A block of mass m 1 =1.6kg initially moving to the right with a speed of3.4m/s o

Question

A block of massm1=1.6kg initially moving to the right with a speed of3.4m/s on a frictionless, horizontal track collides with a spring attached to a second block of massm2=3.2kg initially moving to the left with a speed of2.4m/s as shown in figure (a). The spring constant is552N/m.

(A) Find the velocities of the two blocks after the collision.
(B) During the collision, at the instant block 1 is moving to the right with a velocity of1.0m/s as in figure (b), determine the velocity of block 2.
(C) Determine the distance the spring is compressed at that instant.

What ifm1is initially moving at3.2m/s whilem2is initially at rest?

Explanation / Answer

for maximum compression all kinetic energy gets converted into spring energy.

a)Hence - 1/2 mv*v = 1/2 kx*x.

hence x=.1722m.

b)for velocity conservation of momemtum(at last they move together)

m1*v1 = (m1+m2)*v

hence v = 1.067 m/s

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