21. The diagram shows a 0.12-kg square block at four positions along a track. Th

Question

21.

The diagram shows a 0.12-kg square block at four positions along a track. The track is frictionless between points A and B. Elsewhere, the coefficient of static friction on the block is 0.26.

Initially, the block is held in place against a spring by a horizontal external force of magnitude 35 N. Then the external force is removed, and the block is projected forward with speed V1=1.2m/s. The block descends a ramp and has speed V2=1.4m/s at the bottom. At point C, its speed is V3=1.4m/s. The block stops at point D.

What is the initial compression of the spring?

0.99 cm

0.49 cm

0.26 cm

0.67 cm

0.18 cm

36.

The diagram shows a 0.74-kg square block at four positions along a track. The track is frictionless between points A and B. Elsewhere, the coefficient of static friction on the block is 0.36.

Initially, the block is held in place against a spring by a horizontal external force of magnitude 29 N. Then the external force is removed, and the block is projected forward with speed V1=1.2m/s. The block descends a ramp and has speed V2=1.9m/s at the bottom. At point C, its speed is V3=1.4m/s. The block stops at point D.

What is the height h of the ramp?

2.6 m

82 cm

1.5 m

34 cm

11 cm

A steel wire of length L connects a hook on the ceiling to a bowling ball, With the steel wire kept taut, the bowling ball is lifted to a height h above the floor, and then released. The bowling ball swings back and forth in the motion of a pendulum. After the bowling ball is released, what is the maximum height above the floor that it reaches? Assume that friction does not affect its motion.

1.33h

h

h/2

L

21.

The diagram shows a 0.12-kg square block at four positions along a track. The track is frictionless between points A and B. Elsewhere, the coefficient of static friction on the block is 0.26.

Initially, the block is held in place against a spring by a horizontal external force of magnitude 35 N. Then the external force is removed, and the block is projected forward with speed V1=1.2m/s. The block descends a ramp and has speed V2=1.4m/s at the bottom. At point C, its speed is V3=1.4m/s. The block stops at point D.

What is the initial compression of the spring?

0.99 cm

0.49 cm

0.26 cm

0.67 cm

0.18 cm

36.

The diagram shows a 0.74-kg square block at four positions along a track. The track is frictionless between points A and B. Elsewhere, the coefficient of static friction on the block is 0.36.

Initially, the block is held in place against a spring by a horizontal external force of magnitude 29 N. Then the external force is removed, and the block is projected forward with speed V1=1.2m/s. The block descends a ramp and has speed V2=1.9m/s at the bottom. At point C, its speed is V3=1.4m/s. The block stops at point D.

What is the height h of the ramp?

2.6 m

82 cm

1.5 m

34 cm

11 cm

V. 4. Smooth B D E Rough

Explanation / Answer

36)

For initial compression,

Initial spring Potential energy = Initial Kinetic energy

So, 0.5*k*x^2 = 0.5*mv1^2

where k = spring constant

x = maximum compression of the spring

Also, for the spring, force needed = F= k*x = 35 N

So, 0.5*(k*x)*x = 0.5*mv1^2

So, 0.5*35*x = 0.5*0.12*1.2^2

So, x = 0.494 m = 49 cm <-------answer(1)

35)

Now, after travelling to point B, the total energy of the body,

0.5*mv1^2 + mgh = 0.5*mv2^2

So, 0.5*0.74*1.2^2 + 0.74*9.8*h = 0.5*0.0.74*1.9^2

So, h = 0.11 m = 11 cm

37)

answer will be = h

This is due to to the fact that energy needs to be conserved. So, the initial height must be reached to regain the same configuration as before <---answer

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