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N1M.5 Suppose an object of mass m hanging at the end of a spring oscillates vert

ID: 1776017 • Letter: N

Question

N1M.5 Suppose an object of mass m hanging at the end of a spring oscillates vertically in such a way that its vertical position is z(t) = Asin at, where A and are positive con- stants and the +z axis is upward. (a) What are the SI units of A and w? (b) At what time t is the object's acceleration maximum in the upward direction? [Hint: First evaluate v,(1).] ing on the object? (Be sure to check your units!) spring exerts on the object? [Hint: This is not the same (c) What is the magnitude of the maximum net force act- (d) What is the magnitude of the maximum force that the as the answer to part (c).J

Explanation / Answer

(A) A - meter

w - rad/second


(B) a = d^2z/dt^2 = - A w^2 sin(wt)

a will be max when

sin(wt) = -1

w t = 1.5 pi

t = 1.5 pi / w

(c) a_max = A w^2

F_max = m a_max = m A w^2

(d) Fnet = Fs - mg = 0

Fs = mg + m A w^2