A block rests in equilibrium on the centre of a uniform horizontal plank. The block is attached to two ropes, each of which passes over a fixed pulley and then attaches to an end of the plank, as shown in Figure 2.1.

Figure 2.1, apparatus diagram (not to scale): a block of mass 8.1 kg sits on the centre of a horizontal plank of mass 4.5 kg; a rope runs from each end of the plank up over a fixed pulley and down to the block, each rope making angle θ with the vertical both where it meets the plank and where it meets the block

Where the ropes attach to the block and to the plank, the angle between the ropes and the vertical is

θ

. There is negligible friction between the pulleys and the ropes.

The mass of the block is 8.1 kg. The mass of the plank is 4.5 kg.

Figure 2.2 shows the directions of the forces acting on the plank and the block. The weight of the plank is

W_{P}

, the weight of the block is

W_{B}

, the tension in each rope is

T

and the forces that the plank and the block exert on each other each have magnitude

R

Figure 2.2, two free-body force diagrams side by side (not to scale). Left: the plank, with a tension T at angle θ to the vertical pulling up from each end, its weight W_P acting downward at the centre, and the block's push R acting downward at the centre. Right: the block, with a tension T at angle θ to the vertical pulling up on each side, the reaction R acting upward at the centre, and its weight W_B acting downward

Use Figure 2.2 to show that

R + W_{P} = W_{B} - R

Draw with the mouse or a finger.

2(b)(ii)Moments Equilibrium Centre MassEasy2 marks

Use the equation in 2(b)(i) to calculate the magnitude of

R

2(c)(i)Elasticity Hookes Law Young ModulusEasy1 mark

The extension of each rope in 2(b) is proportional to the force applied to it.

State the name of the law that describes this behaviour.

2(c)(ii)Elasticity Hookes Law Young ModulusMedium1 mark

The ropes have elastic deformation.

State what is meant by elastic deformation.