Momentum
Momentum
Momentum
Q1. Fig. 2.1 shows a dummy of mass 70 kg used in a crash test to investigate the safety of a
new car.
The car approaches a solid barrier at 20 m / s. It crashes into the barrier and stops suddenly.
(a) (i) Calculate the momentum of the dummy immediately before the crash.
Calculate the average resultant force applied to the dummy, of mass 70 kg.
(d) The deceleration of the dummy is less than the deceleration of the passenger compartment.
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[Total: 9]
Q2. Fig. 2.1 shows a hammer being used to drive a nail into a piece of wood.
impulse = ...........................................................[1]
(c) Calculate the average force between the hammer and the nail.
(b) The mass of the truck is 0.30kg. Using the principle of conservation of momentum,
calculate the speed of the joined engine and truck immediately after the collision.
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(b) The crumple zone at the front of a car is designed to collapse during a collision.
In a laboratory test, a car of mass 1200kg is driven into a concrete wall, as shown in Fig. 2.1. A
video recording of the test shows that the car is brought to rest in 0.36s when it collides with the
wall.
The speed of the car before the collision is 7.5m/s. Calculate
(i) the change of momentum of the car,
(c) A different car has a mass of 1500kg. It collides with the same wall and all of the energy
transferred during the collision is absorbed by the crumple zone.
(i) The energy absorbed by the crumple zone is 4.3 × 105 J.
Show that the speed of the car before the collision is 24m/s.
[2]
(ii) Suggest what would happen to the car if it is travelling faster than 24m/s when it hits the wall.
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[Total: 8]
Q5. (a) (i) State an expression for the kinetic energy of an object of mass m that is moving with
a speed v.
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(ii) State and explain whether kinetic energy is a scalar quantity or a vector quantity.
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The car with passengers, of total mass 200 kg, is moving in a straight line. It is travelling at 2.5
m / s when it hits a stationary empty car of mass 50 kg.
After the collision, the empty car moves forwards in the same direction at a speed of 4.0 m / s.
For the car with passengers, determine
(i) its momentum when it is travelling at 2.5 m / s,
(ii) the speed and direction of its motion immediately after the collision.
speed = ...............................................................
direction: ............................................................... [3]
iii) Fixed to the front and the back of the cars are large springs. When the cars collide the
springs compress.
The total kinetic energy of the cars after the collision is equal to the total kinetic energy before
the collision.
Describe the energy transfers that occur as the cars collide and then separate.
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[Total: 9]
Q6. Fig. 3.1 shows a shooting competition, where air rifles fire soft metal pellets at distant
targets
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[Total: 9]
Q7. Fig. 2.1 shows an athlete crossing the finishing line in a race. As she crosses the finishing
line, her speed is 10.0m/ s. She slows down to a speed of 4.0m/s.
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(ii) The athlete takes 1.2s to slow down from a speed of 10.0m/s to a speed of 4.0m/s.
Calculate the average resultant force applied to the athlete as she slows down.
(c) Calculate the force required to give a mass of 71kg an acceleration of 6.4m/s2.
The total mass of the train and its passengers is 750000kg. The train is travelling at a speed of
84m/s.
The driver applies the brakes and the train takes 80s to slow down to a speed of 42m/s.
(c) Suggest how the shape of the train helps it to travel at high speeds.
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(d) The train took 80s to reduce its speed from 84m/s to 42m/ s. Explain why, with the same
braking force, the train takes more than 80s to reduce its speed from 42m/ s to zero.
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(e) On a wet day, the train travels a greater distance before it stops along the same track. The
train has the same speed of 84m/s before the brakes are applied.
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[Total: 8]
Q9. Fig. 1.1 shows an ice-hockey player moving on ice. He is preparing to hit the solid disc
called a puck.
The disc of mass 0.16 kg is moving horizontally across the surface of the ice at a speed of 15 m
/ s.
(a) Calculate the magnitude of the momentum of the disc.
(b) The hockey player strikes the disc with his hockey stick and the momentum of the disc
changes.
The disc gains momentum of 3.0 kg m / s at 45° to the original direction of travel of the disc, as
shown in Fig. 1.2.
(i) State the magnitude of the impulse exerted on the disc and the direction, in degrees, of the
impulse relative to the original direction of travel.
A ball falls over the edge of the cliff. The mass of the ball is 160g.
(a) Calculate the vertical speed of the ball as it hits the water. Air resistance can be ignored.
(b) Calculate the vertical momentum of the ball as it hits the water.
A ball of mass 0.52g travels horizontally towards the trolley. The ball embeds itself in the wood
of the trolley. The trolley moves with an initial speed of 0.065m/s.
(a) Calculate:
(b) As the trolley moves across the rough surface, it slows down and stops.
Explain, in terms of the work done, the energy change that takes place as the trolley slows
down.
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[Total: 7]
Q12. Fig. 3.1 shows a collision at very slow speed between two cars travelling along a straight
road
Car B, of mass 800kg, is moving at 2.0m/s and collides with car A, of mass 1000kg, which is
stationary.
After the collision, both cars travel in the same direction as the initial direction of car B.
Show that the speed of car B after the collision is approximately 0.4m/s.
[3]
(b) (i) Calculate the impulse exerted by car A on car B.
Q13. (a) The velocity of an object of mass m increases from u to v. State, in terms of m, u and v,
the change of momentum of the object.
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(b) In a game of tennis, a player hits a stationary ball with his racquet.
(i) The racquet is in contact with the ball for 6.0ms. The average force on the ball during this
time is 400N.
Calculate the impulse on the tennis ball.
impulse = ...........................................................[2]
(ii) The mass of the ball is 0.056kg.
Calculate the speed with which the ball leaves the racquet.
speed = ...........................................................[2]
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[Total: 7]
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(b) A metal block A, travelling in a straight line at 4.0m/ s on a smooth surface, collides with a
second metal block B which is at rest.
Fig. 2.1 shows the two metal blocks A and B before and after the collision
The mass of A is 3.2kg. The mass of B is 1.6kg. After the collision, the velocity of A is 1.5m/s.
Calculate
(i) the momentum of A before the collision,
momentum = ...........................................................[2]
(ii) the velocity v of B after the collision.
v = ...........................................................[3]
(c) In the collision that occurred in (b), block A and block B are in contact for 0.050s. Calculate
the average force that is exerted on B during the collision.
(d) After the collision in (b), the total kinetic energy of the two blocks is less than the kinetic
energy of block A before the collision.
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[Total: 9]
Q15. A footballer kicks a ball vertically upwards. Initially, the ball is stationary. (a) His boot is in
contact with the ball for 0.050s.
The average resultant force on the ball during this time is 180N. The ball leaves his foot at
20m/s.Calculate
(i) the impulse of the force acting on the ball,
impulse = ...........................................................[2]
(ii) the mass of the ball,
mass = ...........................................................[2]
(iii) the height to which the ball rises. Ignore air resistance.
height = ...........................................................[3]
(b) While the boot is in contact with the ball, the ball is no longer spherical.
State the word used to describe the energy stored in the ball.
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[Total: 8]
Q16. (a) A father pushes his child in a cart. The cart starts to move.
Scientists can use many physical quantities to describe what is happening. Four of these are
shown in the box.
force = ..................................................... N
(v) Momentum is a vector quantity. State what is meant by a vector quantity. (1)
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(b) The photograph shows a mother and her daughter stationary on an ice rink.
The mother and daughter push each other away. They move in opposite directions with different
speeds. Explain why they have different speeds. (3)
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(Total for Question 3 = 10 marks)
(a) Andrew starts from the top of the hill and his speed increases as he goes downhill. He
controls his speed and direction by using his skis. He brings himself to a stop at the bottom of
the hill. Describe the energy changes that happen between starting and stopping. (3)
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(b) Andrew returns (i) His mass is 67 kg. Show that his momentum is about 2000 kg m/s when
his velocity is 31 m/s. (2)
ii) He falls over when his momentum is 2000 kg m/s. After he falls over, he slows down by
sliding across the snow. It takes 2.3 s for his momentum to reduce to zero.
Calculate the average force on Andrew as he slows down. (2)
force = .............................................................. N
(iii) Andrew is not injured by the fall even though he was moving quickly. Use ideas about force
and momentum to explain why he is not injured. (2)
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(Total for Question 2 = 9 marks)
Q18. A pilot begins to land an aircraft. (a) The height of the aircraft decreases from 200 m
above the ground to 100 m.
(i) What happens to the gravitational potential energy of the aircraft?
(b) The aircraft lands with its wheels on the runway as shown
(ii) The velocity of the aircraft when it lands is 75 m/s. The mass of the aircraft is 130 000 kg.
Calculate the momentum of the aircraft. (2)
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(ii) Suggest why some aircraft need a very long runway to land safely. (2)
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(Total for Question 4 = 10 marks)
Q19. The photograph shows a hammer just before it hits a nail.
(a) The mass of the hammer is 0.50kg. When it hits the nail, the hammer is travelling
downwards with a velocity of 3.1m/s.
(i) State the relationship between momentum, mass and velocity. (1)
(iii) The hammer stops quickly when it hits the nail. The momentum of the hammer reduces to
zero in 0.070s. Calculate the amount of force that causes this to happen. (2)
force = ........................................ N
(b) As it enters the wood, the nail exerts a force on the wood. At the same time, the wood exerts
a force on the nail. Explain how these two forces are related. (2)
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(c) Both ends of the nail exert pressure when the nail goes into the wood
Explain why the nail exerts more pressure on the wood than it does on the hammer. (2)
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(Total for Question 2 = 9 marks)