[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)

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

[ 1 ]

(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 ]

(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 form a couple.
Which statement describes the two forces?

A

They are in the same direction.

B

They are perpendicular to each other.

C

They have the same magnitude.

D

They pass through the same point.

[Maximum number: 1]

A horizontal wooden plank is pivoted at one end, as shown.

The plank has a mass of 100 kg and a length of 10 m . The centre of gravity of the plank is a distance of 4 m from the pivot.

What is the moment of the weight of the plank about the pivot?

A

$4 \times 10^{2} \mathrm{Nm}$

B

$5 \times 10^{2} \mathrm{Nm}$

C

$\quad 4 \times 10^{3} \mathrm{Nm}$

D

$\quad 5 \times 10^{3} \mathrm{Nm}$

[Maximum number: 1]

Which diagram shows a couple formed by two forces, each of magnitude F, acting on a rod?

A

Question 2

Question 2(a)

Question 2(a)(i)

Question 2

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Question 2(a)(i)

Question 2

Question 2(a)

Question 2

Question 2(a)

Question 2(b)

Question 2(b)(i)

Question 2

Question 2(a)

Question 2(c)

Question 2(c)(ii)

Question 10

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Question 11

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Question 11