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OCR Gateway P3 Revision

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Lee Nicholson

on 21 November 2014

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Transcript of OCR Gateway P3 Revision

area
P3
Speed
Acceleration
Force, Work & Power
Car Safety
Energy
Braking
You need to know...
Notes
Questions
how to use an equation to calculate average speed
how to draw and interpret distance-time graphs
how different speeds affect the distance travelled or time taken
distance = average speed x time
distance = x t
u + v
2
This part of the equation represents average speed. u is the initial velocity, and v is the final velocity. You might need to use this to calculate u or v.
If the speed of an object increases, it will either:
travel a longer distance in the same time
or
travel the same distance in a shorter time
distance
time
constant speed
not moving
constant speed
accelerating
decelerating
the
gradient
of a distance-time graph tells you the speed of the object
1. A toy train takes 20 seconds to travel around a 4 metre long track. Calculate its average speed. [2]

2. Calculate the average speed of an athlete who runs 5km in 20 minutes. [2]

3. Calculate how far a car travels in 30 seconds if it has an average speed of 15 m/s. [2]

4. A car accelerates from 15 m/s to 25 m/s in 10 seconds. Calculate how far it travels in this time. [3]

5. A train sets off from a station and accelerates for 20 seconds, travelling 0.5 km. Calculate its final speed. [2]

6. The driver of a car sees a speed camera ahead and realises he is driving too fast so applies the brakes. The car was travelling at 27 m/s and was 60m from the camera when the driver applied the brakes, taking 3 seconds to reach it. The speed limit is 30 mph (13.5 m/s). Calculate the car's speed when it passes the camera, and state whether or not the driver receives a speeding ticket. [3]
50
40
20
300
400
200
distance (m)
time (s)
7. Below is a graph showing the distance travelled by an athlete during a 400m race. Using the graph, calculate:
(a) The athlete's speed during the first 20 seconds [2]
(b) The athlete's speed between 20 and 40 seconds [2]
(c) The athlete's speed during the last 10 seconds [2]
(d) The athlete's average speed during the whole race [2]
Answers
1. average speed = distance / time
= 4m / 20s
=
0.2 m/s

2. average speed = distance / time
= 5000m / 1200s
(5km = 5000m, 20 mins = 1200s)
=
4.2 m/s
(15 km/h)

3. distance = average speed x time
= 15 x 30
=
450 m

4. distance = (u + v)/2 x t
= (15 + 25)/2 x 10
= 20 x 10
=
200 m
5. distance = (u + v)/2 x t
500 = (0 + v)/2 x 20
500/20 = v/2
2 x 25 = v
v =
50 m/s

6. distance = (u + v)/2 x t
60 = (27 + v)/2 x 3
(60 x 2)/3 = 27 + v
40 - 27 = v
v =
13 m/s

7. (a) 200 / 20 =
10 m/s
(b) 100 / 20 =
5 m/s
(c) 100 / 10 =
10 m/s
(d) average speed = 400 / 50
=
8 m/s
You need to know...
how to use an equation to calculate acceleration
how to draw and interpret speed-time graphs
what is meant by the acceleration of an object
how to work out the relative speeds of two objects
equations
distance-time graphs
speed, distance and time
relative velocity
If two objects are travelling parallel to each other in the same direction, their relative velocity is the difference between the two speeds.
e.g.
relative velocity = 10 m/s - 6 m/s =
4 m/s
The two object are travelling in opposite directions, then their relative velocity is their speeds added together.
e.g.
v = 6 m/s
relative velocity = 10 m/s + 6 m/s =
16 m/s
8. A van travelling at 20 m/s is overtaken by a car which is travelling at 28 m/s. What is the relative velocity of the two vehicles? [2]

9. Two trains are heading in opposite directions down a track. One train is moving at a speed of 60 m/s, and the trains have a relative velocity of 135 m/s. What is the speed of the other train? [2]
8. relative velocity = 28 - 20
=
8 m/s

9. train speed = 135 - 60
=
75 m/s
Notes
acceleration =
change in speed
time
An object is
accelerating
if either its
speed
or
direction
is changing. For example, a car which is driving at a constant speed around a roundabout is accelerating because its direction in changing.

Things can also have
negative acceleration
, which would mean they are slowing down (
decelerating
).
speed
time
constant speed
accelerating
the
gradient
of a speed-time graph tells you the acceleration of the object
equation
speed-time graphs
Acceleration
decelerating
stationary
Questions
40
25
10
12
20
speed (m/s)
time (s)
35
1. Describe a situation in which an object can be travelling at a constant speed but also accelerating. [1]

2. Calculate the acceleration of a car which increases its speed from 24 m/s to 30 m/s in 3 seconds. [2]

3. Calculate the acceleration of a rocket which takes off and reaches a speed of 300 m/s in 12 seconds. [2]

4. A penny is dropped from the top of a tall building and accelerates towards the ground at 10 m/s . The penny takes 6 seconds to hit the ground. Calculate its speed when it hits the ground. [2]

5. A car applies its brakes and takes 4 seconds to come to a stop. The brakes apply a force which causes the car to decelerate at a rate of
5 m/s . Calculate the car's initial speed. [2]
2
2
The graph below shows the motion of a car during a short journey. Using the graph, calculate:
(a) The acceleration of the car during the first 10 seconds [2]
(b) The deceleration of the car later in the journey [2]
(c) The distance travelled while the car is travelling at a speed of 20 m/s [2]
(d) The distance travelled while the car is accelerating during the first 10 seconds [2]
(e) The total distance travelled during the 40 second journey [3]
1. Changing direction, e.g. going around a bend.

2. acceleration = change in speed / time
= (30 - 24) / 3
= 6 / 3
=
2 m/s

3. acceleration = change in speed / time
= 300 / 12
=
25 m/s

4. acceleration = change in speed / time
10 = change in speed / 6
10 x 6 = change in speed
change in speed =
60 m/s
2
2
5. acceleration = change in speed / time
5 = change in speed / 4
5 x 4 = change in speed
initial speed = 20 m/s

6. (a) gradient = 20 / 10 =
2 m/s
(b) gradient = (20 - 12) / (35 - 25)
= 8 / 10 =
0.8 m/s
(c) distance = 20 x (25 - 10)
= 20 x 15 =
300 m
(d) distance = 1/2 x 10 x 20
=
100 m
(e) distance = 100 + 300 + 160 + 60
=
620 m
2
2
Answers
average speed =
distance
time
the
area
underneath a speed-time graph tells you the distance travelled by the object
To calculate the area, split the graph up into rectangles and triangles
units
Acceleration represents how much the speed, measured in m/s, changes per second. So it's units are metres per second per second, which is written as...
m/s
2
You need to know...
factors which affect thinking and braking distance
how different forces can cause a car to slow down
what is meant by thinking, braking and stopping distance
how braking forces are linked to energy transfers
Notes
force = mass x acceleration
This equation can be used to explain why the
force applied by a car's brakes
and the
frictional force between the tyres and the road
cause the car to
decelerate
.

When a car needs to slow down, the brakes apply a frictional force to the wheels of the car. This converts the car's kinetic energy into heat energy, slowing the car down. There is also another frictional force between the tyres and the road which helps to slow the car down.
distance
speed
equations
braking forces
more force = more acceleration (car slows down faster)
more mass = less acceleration (car takes longer to slow down)
work done = force x distance
This equation can be used to calculate
braking distances
. Work done means energy transferred, in this case the kinetic energy of the car is transferred into heat energy by the brakes.

work done
= the car's
kinetic energy
force
= the frictional
force applied by the brakes/tyres
distance
=
braking distance
v = 10 m/s
v = 6 m/s
v = 10 m/s
stopping distances
A car's overall stopping distance is made up of two components; thinking distance and braking distance
stopping distance = thinking distance + braking distance
Thinking distance is related to a driver's
reaction time
. It is the distance the car travels while the driver is reacting to a situation.
thinking distance = speed x reaction time
Factors which can
increase
thinking distance include:
greater speed
distractions
alcohol/drugs
tiredness
If the car is moving faster, it will travel further during the driver's reaction time
Distractions (e.g. loud music, children, mobile phone) can increase a driver's reaction time, which will increase thinking distance
Alcohol or drugs can increase a driver's reaction time, which increases thinking distance
If a driver is tired, their reaction time will be longer, which will increase the thinking distance
Braking distance is related to the frictional
force applied
by the brakes and the tyres, and also depends on the car's
kinetic energy
.
braking distance = kinetic energy / force applied
Factors which can
increase
braking distance include:
greater speed
If the car is moving faster, it will have more kinetic energy for the brakes to convert to heat, increasing the braking distance
worn brakes
If the cars brakes are worn out then they will not be able to apply as much force, meaning the braking distance will be longer
worn Tyres
If the car's tyres are worn out, they do not have as much frictional force with the road, increasing the braking distance
slippery road
Wet, icy or oily road surfaces will mean there is less frictional force, so the braking distance will increase
thinking distance and speed
If the speed doubles, thinking distance also doubles.
Thinking distance is proportional to speed, so a graph of speed and thinking distance will also be proportional, i.e. a straight line.
distance
speed
braking distance and speed
If the speed doubles, braking distance
quadruples
.
Braking distance depends on kinetic energy, so is proportional to
speed squared
. This gives a curved graph where the gradient increases.
Questions
1. State and explain three factors, other than a higher speed, which could increase:
(a) thinking distance [3]
(b) braking distance [3]

2. A car is driving at 20 mph when the driver sees an animal run out into the road. The driver reacts to this and applies the brakes, coming to a stop after a thinking distance of 4 metres and a braking distance of 6 metres. The driver then increases their speed to 40 mph.
Describe and explain the effect that this increased speed will have on:
(a) the driver's thinking distance [3]
(b) the car's braking distance [3]

3. Describe the energy transfer which takes place when a car applies the brakes and comes to a stop. [1]

4. Describe three measures a driver could take to reduce their overall stopping distance. [3]
5. Calculate the braking force that would be required to decelerate a car with a mass of 1800 kg at a rate of 5 m/s . [2]

6. A car and driver have a total mass of 1250 kg and brakes which apply an average braking force of 5 kN.
(a) Calculate the deceleration of the car when the brakes are applied [2]
(b) Calculate the deceleration of the car if it is carrying 3 additional passengers, with a total mass of 200 kg [2]
(c) The brakes of the car wear out, and can only provide a braking force of 4 kN. Calculate the deceleration of the car with the driver and 3 additional passengers [2]

7. Under braking, a car's brakes apply a force of 2000 N over a distance of 50 metres. Calculate the work done by the brakes. [2]

8. A car has a mass of 1500 kg, and its brakes apply an average braking force of 3000 N over a distance of 60 metres.
(a) Calculate the change in kinetic energy of the car [2]
(b) The car comes to a stop. Calculate the initial speed of the car. [2]
2
Answers
1. (a)
thinking distance
- examples which increase a driver's reaction time, e.g. distractions (specific examples e.g. loud music, children, mobile phone), alcohol/drugs, tiredness
(b)
braking distance
- examples which reduce the force applied by
the brakes, e.g. wet/icy road, worn tyres, worn brakes

2. (a) Increasing the car's speed will increase the driver's thinking distance. The driver's thinking distance will be
doubled
to 8 metres, because thinking distance is proportional to speed.
(b) Increasing the car's kinetic energy will increase the braking distance. The car's braking distance will be
quadrupled
to 24 metres, because braking distance is proportional to speed squared.

3. Kinetic energy is converted into heat energy (+ sound energy)

4. A driver could:
Fit better brakes
Fit new tyres
Driver slower
5. Force = mass x acceleration
= 1800 x 5 =
9000 N

6. (a) Force = mass x acceleration
5000 = 1250 x a
a = 5000 / 1250 =
4 m/s
(b) Force = mass x acceleration
5000 = 1450 x a
a = 5000 / 1450 =
3.45 m/s
(c) Force = mass x acceleration
4000 = 1450 x a
a = 4000 / 1450 =
2.76 m/s

2
2
2
7. work done = force x distance
= 2000 x 50 =
100 000 J

8. (a) change in KE = work done
work done = force x distance
work done = 3000 x 60 =
180 000 J
(b) initial KE = 180 000 J
180 000 = 1/2 x m x v
180 000 = 1/2 x 1500 x v
v = sqrt(180 000 / 750) =
15.5 m/s
2
2
You need to know...
factors which affect the fuel consumption of a car
the factors which affect the amount of kinetic energy an object has
how to use an equation to calculate kinetic energy
the different energy sources which can be used to power cars
Notes
equations
Questions
1. Describe in detail the energy transfers that take place in the following situations:
(a) A person climbing some stairs [2]
(b) A ball being thrown up in the air and then caught [3]
(c) A skier skiing down a slope and then coming to a stop [3]
(d) A bungee jump [4]

2. Explain why the second hill on a roller coaster must be smaller than the first hill. [2]

3. A skydiver jumps from a plane and begins accelerating towards the ground. After about 10 seconds, the skydiver reaches terminal speed. Later, the skydiver opens their parachute, causing them to slow down.
(a) Explain why the skydiver initially accelerates [1]
(b) Explain what is meant by terminal speed, and why the skydiver reaches it. [2]
(c) When the skydiver is at terminal speed, their GPE is decreasing, but their KE does not increase. Describe the energy transfer that is taking place. [2]
(d) Explain why opening the parachute causes the skydiver to slow down. [1]
Answers
how to describe situations in which energy is transferred
how to calculate gravitational potential energy
KE = 1/2mv
2
kinetic energy = 1/2 x mass x speed
2
Kinetic energy depends on the mass and speed of an object. Note that it is
only the speed that is squared
.
If the
mass doubles
= kinetic energy
doubles
If the
speed doubles
= kinetic energy
quadruples
GPE = mgh
gravitational potential energy = mass x gravitational field strength x height
Gravitational potential energy (GPE) depends on the mass and height of an object. It will change its GPE if its height changes, this is an example of an energy transfer or
work done
.
g = 10 N/kg
energy types
Energy is a property of objects, just like mass. The entire universe is made from things which have mass, energy or both. Objects can have different types of energy. There are eight main types of energy:
kinetic
thermal
sound
light
electrical
gravitational potential
elastic potential
chemical potential
The energy that moving objects have
Another word for
heat
energy. Represents molecular kinetic energy.
Objects can release energy as light (electromagnetic radiation)
Sound is movement of air molecules, so is a type of kinetic energy
An object has GPE if it is raised to a height in a gravitational field
The type of energy that is stored in a stretched spring, for example
Stored energy that is found in fuels and food
Energy carried by electric charges moving around a circuit
energy transfers
The
principle of energy conservation
says that energy cannot be created or destroyed, it can only be
transferred
from one form to another. If an object gains a type of energy, there must be some kind of energy input. If an object "loses" energy, it must be transferred into another kind of energy.
example
A lightbulb converts
electrical
energy into
light
and
heat
energy
electrical
light
heat
roller coasters
Traditional roller coasters make use of energy transfers to propel the ride around the track. Gravitational potential energy at the top of a hill is converted to kinetic energy as the ride travels down the track. Some energy is also converted into heat and sound energy. Kinetic energy is then converted back to gravitational potential energy as it travels up the next hill.
maximum GPE
GPE transferred to KE
maximum KE
KE converted to GPE
second hill must be smaller due to some of initial GPE being transferred to sound and heat
falling objects
1.
2.
3.
1.
As a skydiver jumps from a plane, they have
maximum GPE
and
zero KE
. Their weight causes them to accelerate and move downwards,
increasing KE
and
decreasing GPE
.
2.
The skydiver's speed increases as they fall, which increases the
drag
force acting upwards. Eventually,
drag becomes equal to weight
and the skydiver stops accelerating. They are now travelling at a constant speed known as
terminal speed
. The skydiver's kinetic energy is also now constant, but GPE is still decreasing. The GPE is being transferred into the kinetic energy of the air molecules that are being pushed out of the way.
3.
When the parachute opens, the
drag
becomes bigger than
weight
, causing the skydiver to
decelerate
. The skydiver's kinetic energy is transferred to the air molecules. As the skydiver slows down, the drag decreases until it is equal to weight again, and the skydiver reaches a new terminal speed.
car fuels
fossil fuels
Fossil fuels include coal, oil and natural gas, which are all extracted from underground. Most cars use petrol or diesel, which is refined from crude oil. The fuel contains chemical potential energy, which is burned, transferring the energy into heat. The car's engine then transfers the heat into kinetic energy.
advantages
Technology and infrastructure (i.e. petrol stations etc) are already established and widely available.
disadvantages
Non-renewable (i.e. will run out)

Burning fuel releases carbon dioxide into the atmosphere
biofuels
Biofuels are produced using organic matter. Common biofuels include vegetable oil and ethanol, which is produced by the fermentation of sugar plants. Methane, produced by decaying matter, can also be used as a biofuel. Biofuels are used in car engines in the same way that fossil fuels are.
advantages
The carbon dioxide that they release was originally removed from the atmosphere through photosynthesis, so less
new
carbon dioxide is created.

Biofuels use crops that grow quickly, so are
renewable
disadvantages
Land is needed to produce biofuels, which would have otherwise been used for food production. This could potentially lower food production, increasing food prices.

Carbon dioxide still produced during car production.
electric
Electric cars use motors powered by rechargeable batteries. The batteries must be recharged by plugging the car into a mains power supply.
advantages
No carbon dioxide emissions produced by the car.

Can lead to a reduction in use of fossil fuels, dependent on energy sources used to produce electricity.
disadvantages
Carbon dioxide still released in the production of electricity.

Current electric cars have a limited range, and long recharging times.

Still relies partially on the use of fossil fuels, which are non-renewable.
solar
Solar powered cars work like electric cars, but use solar panels to recharge batteries.
advantages
No carbon dioxide emissions produced by the car.

Uses no fossil fuels at all.

Renewable.
disadvantages
Current solar powered cars are expensive, and have limited performance and range.

Will not generate sufficient power if there is not enough sunlight.
hybrid cars
Hybrid cars have two motors, a fuel-burning fossil fuel or biofuel engine and an electric motor. The fuel-burning engine is used to recharge the batteries used by the electric motor, so the car does not need to be plugged in.
advantages
disadvantages
Uses less fuel than most normal petrol engines, meaning better fuel economy.

Less fuel use results in lower carbon dioxide emissions.
Still produces carbon dioxide emissions.

Still relies on the use of fossil fuels.
fuel efficiency
kinetic energy = 1/2 x mass x speed
2
A car's
kinetic energy
comes from its fuel.
If the car is
heavier
, then it will need to use
more fuel
to reach the same kinetic energy
If the car is driver
faster
, then more energy will be needed, using
more fuel
factors which can increase fuel consumption:
Fuel consumption is measured in
kilometers per litre
(km/l), which tells you how many kilometers the car can travel on one litre of fuel. The higher the number, the better a car's
fuel efficiency
, also known as fuel economy.
rapid acceleration
greater mass
driving uphill
stop-start journeys
fast driving
All energy values are measured in
Joules (J)
4. Calculate the kinetic energy of a car which has a mass of 1200 kg and is travelling at a speed of 10 m/s. [2]

5. Calculate the gravitational potential energy of a cat which has a mass of 5 kg and climbs to a tree branch which is 6 metres above the ground. [2]

6. A lift in an apartment building carries 3 passengers from the 5th floor, at a height of 15 m, to the 10th floor, at a height of 30 m. The lift has a mass of
800 kg, and the 3 passengers have a combined mass of 200 kg.
(a) Calculate the change in gravitational potential energy of the passengers [2]
(b) Calculate the minimum energy required to raise an empty lift from the ground floor up to the 10th floor [2]
(c) Explain why the value you calculated in (b) is a
minimum
value [1]

7. A roller coaster with a mass of 4000 kg is released from a hill which is 50 m high.
(a) Calculate the maximum kinetic energy at the bottom of the hill [3]
(b) Explain why the value you calculated in (a) is a minimum value [1]
(c) Calculate the maximum speed the roller coaster could have at the bottom of the hill [2]
8. Describe three factors which could increase the fuel consumption of a car. [3]

9. A car with a 50 litre fuel tank has an average fuel economy of 16 km/l.
(a) Determine the maximum range of the car [1]
(b) Explain why the car may be able to exceed this range [2]

10. A customer would like to purchase an environmentally friendly car to replace their petrol engined one, and finds that there are three different options available. The first is an electric car, the second is a hybrid electric, and the third uses biofuels. Evaluate the three options, and make a recommendation to the customer, justifying your choice of engine. [6]
1. (a) Chemical energy (in the person's cells) transferred to kinetic energy (and
some heat). Kinetic energy (KE) is then transferred into gravitational potential energy (GPE).
(b) KE is transferred from the person to the ball. KE is transferred into GPE. GPE is then transferred back to KE as the ball falls.
(c) GPE is converted into KE (and some sound and heat due to friction). To come to a stop, KE is converted into sound and heat.
(d) GPE is transferred into KE as the jumper falls. GPE and KE are then both transferred into elastic potential energy (as the bungee cord stretches). Elastic potential energy is then transferred back into KE and GPE (as the cord springs back). Finally, KE is converted to GPE (as the jumper continues upwards).

2. Some energy is transferred to the surroundings (as heat and sound), so the roller coaster would not have enough energy to reach a hill which was the same height as the first.

3. (a) Their weight is acting downwards.
(b) Terminal speed is a maximum, constant speed, that is reached when the downward force (weight) is equal to the upward force (drag).
(c) GPE is transferred to the surroundings as kinetic energy of the air molecules.
(d) The drag force created by the parachute is greater than than downward force (weight).
4. KE = 1/2 mv = 1/2 x 1200 x 10
= 600 x 100 =
60 000 J

5. GPE = mgh = 5 x 10 x 6
=
300 J

6. (a) GPE = mgh = 200 x 10 x 15
=
30 000 J
(b) energy required = change in GPE
GPE = 800 x 10 x 30 =
240 000 J
(c) Some energy will be transferred to the surroundings (as heat and sound), so more energy will be required to produce the required increase in GPE.

7. (a) KE = change in GPE
KE = mgh = 4000 x 10 x 50
=
2 000 000 J
(b) Some energy will be transferred to the surroundings (as heat and sound)
(c) KE = 1/2 mv = 1/2 x 4000 x v
2 000 000 = 2000 x v
v = 2 000 000 / 2000 = 1000
v = sqrt(1000) =
32 m/s
2
2
2
2
2
2
8. Greater mass (e.g. more passengers, carrying luggage) / higher speed / high acceleration / stop-start journey (e.g. encountering traffic, traffic lights) / driving uphill / poor road conditions

9. A car with a 50 litre fuel tank has an average fuel economy of 16 km/l.
(a) range = 50 x 16 =
800 km
(b) Fuel economy is an
average
value, so actual value could exceed this, for example if the driver drives slowly / not much mass in car / driving at a constant speed etc

10.
electric car
advantages - no carbon dioxide from car
disadvantages - carbon dioxide released in production of electricity, limited range, long recharge time

hybrid electric
advantages - lower carbon dixoide emissions than petrol, better fuel consumption
disadvantages - still uses fossil fuels, releases carbon dioxide

biofuel
advantages - re-releasing carbon taken in via photosynthesis (carbon neutral), doesn't use fossil fuels
disadvantages - carbon dioxide releasedin prouction of fuel and manufacture of car, takes up land used for food production

You need to know...
how to calculate the weight of an object
how to calculate work done and power
what is meant by 'work done' and 'power'
Notes
power =
work done
time
Questions
Answers
how gravity and drag affect objects
forces
A force is an interaction between two objects. Unbalanced forces cause things to accelerate.
force = mass x acceleration
units
All forces are measured in
Newtons (N)
weight
Weight is the downward force on objects due to gravity
weight = mass x g
g = gravitational field strength = 10 N/kg
The gravitational field strength, g (also known as the acceleration due to gravity), is the same for all objects at a given point on the Earth. Its value gets smaller further from the Earth's surface.
drag
Drag is a frictional force which opposes the direction of motion of an object. This can reduce its acceleration or cause it to accelerate the other way (slow down).

The amount of drag depends on:
speed
surface area
work done
If a force causes an energy transfer, then work is being done by that force. The amount of work done is equal to the amount of energy transferred.
work done = force x distance
power
Power is a measure of the rate at which work is done. The power of an object tells you how much energy it transfers per second.
units: Joules (J)
units: Watts (W)
units: Newtons (N)
units
speed = m/s
distance = m
time = s
1. An object on Earth has a mass of 20 kg. The gravitational field strength on the Moon is 1.6 N/kg. Calculate the weight of the object:
(a) on the Earth [2]
(b) on the Moon [2]

2. A person pushes a car with a force of 200 N. Calculate the work done when the car is pushed 100 m. [2]

3. A small lizard, with a mass of 200 g, climbs up a 5 m wall in 20 seconds.
(a) Calculate the weight of the lizard [2]
(b) Calculate the work done by the lizard climbing up the wall [2]
(c) Calculate the power of the lizard [2]

4. Calculate the power of a 60 kg hiker who carries a 10 kg backpack up a 400 m high hill in 30 minutes. [4]
1. (a) weight = mass x g
= 20 x 10 =
200 N
(
b) weight = mass x g
= 20 x 1.6 =
32 N

2. work done = force x distance
= 200 x 100 =
20 000 J
3. (a) weight = mass x g
= 0.2 x 10 =
2 N
(b) work done = force x distance
= 2 x 5 =
10 J
(c) power = work done / time
= 10 / 20 =
0.5 W

4. weight = mass x g
= 70 x 10 = 700 N
work done = force x distance
= 700 x 400 = 280 000 J
power = work done / time
= 280 000 / 1800 =
156 W
You need to know...
how the force on an object when stopping is linked to change in momentum and collision/stopping time
Notes
Questions
1. Calculate the momentum of a train which has a mass of 20 000 kg and is travelling at 25 m/s. [2]

2. A car is driving at 20 m/s when it applies its brakes and comes to a stop in 4 seconds. The car has a mass of 1500 kg, and the driver has a mass of 60 kg.
(a) Calculate the driver's change in momentum [2]
(b) Calculate the force on the driver [2]
(c) Calculate the overall braking force [2]

3. The owner of a racetrack decides to place several layers of rubber tyres in front of the rigid crash barriers around the circuits. Explain why this could help to reduce injuries to drivers if they were to crash into the barriers. [3]

4. Explain the advantages of ABS (Anti-lock Braking System) brakes. [3]
Answers
examples of safety features which are designed to reduce collision or stopping forces
how to calculate the momentum of an object
momentum
reducing forces
car safety features
Momentum is a quantity which represents the motion of an object, and is the product of its mass and velocity.
momentum = mass x velocity
units
kg m/s
change in momentum
If a force is applied to an object, its momentum will change. The size of the force required to change an object's momentum depends on how long that force is applied for.
force =
change in momentum
The shorter the time for a given change in momentum, the bigger the force
time taken
When an object slows down (i.e. changes its momentum), it will experience a force. The size of this force depends on how long the change in momentum takes. This is shown by the formula on the right.
force =
change in momentum
time taken
If you want to
reduce the force
on an object when it changes its momentum and comes to a stop, then the
stopping/collision time must be as long as possible
.
examples of things which increase stopping/collision time:
crumple zones
longer braking distance
escape lanes
crash barriers
seatbelts
air bags
padded restraints
crash mats
Area at the front of a car which is designed to 'crumple' to absorb energy in a crash
Air-filled bags which deploy from the steering wheel/dashboard in the event of a crash
As well as holding the driver in their seat, they stretch in the event of a sudden stop
The distance over which a car comes to a stop after the brakes have been applied
Soft padding on, for example, roller coaster harnesses
Around race tracks, crash barriers are often made from rows of rubber tyres
Large sandpits on steep downhill roads for large vehicles to turn into if their brakes fail
Used by climbers and gymnasts to soften landing impacts from large falls
All of these features do the following:
increase collision / stopping time
increase collision / stopping distance
reduce acceleration (deceleration)
reduce force
If you are asked about any of these features, or any other feature which softens an impact, these are the points you need to make. Use whichever word - collision/stopping - is most appropriate.
Cars have many safety features which are designed to protect the driver in the event of a crash, or prevent an accident from occurring in the first place.
active safety features
passive safety features
crumple zones, air bags & seat belts
These features are designed to reduce collision forces on a driver if they are in a crash. They do this by increasing the collision time.
Active
safety features are specifically designed to reduce injury or prevent accidents
ABS (Anti-lock Braking System)
If a car's wheel 'lock up' during braking, the driver can lose control of the car. ABS brakes prevent the wheels from locking up during hard braking by automatically pumping the brakes on and off. The benefits of ABS brakes, compared to normal brakes, are:
Car does not skid
The driver can continue to steer the car during braking
Can sometimes reduce braking distances
Passive
safety features are convenience features in a car which can make driving safer by assisting the driver. Many of these features allow the driver to
keep both hands on the wheel
as much as possible, or to
keep their eyes on the road
, rather than looking at things in the car. Other features keep the driver as
comfortable
as possible while driving.
examples of passive safety features:
electric windows
cruise control
SATNAV voice commands
bluetooth/handsfree phone
steering wheel controls
adjustable seating
power steering
sun visor
5. A car crashes into a stationary vehicle while travelling at 25 m/s. The driver, who has a mass of 60 kg, was wearing his seatbelt and has an airbag which bring him to a stop in 0.25 seconds. The front passenger, who also has a mass of 60kg, was not wearing a seatbelt and has no airbag on the passenger side. The passenger hits the windscreen and comes to a stop in 0.02 seconds.

(a) Calculate the change in momentum of the driver and passenger [2]
(b) Calculate the force on both the driver and passenger [3]
(c) Use your answer to (b) to comment on the effectiveness of seat belts and air bags during a collision [1]
(d) Explain how seat belts and airbags are able to affect the collision force on the occupant of a car during a collision [3]
1. momentum = mass x velocity
= 20 000 x 25 =
500 000 kg m/s

2. (a) change in momentum = final momentum - initial momentum
final momentum = 0, so change in momentum = initial momentum
initial momentum = 60 x 20 =
1200 kg m/s
(b) force = change in momentum / time
= 1200 / 4 =
300 N
(c) force = change in momentum / time
= (1560 x 20) / 4 =
7800 N

3. The tyres increase collision time and distance, which reduces acceleration, reducing the force on a driver.

4. ABS brakes prevent the wheels of a car from locking up under braking, which allows the driver to keep control of the car and prevents skidding. It can also reduce braking distances in some situations.
5. (a) initial momentum = mass x velocity
= 60 x 25 =
1500 kg m/s

final momentum = 0 so change in momentum = initial momentum

(b) force on driver = change in momentum / time
= 1500 / 0.25 = 6000 N
force on passenger = change in momentum / time
= 1500 / 0.02 = 75 000 N

(c) Seat belts and airbags reduce the forces on a car's occupant. The force on the passenger is 12.5x bigger than on the driver.

(d) Seat belts and airbags increase the collision time and distance, which reduces acceleration, lowering the force on an occupant.
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