A 3.0-kg block slides along a frictionless tabletop at 8.0 m/s toward a second b

Question

A 3.0-kg block slides along a frictionless tabletop at 8.0 m/s toward a second block (at rest) of mass 4.5 kg. A coil spring, which obeys Hooke's law and has spring constant k = 730 N/m , is attached to the second block in such a way that it will be compressed when struck by the moving block

1. What will be the maximum compression of the spring?

2.What will be the final velocities of the blocks after the collision? Enter your answers numerically separated by a comma. (v'first, v' second)

3. Is the collision elastic? Ignore the mass of the spring.

Explanation / Answer

part 1 )

maximum compression when both block move same velocity

using momentum conservation

m1v1 = (m1+m2)*V

v = m1v1/(m1+m2)

v = 3.2 m/s

using energy conservation

m1v1^1/2 = (m1+m2)v^2/2 + kx^2/2

x = 0.397 m

part b )

force is spring by conservative , so collision is elastic

v'first = (m1-m2)v1/(m1+m2)

v'first = -1.6 m/s

v'second = 2m1v1/(m1+m2)

v'second = 6.4 m/s

part 3 )

yes

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