In the figure below, a block of mass m- 2.0 kg slides head into a spring of spri

Question

In the figure below, a block of mass m- 2.0 kg slides head into a spring of spring constant k-320 N/m. When the block stops, it has compressed the spring by 5.5 cm. The coefficient of kinetic friction between the block and floor is 0.20. 0 (a) While the block is in contact with the spring and being brought to rest, how much work is done by the spring force? -48.4 (b) What is the increase in the thermal energy of the block-floor system? 2.156 (c) What is the block's speed just as it reaches the spring? 6.8 X m/s

Explanation / Answer

Given,

m = 2 kg ; k = 320 N/m ; x = 5.5 cm ; uk = 0.2

a)The wotk done by the spring is:

Ws = - 1/2 k x^2

Ws = - 0.5 x 320 x 0.055^2 = 0.484 J

Hence, Ws = - 0.484 J

b)the work by the frictional force is dissipated as thermal energy

Wf = -uk m g x

Wf = -0.2 x 2 x 9.8 x 0.055 = -0.2156 J

Wf = -0.2156 J

c)intial energy is such that

E = Ws + Wf = 0.484 + 0.2156 = 0.6996

1/2 m v^2 = 0.6996

v = sqrt (2 x 0.6996/2) = 0.836 m/s

Hence, v = 0.836 m/s

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