1.
State Newton’s second and third laws of motion.
In your answer, you should use appropriate technical terms spelled correctly.
(i)
second law
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[1]
(ii)
third law
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[1]
[Total 2 marks]
2.
Most cars are now fitted with safety airbags. During a sudden impact, a triggering
mechanism fires an ammunition cartridge that rapidly releases nitrogen gas into the
airbag.
In a particular simulated accident, a car of mass 800 kg is travelling towards a wall.
Just before impact, the speed of the car is 32 m s–1. It rebounds at two-thirds of its
initial speed.
The car takes 0.50 s for the car to come to rest. During the crash, the car’s airbag fills
up to a maximum volume of 3.4 × 10–2 m3 at a pressure of 1.0 × 105 Pa. The
temperature inside the airbag is 20 °C. Calculate:
(i)
the change in the momentum of the car
momentum change = ............................................................
[2]
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(ii)
the magnitude and direction of the average force acting on the car during impact.
force = .........................................................N
[2]
direction:...........................................................................................................
[1]
(iii)
the mass of nitrogen inside the cartridge.
Molar mass of nitrogen = 0.014 kg mol–1
mass = .....................................................kg
[3]
[Total 8 marks]
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3.
A cricketer throws a cricket ball of mass 0.16 kg.
(a)
The figure below shows how the force on the ball from the cricketer’s hand varies
with time. The ball starts from rest and is thrown horizontally.
25
force / N
20
15
10
5
0.0
(i)
0.1
0.2 0.3
time / s
0.4
Estimate the area under the graph.
area = ...................... Ns
[1]
(ii)
The area under the graph represents a change in a physical quantity for the
ball.
State the name of this quantity.
...............................................................................................................
[1]
(iii)
Calculate the speed of the ball, mass 0.16 kg, when it is released.
speed = ...................... m s–1
[2]
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(iv)
Calculate the maximum horizontal acceleration of the ball.
acceleration = ...................... m s–2
[2]
(b)
The ball bounces several times on a hard surface. The maximum height to which
it rises after each bounce is given in the table below.
bounce number, n
maximum height, h/ m
1
0.71
2
0.33
3
0.16
The data given in the table fit a relationship for the variation in maximum height
with bounce number of the form
h = 1.5 e–kn
where k is a constant.
(i)
State the name of this form of relationship.
...............................................................................................................
[1]
(ii)
Calculate the value of k.
k = ...................
[2]
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(iii)
What is the height from which the ball was thrown?
height = ...................... m
[1]
(iv)
Show that the loss of kinetic energy of the ball at the second bounce is
about 0.6 J.
Assume that the horizontal speed of the ball is unchanged.
[2]
[Total 12 marks]
4.
This question is about kicking a football.
(a)
The diagram below shows how the force F applied to a ball varies with time t
whilst it is being kicked horizontally. The ball is initially at rest.
60
50
F/N
40
30
20
10
0
0
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0.1
0.2
0.3
t/s
5
(i)
Use the graph to find
1
the maximum force applied to the ball
maximum force = ……………………N
2
the time the boot is in contact with the ball.
time = …….…………..s
[1]
(ii)
The mean force multiplied by the time of contact is called the impulse
delivered to the ball. Use the graph to estimate the impulse delivered to the
ball.
impulse = …...…………N s
[2]
(b)
The mass of the ball is 0.50 kg. Use your answers to (a) to calculate
(i)
the maximum acceleration of the ball
acceleration = ......................m s–2
[2]
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(ii)
the final speed of the ball
speed = ......................m s–1
[2]
(iii)
the kinetic energy of the ball after the kick.
kinetic energy = ......................J
[2]
(c)
The ball hits a wall with a speed of 14 m s–1. It rebounds from the wall along its
initial path with a speed of 8.0 m s–1. The impact lasts for 0.18 s. Calculate the
mean force exerted by the ball on the wall.
force = ………………..N
[3]
[Total 12 marks]
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5.
State what is meant by kinetic energy and momentum. This should not be answered
just in terms of the equations Ek = ¹⁄₂ mv2 and p = mv.
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[Total 4 marks]
6.
This question is about an alpha particle making a head on collision with a gold nucleus.
(a)
(i)
When the alpha particle is at a large distance from the gold nucleus it has a
kinetic energy of 7.6 × 10–13 J. Show that its speed is about
1.5 × 107 m s–1.
mass of alpha particle = 6.6 × 10–27 kg
[2]
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(ii)
As the alpha particle approaches the gold nucleus, it slows down and the
gold nucleus starts to move, Fig. 1.
gold nucleus
alpha particle
Fig.1
Explain this and explain how it is possible to calculate the speed of the gold
nucleus.
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[3]
(iii)
Fig.2 shows the alpha particle and the gold nucleus at the distance of
closest approach. At this instant the gold nucleus is moving with speed V
and the alpha particle is stationary.
V
gold nucleus
alpha particle
Fig. 2
Calculate the speed V of the gold nucleus.
mass of gold nucleus = 3.0 × 10–25 kg
V = ......................m s–1
[2]
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(iv)
The alpha particle bounces back. Its final speed approximately equals its
initial speed of approach. Assume that the mean force on the nucleus is 9.0
N during the interaction.
Estimate the time of the collision.
time = ….…………… s
[2]
(b)
15
F/N
10
5
0
0
5
10
15
20
–14
r / 10 m
Fig. 3
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(i)
Fig. 3 shows two points on the graph of the electrostatic repulsive force F
between the alpha particle and nucleus against their separation r. The
particle and the nucleus are being treated as point charges. Use data from
the graph to calculate the values of the force at distances r = 10 × 10–14 m
and 15 × 10–14 m.
F at 10 × 10–14 m =…………….N
F at 15 × 10–14 m =…………….N
[3]
(ii)
Plot the two points on the graph and draw the curve.
[1]
[Total 13 marks]
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