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?
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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