Download Q1. (a) State the difference between vector and scalar quantities

Q1.
(a)
State the difference between vector and scalar quantities.
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(1)
(b)
State one example of a vector quantity (other than force) and one example of a scalar
quantity.
vector quantity .............................................................................................
scalar quantity ..............................................................................................
(2)
(c)
A 12.0 N force and a 8.0 N force act on a body of mass 6.5 kg at the same time.
For this body, calculate
(i)
the maximum resultant acceleration that it could experience,
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(ii)
the minimum resultant acceleration that it could experience.
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(4)
(Total 7 marks)
Q2.
(a)
(i)
State what is meant by a scalar quantity.
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(ii)
State two examples of scalar quantities.
example 1: .........................................................................................
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example 2: ..........................................................................................
(3)
Page 1 of 23
(b)
An object is acted upon by two forces at right angles to each other. One of the forces has
a magnitude of 5.0 N and the resultant force produced on the object is 9.5 N.
Determine
(i)
the magnitude of the other force,
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(ii)
the angle between the resultant force and the 5.0 N force.
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(4)
(Total 7 marks)
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Q3.
The graph represents the motion of two cars, A and B, as they move along a straight,
horizontal road.
(a)
Describe the motion of each car as shown on the graph.
(i)
car A: ..........................................................................……………..….
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(ii)
car B: ...........................................................................………………..
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(3)
(b)
Calculate the distance travelled by each car during the first 5.0 s.
(i)
car A: ....................................….....................................................................
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(ii)
car B: ........….......................................................................................
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(4)
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(c)
At time t = 0, the two cars are level. Explain why car A is at its maximum distance ahead
of B at t = 2.5 s
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(3)
(Total 10 marks)
Q4.
Gliders can be launched with a winch situated on the ground. The winch pulls a rope that is
attached to the glider. The diagram below shows the forces acting on the glider at one instant
during the launch.
(a)
The combined weight of the glider and pilot is 6500 N.
(i)
Show that the magnitude of the resultant force acting on the glider is about 6100 N.
(2)
(ii)
Calculate the angle between this resultant force and the horizontal.
angle ................................. degrees
(2)
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(iii)
Calculate the resultant acceleration of the glider in the diagram above.
resultant acceleration ..................................... m s−2
(2)
(b)
The glider climbs a vertical distance of 600 m in 55 s. The average power input to the
winch motor during the launch is 320 kW.
(i)
Calculate the gain in gravitational potential energy (gpe) of the glider.
gain in gpe ............................................ J
(2)
(ii)
Calculate the percentage efficiency of the winch system used to launch the glider.
Assume the kinetic energy of the glider after the launch is negligible.
efficiency .......................................... %
(3)
(Total 11 marks)
A steel ball has a diameter of 2.2 × 10−2 m.
Q5.
(a)
Calculate the weight of the steel ball. Give your answer to an appropriate number of
significant figures.
density of steel = 8100 kg m−3
weight ...........................................N
(4)
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(b)
Figure 1 shows two identical steel balls dropped from rest into containers of oil.
Figure 1
(i)
Figure 2 shows the velocity-time graph for steel ball A.
Figure 2
Explain the shape of the graph in Figure 2. Your account should include
•
how the velocity and acceleration of the steel ball vary with time
•
reference to how Newton’s First and Second laws of motion apply in this
situation.
The quality of written communication will be assessed in your answer.
(6)
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(ii)
On Figure 3, sketch the velocity-time graph you would expect to see for steel ball B.
Assume air resistance is negligible.
Figure 3
(3)
(Total 13 marks)
Q6.
The world record for a high dive into deep water is 54 m.
(a)
Calculate the loss in gravitational potential energy (gpe) of a diver of mass 65 kg falling
through 54 m.
loss in gpe = ................................... J
(2)
(b)
Calculate the vertical velocity of the diver the instant before he enters the water. Ignore the
effects of air resistance.
velocity = ............................ ms−1
(2)
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(c)
Calculate the time taken for the diver to fall 54 m. Ignore the effects of air resistance.
time = ................................... s
(2)
(d)
Explain, with reference to energy, why the velocity of the diver is independent of his mass if
air resistance is insignificant.
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(3)
(Total 9 marks)
Q7.
A skydiver of mass 70 kg, jumps from a stationary balloon and reaches a speed of 45 m s–1
after falling a distance of 150 m.
(a)
Calculate the skydiver’s
(i)
loss of gravitational potential energy,
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(ii)
gain in kinetic energy.
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(4)
(b)
The difference between the loss of gravitational potential energy and the gain in kinetic
energy is equal to the work done against air resistance. Use this fact to calculate
(i)
the work done against air resistance,
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(ii)
the average force due to air resistance acting on the skydiver.
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(3)
(Total 7 marks)
Q8.
(a)
(i)
State two vector quantities.
vector quantity 1 ...................................................................................
vector quantity 2 ...................................................................................
(ii)
State two scalar quantities.
scalar quantity 1 ...................................................................................
scalar quantity 2 ...................................................................................
(2)
(b)
The helicopter shown in Figure 1a is moving horizontally through still air. The lift force
from the helicopter’s blades is labelled A.
Figure 1a
(i)
Figure 1b
Name the two forces B and C that also act on the helicopter.
B ...........................................................................................................
C ...........................................................................................................
(2)
Page 9 of 23
(ii)
The force vectors are also shown arranged as a triangle in Figure 1b.
State and explain how Figure 1b shows that the helicopter is moving at a constant
velocity.
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(2)
(c)
The lift force, A, is 9.5 kN and acts at an angle of 74° to the horizontal.
Calculate the weight of the helicopter. Give your answer to an appropriate number of
significant figures.
answer = ................................. N
(3)
(Total 9 marks)
Q9.
A student measures the acceleration due to gravity, g, using the apparatus shown in the
figure below. A plastic card of known length is released from rest at a height of 0.50m above a
light gate. A computer calculates the velocity of the card at this point, using the time for the card
to pass through the light gate.
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(a)
The computer calculated a value of 3.10 m s–1 for the velocity of the card as it travelled
through the light gate. Calculate a value for the acceleration due to gravity, g, from these
data.
answer = ...................................... m s–2
(2)
(b)
The student doubles the mass of the card and finds a value for g that is similar to the
original value. Use the relationship between weight, mass and g to explain this result.
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(1)
(c)
State and explain one reason why the card would give more reliable results than a table
tennis ball for this experiment.
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(2)
(Total 5 marks)
Page 11 of 23
Q10.
The figure below shows a rollercoaster train that is being accelerated when it is pulled
horizontally by a cable.
(a)
The train accelerates from rest to a speed of 58ms–1 in 3.5 s. The mass of the fully loaded
train is 5800 kg.
(i)
Calculate the average acceleration of the train.
answer = ...................................... ms–2
(2)
(ii)
Calculate the average tension in the cable as the train is accelerated, stating an
appropriate unit.
answer = ...............................................
(3)
(iii)
Calculate the distance the train moves while accelerating from rest to 58ms–1.
answer = ...................................... m
(2)
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(iv)
The efficiency of the rollercoaster acceleration system is 20%.
Calculate the average power input to this system during the acceleration.
answer = ..................................... W
(3)
(b)
After reaching its top speed the driving force is removed and the rollercoaster train begins
to ascend a steep track. By considering energy transfers, calculate the height that the train
would reach if there were no energy losses due to friction.
answer = ...................................... m
(3)
(Total 13 marks)
Page 13 of 23
Q11.
It has been predicted that in the future large offshore wind turbines may have a power
output ten times that of the largest ones currently in use. These turbines could have a blade
length of 100 m or more. A turbine such as this is shown in the diagram below.
(a)
At a wind speed of 11 m s–1 the volume of air passing through the blades each second is
3.5 × 105 m 3.
(i)
Show that the mass of air that would pass through the blades each second is about
4 × 105 kg.
The density of air is 1.2 kg m–3
(2)
(ii)
Calculate the kinetic energy of the air that would enter the turbine each second.
answer = ...................................... J
(2)
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(iii)
It has been predicted that the turbine would produce an electrical power output of
10 MW in these wind conditions. Calculate the percentage efficiency of the turbine in
converting this kinetic energy into electrical energy.
answer = .................................... %
(2)
(b)
State one advantage and one disadvantage of wind power in comparison to fossil fuel.
Advantage ....................................................................................................
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Disadvantage ...............................................................................................
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(2)
(Total 8 marks)
Q12.
A car is travelling on a level road at a speed of 15.0 m s–1 towards a set of traffic lights
when the lights turn red. The driver applies the brakes 0.5 s after seeing the lights turn red and
stops the car at the traffic lights. The table below shows how the speed of the car changes from
when the traffic lights turn red.
time/s
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
speed/m s–1
15.0
15.0
12.5
10.0
7.5
5.0
2.5
0.0
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(a)
Draw a graph of speed on the y-axis against time on the x-axis on the grid provided.
(5)
(b)
(i)
State and explain what feature of the graph shows that the car’s deceleration was
uniform.
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(2)
Page 16 of 23
(ii)
Use your graph to calculate the distance the car travelled after the lights turned red to
when it stopped.
Answer .................. m
(4)
(Total 11 marks)
Q13.
(a)
(i)
State the difference between a scalar quantity and a vector quantity.
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(1)
(ii)
State two examples of a scalar quantity and two examples of a vector quantity.
scalar quantities ..................................................................................
vector quantities …..............................................................................
(3)
Page 17 of 23
(b)
The diagram below shows a ship fitted with a sail attached to a cable. The force of the
wind on the sail assists the driving force of the ship’s propellors.
The cable exerts a steady force of 2.8 kN on the ship at an angle of 35° above a horizontal
line.
(i)
Calculate the horizontal and vertical components of this force.
horizontal component of force ............. kN
vertical component of force ................. kN
(2)
(ii)
The ship is moving at a constant velocity of 8.3 m s–1 and the horizontal component
of the force of the cable on the ship acts in the direction in which the ship is moving.
Calculate the power provided by the wind to this ship, stating an appropriate unit.
Answer ..................................
(3)
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(c)
The cable has a diameter of 0.014 m. Calculate the tensile stress in the cable when it
exerts a force of 2.8 kN on the ship, stating an appropriate unit.
Assume the weight of the cable is negligible.
Answer ................................
(5)
(Total 14 marks)
Q14.
The figure below shows apparatus that can be used to investigate energy changes.
The trolley and the mass are joined by an inextensible string. In an experiment to investigate
energy changes, the trolley is initially held at rest, and is then released so that the mass falls
vertically to the ground.
You may be awarded marks for the quality of written communication in your answer.
(a)
(i)
State the energy changes of the falling mass.
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(ii)
Describe the energy changes that take place in this system.
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(4)
(b)
State what measurements would need to be made to investigate the conservation of
energy.
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(2)
(c)
Describe how the measurements in part (b) would be used to investigate the conservation
of energy.
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(4)
(Total 10 marks)
Page 20 of 23
Q15.
An ‘E-bike’ is a bicycle that is assisted by an electric motor. The figure below shows an Ebike and rider with a total mass of 83 kg moving up an incline.
(a)
(i)
The cyclist begins at rest at A and accelerates uniformly to a speed of 6.7 m s–1 at B.
The distance between A and B is 50 m.
Calculate the time taken for the cyclist to travel this distance.
answer = .................................. s
(2)
(ii)
Calculate the kinetic energy of the E-bike and rider when at B. Give your answer to
an appropriate number of significant figures.
answer = .................................. J
(2)
(iii)
Calculate the gravitational potential energy gained by the E-bike and rider between A
and B.
answer = .................................. J
(2)
Page 21 of 23
(b)
Between A and B, the work done by the electric motor is 3700 J, and the work done by the
cyclist pedalling is 5300 J.
(i)
Calculate the wasted energy as the cyclist travels from A to B.
answer = .................................. J
(2)
(ii)
State two causes of this wasted energy.
Cause 1 ................................................................................................
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Cause 2 ................................................................................................
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(2)
(Total 10 marks)
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