.25 :
" = ) />= â&#x2C6;&#x2020;
A + .
; :
" = ) E= â&#x2C6;&#x2020;
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1 3 2
1 3 2
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G10 Physics: Predicting the Next Move Combining GPE and KE Equations
So we have; â&#x2C6;&#x2020;
1 3 2
In other words, Ernieâ&#x20AC;&#x2122;s total energy on the diving board (which is his gravitational potential energy only since he is not moving) is equal to his total energy just before he hits the water (which is his kinetic energy only since he is at zero height). Notice that the term for mass m appears on both sides of the equation;
2 J : â&#x2C6;&#x2020;
1 3 2
1 : .
K2 â&#x2C6;&#x2020;
1 : . â&#x2C6;&#x2020; â&#x2C6;&#x2020;
3 2
These are very useful equations. They can be used to find the speed of a falling object if we only know the initial height. They can also be used to find the height that an object will reach if we know only the initial velocity. In Ernieâ&#x20AC;&#x2122;s case we get;
1.25 + :
K2 â&#x2C6;&#x2020; â&#x2C6;&#x161;2 10 1.25 â&#x2C6;&#x161;25 5.0
5.0 + :
K2 â&#x2C6;&#x2020; â&#x2C6;&#x161;2 10 5.0 â&#x2C6;&#x161;100 10
Notice that, since there is no information about Ernie in the equations (we do not need to know his mass) then these answers would apply to anyone jumping from these diving boards.
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G10 Physics: Predicting the Next Move Practice Questions on Work
Alicia has a mass 40 kg and she climbs up to a diving platform 1.5 m high. a) What is her weight, in N? b) When she climbs up to the diving platform, what is her change in GPE? c) Alicia walks off the platform and falls down. What is her KE just before she hits the water? d) What is her speed just before she hits the water? Alicia now climbs to a 13.5 m platform, nine times higher than the 1.5m platform. e) How much larger is her GPE compared to question 1? f)
What is her speed as he hits the water?
g) How many times more is this compared to question 1? Aliciaâ&#x20AC;&#x2122;s friend David, of mass 80 kg, climbs to the 13.5 m platform. h) What is Davidâ&#x20AC;&#x2122;s speed just before he hits the water? i)
What do you notice about your answer compared to the one in question 2?
j)
A stone is dropped from a window 13.0 m high. At what speed does it hit the ground?
k) Miguel is a tennis player. He hits a ball vertically with a speed of 16 ms-1. How high does it go? A car of mass 600 kg is travelling at 10 ms-1. When the brakes are applied, it comes to rest in a distance of 40 m. l)
What is the kinetic energy of the car before braking?
m) What is the average force exerted by the brakes? A car of mass 800 kg is at rest. The engine exerts a resultant force of 10 000 N for a distance of 400 m. n) What is the work done by the engine? o) Assuming that all of this work is transferred to kinetic energy (KE), what is the KE of the car? p) What is the final velocity of the car?
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G10 Physics: Predicting the Next Move A Question of Power
The concept of power is very important in Physics. Power is define as the â&#x20AC;&#x153;rate of doing workâ&#x20AC;?;
> ;
9 " â&#x2C6;&#x2020;= â&#x2C6;&#x2020;
We can also think of power as the â&#x20AC;&#x153;rate of change of energyâ&#x20AC;? or the â&#x20AC;&#x153;rate of transfer of energyâ&#x20AC;?. Since energy is measured in Joules and time in seconds, then power is measured in â&#x20AC;&#x153;Joules per secondâ&#x20AC;? or Watts (W). 1 9
1 A
Examples An engine uses 6 000 kJ of energy per minute in order to keep a car moving at a steady speed of 50 ms-1. What is the power of the engine?
>
â&#x2C6;&#x2020;= 6 000 A 100 9 â&#x2C6;&#x2020;
60
A cyclist of mass 80 kg generates a power of 120 W when riding a bicycle. How much chemical energy (from food) would be transferred to kinetic energy (for moving the bicycle) over a period of 5 minutes?
â&#x2C6;&#x2020;= > â&#x2C6;&#x2020; 120 *5 60, 36 000 A
Use your answer to a) to calculate the speed of the cyclist.
E=
1 2 E= 2 36 000 3 : L L 30 2 80
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G10 Physics: Predicting the Next Move A Question of Power
Example The aircraft in the picture above flies horizontally at a steady speed of 500 km per hour. The air resistance force acting against the movement of the aircraft is 5.0 x 103 N. Calculate the power developed by the engine! In questions like this it is always useful to label the forces involved. These are; â&#x20AC;˘
The engine force (forwards).
â&#x20AC;˘
The air resistance force (backwards).
â&#x20AC;˘
The weight force (downwards).
â&#x20AC;˘
The lift force (upwards)
First we use the fact that the aircraft is travelling horizontally at a steady speed. Newtonâ&#x20AC;&#x2122;s first law tells us that, since it is travelling in a straight line at a steady speed, then there is no resultant force acting on the aircraft. This means that the weight and the lift force are balanced (and we do not need to think about these two forces any longer) It also means that the engine force and the air resistance force are balanced. So;
5 ; . . 5.0 10M < We need to convert the speed into metres per second.
N )
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G10 Physics: Predicting the Next Move A Question of Power Lift Force
Engine Force
Air Resistance Force
Weight Force
Now we look at the formula for calculating power and the formula for calculating the work done;
> ;
9 A "
9 5
Note â&#x20AC;&#x201C; the distance moved is in the direction of the force. Putting these two together we get;
> ; >
5
" 5 â&#x2C6;&#x2020; â&#x2C6;&#x2020;
5
â&#x2C6;&#x2020; â&#x2C6;&#x2020;
5
So the power is just the engine force (in newtons) multiplied by the velocity (in metres per second);
> 5 5.0 10M 140 7.0 10F 9 700 9
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G10 Physics: Predicting the Next Move Practice Questions on Power
For each question show all your working clearly. a) Max does 500 J of work in 10 seconds. What is his power output? b) Monica pushes a box with a force of 60 N for a distance of 20 m in 10 s. What is her power output? c) Stefan switches on an electric lamp. It is marked 60 W. How much electrical energy does it transfer; i)
in 1.0 second?
ii)
in 100 seconds?
d) Hannah runs a 100 m race in 15 s against a friction force (drag) of 100 N. What is her power output? e) Izzy lifts an object of mass 120 kg through a height of 2.0 m in 3.0 seconds. What is the weight of the object? f)
What is the work done on the object? What is Izzyâ&#x20AC;&#x2122;s power output?
g) Florian weighs 600 N. He runs up the stairs firstly in 3.0 seconds, and then secondly in 6.0 seconds. h) The vertical height of the stairs is 4.0 m. What is his power output in each case? i)
An elevator containing 6 people is raised through a height of 20 m in 10 s. The total mass of the elevator and passengers is 600 kg.
j)
What is the total weight of the lift and passengers?
k) What is the power of the lift motor, in watts? In kilowatts?
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G10 Physics: Predicting the Next Move More Practice Questions
Marina the sky-diver steps out of an aeroplane. After 10 seconds she is falling at a steady speed of 50 ms-1. Marina then opens her parachute. After another 5.0 seconds she is once again falling at a steady speed. This speed is now only 10ms-1.
a) Calculate Marinaâ&#x20AC;&#x2122;s average acceleration during the time from when she opens her parachute until she reaches her slower steady speed. b) Explain, as fully as you can: i)
Why Marina eventually reaches a steady speed (with or without her parachute).
ii)
Why Marinaâ&#x20AC;&#x2122;s steady speed is lower when her parachute is open.
iii)
Marina and her sky diving equipment have a total mass of 75kg. Calculate the gravitational force acting on this total mass.
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G10 Physics: Predicting the Next Move More Practice Questions
Jean-Pierre is running in a straight line during a rugby game. His journey is shown below.
Tom's Journey 18.0 16.0 14.0
Velocity in ms-1
12.0 10.0 8.0 6.0 4.0 2.0 0.0 0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Time in s
a) Describe Tomâ&#x20AC;&#x2122;s motion; i)
In the first 4.0 seconds.
ii)
Between 4.0 and 7.0 seconds.
iii)
Between 7.0 and 12.0 seconds.
b) Calculate Tomâ&#x20AC;&#x2122;s acceleration during the last five seconds. c) Calculate the total distance travelled by Tom in the 12.0 seconds of his journey.
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G10 Physics: Predicting the Next Move More Practice Questions
Sonja goes bungee jumping. A fixed rubber cord is fastened to her ankles.
’s velocity changes during part of the jump. The graph shows how Sonja’s 30
×
25
× 20 Velocity 15 of bungee jumper 10 in m/s
×
×
5 0 –5
1
3
2
4
× 5
6
Time after jumping in seconds
× –10
a) Calculate the acceleration of Sonja between 2.0 and 4.0 seconds. Show your working. b) Describe, in as much detail as you can, what happens to Sonja after 4.0 seconds.
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G10 Physics: Predicting the Next Move More Practice Questions
The diagram below shows an empty cargo ship. It is not moving.
a) The water exerts a force on the ship. In which direction does this force act? b) Compare this size of this force to the weight of the ship.
The diagram below shows the same cargo ship. This time it has a full load of cargo.
a) Compare the size of the force exerted by the water to the weight of the ship. b) How does the force exerted by the water on the ship change as the ship is loaded? c) Why has the force exerted by the water changed?
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G10 Physics: Predicting the Next Move More Practice Questions
Sebastian is crossing the road. In this situation, the car driver needs to stop the car in the shortest possible distance.
At the instant shown in the picture, the car has a speed of 36 km per hour. The car has a mass of 900 kg. a) Calculate the kinetic energy of the car at the instant shown. b) The child is 3.0 m in front of the car. i)
Calculate the braking force needed to bring the car to a stop in a distance of 3.0 m.
ii)
What braking force would be needed to stop in a distance of 2.0 m?
c) Calculate the acceleration of the car for the two different cases given in b). d) Work is done by the brakes in stopping the car. i)
By how much would the braking force have to change if the mass of the car was doubled?
ii)
By how much would the braking force have to change if the speed of the car was doubled?
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