Question

1. An elastic climbing rope is tested by fixing one end of the rope to the top of a crane. The other end of the rope is connected to a block which is initially at position A. The block is released from rest. The mass of the rope is negligible. diagram not to scale A block 60.0 m rope B C The unextended length of the rope is 60.0 m. From position A to position B, the block falls freely. (a) At position B the rope starts to extend. Calculate the speed of the block at position B. (b) At position C the speed of the block reaches zero. The time taken for the block to fall between B and C is 0.759 s. The mass of the block is 80.0 kg. (i) Determine the magnitude of the average resultant force acting on the block between B and C. (ii) Sketch on the diagram the average resultant force acting on the block between B and C. The arrow on the diagram represents the weight of the block. block weight (iii) Calculate the magnitude of the average force exerted by the rope on the block between B and C. (c) For the rope and block, describe the energy changes that take place (i) between A and B. (ii) between B and C. (d) The length reached by the rope at C is 77.4 m. Suggest how energy considerations could be used to determine the elastic constant of the rope. (e) In another test, the block hangs in equilibrium at the end of the same elastic rope. The elastic constant of the rope is 400 Nm?¹. The block is pulled 3.50 m vertically below the equilibrium position and is then released from rest. (i) Calculate the time taken for the block to return to the equilibrium position for the first time. (ii) Calculate the speed of the block as it passes the equilibrium position.

          1. An elastic climbing rope is tested by fixing one end of the rope to the top of a crane. The other end of the rope is connected to a block which is initially at position A. The block is released from rest. The mass of the rope is negligible.

diagram not to scale
A
block
60.0 m
rope
B
C

The unextended length of the rope is 60.0 m. From position A to position B, the block falls freely.

(a) At position B the rope starts to extend. Calculate the speed of the block at position B.

(b) At position C the speed of the block reaches zero. The time taken for the block to fall between B and C is 0.759 s. The mass of the block is 80.0 kg.

(i) Determine the magnitude of the average resultant force acting on the block between B and C.

(ii) Sketch on the diagram the average resultant force acting on the block between B and C. The arrow on the diagram represents the weight of the block.

block
weight

(iii) Calculate the magnitude of the average force exerted by the rope on the block between B and C.

(c) For the rope and block, describe the energy changes that take place

(i) between A and B.

(ii) between B and C.

(d) The length reached by the rope at C is 77.4 m. Suggest how energy considerations could be used to determine the elastic constant of the rope.

(e) In another test, the block hangs in equilibrium at the end of the same elastic rope. The elastic constant of the rope is 400 Nm?¹. The block is pulled 3.50 m vertically below the equilibrium position and is then released from rest.

(i) Calculate the time taken for the block to return to the equilibrium position for the first time.

(ii) Calculate the speed of the block as it passes the equilibrium position.

1. An elastic climbing rope is tested by fixing one end of the rope to the top of a crane. The other end of the rope is connected to a block which is initially at position A. The block is released from rest. The mass of the rope is negligible.

diagram not to scale
A
block
60.0 m
rope
B
C

The unextended length of the rope is 60.0 m. From position A to position B, the block falls freely.

(a) At position B the rope starts to extend. Calculate the speed of the block at position B.

(b) At position C the speed of the block reaches zero. The time taken for the block to fall between B and C is 0.759 s. The mass of the block is 80.0 kg.

(i) Determine the magnitude of the average resultant force acting on the block between B and C.

(ii) Sketch on the diagram the average resultant force acting on the block between B and C. The arrow on the diagram represents the weight of the block.

block
weight

(iii) Calculate the magnitude of the average force exerted by the rope on the block between B and C.

(c) For the rope and block, describe the energy changes that take place

(i) between A and B.

(ii) between B and C.

(d) The length reached by the rope at C is 77.4 m. Suggest how energy considerations could be used to determine the elastic constant of the rope.

(e) In another test, the block hangs in equilibrium at the end of the same elastic rope. The elastic constant of the rope is 400 Nm?¹. The block is pulled 3.50 m vertically below the equilibrium position and is then released from rest.

(i) Calculate the time taken for the block to return to the equilibrium position for the first time.

(ii) Calculate the speed of the block as it passes the equilibrium position.

Added by Xavier V.

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