[Maximum number: 2]

A large bowl is made from part of a hollow sphere.
A small spherical ball is placed inside the bowl and is given a horizontal speed. The ball follows a horizontal circular path of constant radius, as shown in Fig. 2.1.

Fig. 2.1

The forces acting on the ball are its weight W and the normal reaction force R of the bowl on the ball, as shown in Fig. 2.2.

Fig. 2.2

The normal reaction force R is at an angle $\theta$ to the horizontal.

(a)

(i)

By resolving the reaction force R into two perpendicular components, show that the resultant force F acting on the ball is given by the expression

W=F \tan \theta .

[ 2 ]

[Maximum number: 2]

A large bowl is made from part of a hollow sphere.
A small spherical ball is placed inside the bowl and is given a horizontal speed. The ball follows a horizontal circular path of constant radius, as shown in Fig. 2.1.

Fig. 2.1

The forces acting on the ball are its weight W and the normal reaction force R of the bowl on the ball, as shown in Fig. 2.2.

Fig. 2.2

The normal reaction force R is at an angle $\theta$ to the horizontal.

(a)

(i)

By resolving the reaction force R into two perpendicular components, show that the resultant force F acting on the ball is given by the expression

W=F \tan \theta .

[ 2 ]

(a)

Define the torque of a couple.

[ 2 ]

(b)

A uniform rod of length 1.5 m and weight 2.4 N is shown in Fig. 2.1.

Fig. 2.1

The rod is supported on a pin passing through a hole in its centre. Ropes A and B provide equal and opposite forces of 8.0 N .

[ 1 ]

(i)

Calculate the torque on the rod produced by ropes A and B .

torque =Nm [1]

[ 1 ]

(a)

State what is meant by the centre of gravity of an object.

[ 1 ]

(a)

State what is meant by the centre of gravity of an object.

[ 1 ]

(b)

The sphere in (b) is now immersed in a liquid in a container, as shown in Fig. 2.2.

Fig. 2.2

The density of the liquid is $1100 \mathrm{~kg} \mathrm{~m}^{-3}$ . The upthrust acting on the sphere due to the liquid is 2.5 N . The magnitude of F is unchanged so that the horizontal rod is not in equilibrium.

[ 2 ]

(i)

Calculate the magnitude and direction of the resultant moment of the forces on the rod about P.
magnitude of resultant moment = Nm
direction of resultant moment

[ 2 ]

[Maximum number: 1]

The diagram shows the view from above of a sprinkler system used to water a garden.

The sprinkler consists of a tube of length 0.15 m . The tube is pivoted in the middle and spins in a horizontal plane as it lets out jets of water from each end. The two water jets are in opposite directions to each other. Each water jet exerts a horizontal force of 3.0 N on the tube at right angles to the tube.

What is the magnitude of the torque on the tube from the water jets?

A

0 Nm

B

0.23 Nm

C

0.45 Nm

D

0.90 Nm

[Maximum number: 1]

A perfectly elastic collision occurs between two objects X and Y . The mass of X is m and the mass of Y is 4 m. Object X travels at speed v before the collision and speed $\frac{3 v}{5}$ in the opposite direction after the collision. Object Y is stationary before the collision.

after

What is the kinetic energy of Y after the collision?

A

$\frac{8}{10} m v^{2}$

B

$\frac{34}{50} m v^{2}$

C

$\frac{16}{50} m v^{2}$

D

$\frac{1}{5} m v^{2}$

[Maximum number: 1]

Two forces act on an object.
Which diagram represents a couple?

A

B

D

[Maximum number: 1]

The diagrams show two ways of hanging the same picture.

diagram 1

diagram 2

In both cases, a string is attached to the same points on the picture and looped symmetrically over a nail in a wall. The forces shown are those that act on the nail.
In diagram 1, the string loop is shorter than in diagram 2.
Which information about the magnitude of the forces is correct?

A

$R_{1}=R_{2} \quad T_{1}=T_{2}$

B

$R_{1}=R_{2} \quad T_{1}>T_{2}$

C

$R_{1}>R_{2} \quad T_{1}<T_{2}$

D

$R_{1}<R_{2} \quad T_{1}=T_{2}$

(a)

State what is meant by the centre of gravity of a body.

[ 2 ]

(b)

A uniform rectangular sheet of card of weight W is suspended from a wooden rod. The card is held to one side, as shown in Fig. 3.1.

Fig. 3.1

On Fig. 3.1,

[ 2 ]

(i)

mark, and label with the letter C , the position of the centre of gravity of the card,

[ 1 ]

(ii)

mark with an arrow labelled W the weight of the card.

[ 1 ]