please include steps if possible A mass, m1 = 8.93 kg , is at rest on a friction

Question

please include steps if possible

A mass, m1 = 8.93 kg , is at rest on a frictionless horizontal surface and connected to a wall by a spring with k = 72.1 N/m, as shown in the figure. A second mass, = 6.09 kg, is moving to the right at v0 = 17.7 m/s . The two masses collide and stick together. What is the maximum compression of the spring? Please include a multiplication sign (*) to indicate that two units are being multiplied, How long will it take after the collision to reach this maximum compression? Please include a multiplication sign (*) to indicate that two units are being multiplied.

Explanation / Answer

If masses stick together, it is a totally inelastic collision, so momentum only is conserved. Once we find the speed of the combined mass after the collision, we will find the kinetic energy left. This will be 100% converted to spring potential energy. The two masses will slow down due to the spring.

OK momentum. The moving block has all the momentum to start and it gets converted to the momentum of the two blocks right before the spring gets compressed anything.

M2Vi = (M2 + M1)Vf

Vf = M2 Vi /(M1 + M2) = 7.18 m/s

the kinetic energy of the two blocks now gets converted to spring potential energy

(1/2) m v^2 = (1/2) k x ^2

x = SQRT(m v^2 / k) =3.28 m this is the first answer

3 m

For the second part, the average spring force is (1/2) k x.

The average force would slow the masses down with an acceleration of F = ma

a = F/m = ((1/2) 72.1N/m*3.28m)/15.02 kg = 7.86 m/s^2

Vf = Vo + a t

t = Vo/a = 7.18m/s/7.86 m/s^2 = 0.913 s

this is the second answer

0.913 s

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