Q1)A block of mass m slides along a smooth track from one level to a higher leve

Question

Q1)A block of mass m slides along a smooth track from one level to a higher level after passing through an intermediate valley. The higher level has a rough section of length L. After passing this section the block slides head on into a spring. The block momentarily stops after compressing the spring by d. The blocks initial speed is Vo, the height difference is h, and the coefficient of friction is u.
a) find the block's velocity when it reaches the higher level

b) determine the spring constant k

c) in terms of the other given variables (m, h, L, u, and d) find the minimum value of Vo (initial velocity) in order for the block to return to its original position.

Explanation / Answer

a)................

KE1 = KE2 - PE2                                    (note that the "valley" has no bearing on this as a conservation of energy problem

(1/2)m(V1)2 = (1/2)m(V2)2 + mgh                (simplifying w/ masses canceling out and multiplying all by 2, leaving...

(V1)2 = (V2)2 + 2gh             Solving for V2.....

V2 = Sqrt [(V1)2 - 2gh]

B) .................                the rough surface will slow it down, and the spring will bring it to a (temporary) stop. So, we write the energy equation as

KE1 - Wf - Ws = 0         (where Wf is the work of friction, and Ws is the work of the spring)

NOte: Wf = Ff*d (Force of friction x the distance that it acts over; where Ff = N = mg)

(1/2)m(V2)2 - mgL - (1/2)d2 = 0     (solve this for d)

C) Ran out of time.....

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