Question

A mass sitting on a horizontal, frictional surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of

work is required to compress the spring by 0.20 m. If the mass is released from rest with the spring compressed, it
compresses a maximum acceleration of 15 m/s?.

a) Determine the spring constant.
b) Determine the mass.
d) What is the velocity when the mass reaches maximum acceleration?
c) Deterinine the net force when the mass passes 0.10m compression
d) Determine the acceleration when the mass passes 0.10m compression.
e) Determine the velocity when the mass passes 0.10m compression

Answer 1

I started answering this before everything was erases, but briefly

W = 1/2 K x^2 so K = 2 W / x^2 = 6 * 25 = 150

Also F = - K X = 150 * 1/5 = 30 N at max extension

m = F / a = 30 /15 = 2 kg

Since max extension occurs at t = 0 you can write

x = A sin ω t

v = ω A cos ω t

a = -ω^2 A sin ω t note that there is no phase angle here

Also at .1 compression

.1 = .2 sin ω t and sin ω t = 1/2 and ω t = 30 deg = pi / 6

Substiture these values above to get velocity and acceleration when

ω t = 30 deg