A light spring shown on the figure below requires force of 16.00 N to become com

Question

A light spring shown on the figure below requires force of 16.00 N to become compressed by 20.00 cm. A piece of very sticky gum with mass m=50.00 g is held at rest, distance h=50.00 cm above a plate of mass M= 200.0g that is vertically supported by the spring (see the sketch below). Assume that the plate initially causes a negligible compression of the spring and very short duration of the collision, so that the effect of gravity on the linear momentum of the system can be neglected.

1. What is the speed of the gum just before the collision? 2. What is the speed acquired by the system just after the collision? 3. Was the collision elastic or not? Prove by doing necessary calculations. Finally, think (and you don’t have to do it now) how you would determine the maximal compression of the spring!

Explanation / Answer

1. Speed just before collision, v = 0

2. Energy stored in compression,

P.E. = 1/2*K*x^2 = F*x = 16*20*10^-2 = 3.2 J

If this energy is converted in KE of plate,

1/2*m*v^2 = 3.2

v = 2*3.2/200*10^-3

=32 m/s

Speed after the collision,

v' = m*v / m+m'

= 200*32/200+20

=29.09 m/s

Now

1/2m*v^2 1/2(m+m')v'^2

hence the collision is inelastic.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.