A 0.300-kg block along a horizontal track has a speed of 1.80 m/s immediately be
ID: 1769148 • Letter: A
Question
A 0.300-kg block along a horizontal track has a speed of 1.80 m/s immediately before colliding with a light spring of force constant 4.10 N/m located at the end of the track.
(a) What is the spring's maxium compression if the track is frictionless.
(b) If the track is not frictionless, would the spring's maximum compression be greater than, less than, or equal to the value obtained in part (a)?
Can someone explain how to work this problem step by step.. somehow I keep getting the wrong answer, doing it the way the teacher taught us... Thank you!
Explanation / Answer
Mass = 0.3 kg
Speed = 1.8 m/s
k= 4.1 N/m
a. For finding compression we apply law of consv of energy
Here KE of mass converted to PE of spring
or
0.5*m*v*v = 0.5*k*x*x
or x = sqrt (0.237) = 0.486 m
b. If track is frictionless, maximum compression would be less than in part a.
Reason:
We can apply law of conservation of energy here. In friction surface, friction force works against motion and does negative work that reduces KE of body.
As a result, some part of initial KE of body gets lost in form of heat, light or sound energy due to friction. This results in lesser compression on spring.
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