(a)

In practice, the planet in (b) does have an atmosphere that causes a viscous force to act on the moving rock.

State and explain the variation, if any, in the resultant force acting on the rock as it moves vertically upwards.

[ 2 ]

[Maximum number: 8]

A sphere of radius 2.1 mm falls with terminal (constant) velocity through a liquid, as shown in Fig. 1.1.

Fig. 1.1

Three forces act on the moving sphere. The weight of the sphere is $7.2 \times 10^{-4} \mathrm{~N}$ and the upthrust acting on it is $4.8 \times 10^{-4} \mathrm{~N}$ . The viscous force $F_{\mathrm{V}}$ acting on the sphere is given by

F_{\mathrm{V}}=k r v

where r is the radius of the sphere, v is its velocity and k is a constant. The value of k in SI units is 17 .

(a)

(i)

Determine the magnitude of the terminal (constant) velocity of the sphere.

[ 8 ]

(a)

Fig. 1.1 shows a turbine that is used to generate electrical power from the wind.

Fig. 1.1

The power P available from the wind is given by

P=C L^{2} \rho v^{3}

where L is the length of each blade of the turbine, $\rho$ is the density of air, v is the wind speed, C is a constant.

[ 2 ]

(i)

Suggest two reasons why the electrical power output of the turbine is less than the power available from the wind.

1

[ 2 ]

(a)

The variation with time t of vertical speed v of a parachutist falling from an aircraft is shown in Fig. 1.1.

Fig. 1.1

[ 4 ]

(i)

Explain the variation of the resultant force acting on the parachutist from t=0 (point A) to $t=15 \mathrm{~s}$ (point C).

[ 3 ]

(ii)

Describe the changes to the frictional force on the parachutist
1. at $t=15 \mathrm{~s}$ (point C ),
2. between $t=15 \mathrm{~s}$ (point C ) and $t=22 \mathrm{~s}$ (point E).

[ 1 ]

[Maximum number: 1]

A football is kicked so that it moves vertically upwards through the air.
What is the variation in the air resistance and the resultant force acting on the ball as it moves vertically upwards?

air resistance

resultant force

decreases

increases

decreases

increases

[Maximum number: 3]

A sphere floats in equilibrium on the surface of sea water of density $1050 \mathrm{~kg} \mathrm{~m}^{-3}$ , as shown in Fig. 2.1.

Fig. 2.1

(a)

The sphere is now held so that its entire volume is below the surface of the water. The sphere is then released.

[ 3 ]

(i)

The sphere accelerates upwards but remains entirely below the surface of the water. State and explain what happens to the acceleration of the sphere as its velocity begins to increase.

[ 3 ]

(a)

The diver in (b) enters the water and decelerates.

[ 2 ]

(i)

Describe and explain the variation of the viscous drag force acting on the diver in the water as he moves downwards.

[ 2 ]

[Maximum number: 1]

A tennis ball is released from rest at the top of a tall building.
Which graph best represents the variation with time t of the acceleration a of the ball as it falls, assuming that the effect of air resistance is not negligible?

B

C

D

[Maximum number: 1]

A tennis ball is thrown horizontally in air from the top of a tall building.
If the effect of air resistance is not negligible, what happens to the horizontal and vertical components of the ball's velocity?

horizontal component
of velocity

vertical component
of velocity

constant

increases at a constant rate

decreases to zero

increases at a constant rate

decreases to zero

increases to a maximum value

[Maximum number: 1]

A sky diver falls vertically from a stationary balloon. She leaves the balloon at time t=0. At time t=T, she reaches terminal velocity. Beyond the time shown in the graphs, she opens her parachute.

Which graph shows the variation with time t of the force F due to air resistance?

A

B

C

D

Question 1

Question 1(c)

Question 1

Question 1(c)

Question 1(c)(ii)

Question 1

Question 1(b)

Question 1(b)(iii)

Question 1

Question 1(b)

Question 1(b)(ii)

Question 1(b)(iii)

Question 3

Question 2

Question 2(b)

Question 2(b)(ii)

Question 2

Question 2(c)

Question 2(c)(i)

Question 6

Question 6

Question 6