[Maximum number: 4]

A student strikes a tennis ball that is initially at rest so that it leaves the racquet at a speed of $64 \mathrm{~m} \mathrm{~s}^{-1}$ . The ball has a mass of 0.058 kg and the contact between the ball and the racquet lasts for 25 ms .

(a)

Calculate the

[ 2 ]

(i)

average power delivered to the ball during the impact.

[ 2 ]

(b)

The student strikes the tennis ball at point P . The tennis ball is initially directed at an angle of $7.00^{\circ}$ to the horizontal.

The following data are available.

[ 2 ]

(i)

Determine the speed of the tennis ball as it strikes the ground.

[ 2 ]

[Maximum number: 3]

The graph shows the variation with time t of the horizontal force F exerted on a tennis ball by a racket.

The tennis ball was stationary at the instant when it was hit. The mass of the tennis ball is $5.8 \times 10^{-2} \mathrm{~kg}$ . The area under the curve is 0.84 Ns .

(a)

Determine, with reference to the work done by the average force, the horizontal distance travelled by the ball while it was in contact with the racket.

[ 3 ]

[Maximum number: 2]

A toy rocket is made from a plastic bottle that contains some water.

Air is pumped into the vertical bottle until the pressure inside forces water and air out of the bottle. The bottle then travels vertically upwards.

The air-water mixture is called the propellant.
The variation with time of the vertical velocity of the bottle is shown.

The bottle reaches its highest point at time $T_{1}$ on the graph and returns to the ground at time $T_{2}$ . The bottle then bounces. The motion of the bottle after the bounce is shown as a dashed line.

(a)

The bottle bounces when it returns to the ground.

[ 2 ]

(i)

Calculate the fraction of the kinetic energy of the bottle that remains after the bounce.

[ 2 ]

[Maximum number: 1]

A ball of mass 0.250 kg is released from rest at time t=0, from a height H above a horizontal floor.

The graph shows the variation with time t of the velocity v of the ball. Air resistance is negligible. Take $g=-9.80 \mathrm{~ms}^{-2}$ . The ball reaches the floor after 1.0 s .

(a)

Estimate the loss in the mechanical energy of the ball as a result of the collision with the floor.

[ 1 ]

[Maximum number: 3]

A box of mass 1.2 kg is lying at rest on a surface. The coefficient of static friction between the box and the surface is 0.36 and the coefficient of dynamic friction between the box and the surface is 0.28 .

(a)

A force of 14.0 N acts on the box for 0.35 m as shown. The force is then removed and the box continues to move. The box comes to rest after a further displacement d.

Determine d.

[ 3 ]

(a)

A car of mass 1600 kg accelerates from rest.

The graph shows how the resultant force F acting in the direction of motion of the car varies with the distance d travelled by the car.

[ 3 ]

(i)

State what is represented by the area under the graph.

[ 1 ]

(ii)

Calculate the final speed of the car.

A different car travels on a horizontal road at a constant speed of $45 \mathrm{~m} \mathrm{~s}^{-1}$ . The engine of the car develops a power of 140 kW . The resistive force $F_{\mathrm{d}}$ acting on the car is given by

F_{d}=c v^{2}

where v is the speed of the car and c is a constant.

[ 2 ]

(b)

Determine c. State the fundamental SI unit for your answer.

[ 3 ]

[Maximum number: 2]

The diagram below shows part of a downhill ski course which starts at point $\mathrm{A}, 50 \mathrm{~m}$ above level ground. Point B is 20 m above level ground.

(a)

A skier of mass 65 kg starts from rest at point A and during the ski course some of the gravitational potential energy transferred to kinetic energy.

[ 2 ]

(i)

From A to B, 24 % of the gravitational potential energy transferred to kinetic energy. Show that the velocity at B is $12 \mathrm{~m} \mathrm{~s}^{-1}$ .

[ 2 ]

(a)

A second identical ball is placed at the bottom of the bowl and the first ball is displaced so that its height from the horizontal is equal to 8.0 m .

The first ball is released and eventually strikes the second ball. The two balls remain in contact. Determine, in m , the maximum height reached by the two balls.

[ 3 ]

[Maximum number: 4]

A company designs a spring system for loading ice blocks onto a truck. The ice block is placed in a holder H in front of the spring and an electric motor compresses the spring by pushing H to the left. When the spring is released the ice block is accelerated towards a ramp ABC . When the spring is fully decompressed, the ice block loses contact with the spring at A . The mass of the ice block is 55 kg .

Assume that the surface of the ramp is frictionless and that the masses of the spring and the holder are negligible compared to the mass of the ice block.

(a)

(i)

The block arrives at C with a speed of $0.90 \mathrm{~m} \mathrm{~s}^{-1}$ . Show that the elastic energy stored in the spring is 670 J .

[ 2 ]

(ii)

Calculate the speed of the block at A.

[ 2 ]

(a)

In a "loop-the-loop" toy, a car of mass 0.12 kg is released from rest. The initial position of the car is 45 cm above level ground. The radius of the circular loop is 15 cm . The car reaches the top of the loop at position P. Frictional and air resistance forces are negligible.

[ 2 ]

(i)

Show that the speed of the car at P is $1.7 \mathrm{~ms}^{-1}$ .

[ 2 ]

(b)

At point A the car collides with a block of mass 0.18 kg and sticks to it. After the collision, the car and the block move together with speed $1.2 \mathrm{~ms}^{-1}$ .

[ 2 ]

(i)

Calculate the speed of the car just before it collides with the block.

[ 2 ]

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