Question

A 12-kg block is pressed against a spring (spring constant 620 N/mN/m ), compressing it some distance. The block is released from rest and slides across a track as shown in (Figure 1). While most of the track is frictionless, there is a 55-cm section of track that has a coefficient of friction with the block of 0.3. A bit further on, the track ascends into a hill that is 40-cm tall.

Part A: What is the minimum compression of the spring necessary for the block to slide past the section with friction?

Part B: What is the minimum compression of the spring necessary for the block to make it to the top of the hill on the other side?

Answer 1

a)

using conservation of energy

0.5 k x^2 = u mg d

0.5* 620* x^2 = 0.3*12* 9.8* 0.55

x = 0.2502 m

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b)

using conservation of energy again

0.5* 620* x^2 = 0.13* 12.9.8* 0.55 + 12* 9.8* 0.4

x = 0.46296 m

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