A small object of mass m= 2kg is released from rest at the top of a frictionless

Question

A small object of mass m= 2kg is released from rest at the top of a frictionless ramp of height h=0.75m. At the end of the ramp, it smoothly slides onto a horizontal frictionless surface, where it then experiences a perfectly inelastic collision with an object of mass 3m, The object of mass 3m is connected to an ideal spring of constant k=25N/m.

a. How fast is the object of mass m traveling at the bottom of the ramp?

b. What is the kinetic energy of the two mass system after the collision?

c. What is the amplitude of subsequent oscillations of the mass-spring system after the collision?

Explanation / Answer

a) By law of conservation of energy,

1/2mv^2= mgh

v =sqrt(2gh) = sqrt(2*9.8*0.75) = 3.83 m/s

b) Applying law of conservation of momentum for perfectly inelastic collision,

m1v1i+m2v2i = (m1+m2)vf

vf = (m1v1i+m2v2i)/(m1+m2) = (2*2.82+6*0)/(2+6) = 0.705 m/s

c) By law of conservation of energy,

1/2kx^2 = 1/2mv^2

1/2*25*x^2 = 1/2*(6+2)*0.705^2   => x= 0.4m

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