(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A block of mass M is resting on a horizontal, frictionless table and is attached as shown above to a relaxed spring of spring constant k. A second block of mass 2 M and initial speed v0 collides with and sticks to the first block.

Develop expressions for the following quantities in terms of M, K, and v0.

a) v, the speed of the blocks after impact

b) x, the max distance the spring is compressed

c) T, the period of the subsequent simple harmonic motion

2. Relevant equations

- M1V1 + M2V2 = (M1 + M2)(Vf)

- (1/2)(k)(x^2)

- F = -kx

- (1/2)(m)(v^2)

3. The attempt at a solution

a)

M1V1 + M2V2 = (M1 + M2)(Vf)

(2M)(V0) + (M)(0) = (2M + M)(x)

(2M)(V0) = (3M)(Vf)

Vf = (2/3)(V0)

b)

x = max distance spring is compressed

spring constant = k

PE of spring = (1/2)(k)(x^2)

Max distance = PE at MAX, KE = 0

Logic process: We know that v = Vf is solved above, set PE = KE, since complete transfer occurs

(1/2)(m)(v^2) = (1/2)(k)(x^2)

(m)((2/3)(V0))^2 = (k)(x^2)

sqrt(((m)((2/3)(V0))^2) / k) = x

c)

No clue, unknown how to solve this (help???)

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# Homework Help: Springs w/ Collisions

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