A 1.22 kg block slides on a frictionless, horizontal surface with an speed of 1.
ID: 1377424 • Letter: A
Question
A 1.22 kg block slides on a frictionless, horizontal surface with an speed of 1.35 m/sec. The block encounters an unstretched spring with a spring constant of 280 N/m.
1)
What is the initial kinetic energy of the block before it hits the spring?
KE0 =
J
2)
What is the potential energy of the mass and spring system when the spring is at its point of maximum compression?
Umax =
J
3)
How far is the spring compress before the block comes to rest?
A =
meters
4)
If the mass and block were to oscillate, what would be the period of the oscillation?
T =
seconds
5)
How long is the block in contact with the spring before it comes to rest?
t =
seconds
Explanation / Answer
1) KEo = 0.5*m*uo^2
= 0.5*1.22*1.35^2
= 1.11 J
2) Apply conservation of Enrgy
Umax = KEo
= 1.11 J
3) Umax = 0.5*k*A^2
==> A = sqrt(2*Umax/k)
= sqrt(2*1.11/280)
= 0.089 m
4) angular frequency, w = sqrt(k/m) (kg/s^2)
= sqrt(280/1.22)
= 15.15 rad/s
time periode, T = 2*pi/w
= 2*pi/15.15
= 0.414 s
5) the block in contact with the spring before it comes to rest,
t = T/4
= 0.414/4
= 0.103 s
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