A block of mass M = 10 kg starts from rest and slides down a frictionless ramp s

Question

A block of mass M = 10 kg starts from rest and slides down a frictionless ramp such that the center of the block drops 0.8 m. As the block passes from point B to C, it encounters a 2 m section of track that is rough, having a coefficient of kinetic friction = 0.3. After passing point C the block compresses a spring and comes to a momentary stop. Answer the following questions, being sure to show all your work. What is the kinetic energy of the block as it passes point B? What is the total work done by friction on the block in sliding across the rough section? What is the kinetic energy of the block as it passes point C? If the spring has a spring constant k = 160 N/m, what is the spring's maximum compression? In this scenario can the block stop forever to the left of B or to the right of C? Calculate the position of the block when it finally stops forever. Use the left edge of the rough surface as a reference.

Explanation / Answer

i)from energy conservation

PE(A) = KE(B)

KE(B) = m g h = 10 x 9.8 x 0.8 = 78.4 J

Hence, KE(B) = 78.4 J

ii)Work done by the frictional force will be:

Wf = Ff x d

Ff = u m g

Wf = u m g d = 0.3 x 10 x 9.8 x 2 = 58.8 J

Hence, Wf = 58.8 J

iii)From conservation of energy, the KE of the block at C will be:

KE(C) = KE(B) - Wf

KE(C) = 78.4 - 58.8 = 19.6 J

Hence, KE(C) = 19.6 J

d)This KE(C) will get converted to the PE of spring

KE(C) = 1/2 k x^2

x = sqrt (2 KE(C)/k) = sqrt (2 x 19.6/160) = 0.495 m

Hence, x = 0.495

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