The first part involves an inelastic collision. The 5.00kgmass sliding along a h

Question

The first part involves an inelastic collision. The 5.00kgmass sliding along a horizontal frictionless surface at 2.00m/scollides with a 1.00kg stationary mass. After the collision the twomasses stick together What is the velocity of the combinedobject after the collision.

We solve this problem using momentum conservation.

Before the collision:

Assume the mass is moving along the positive x-axisinitially.

Pi = 5kg * 2m/s = 10 kgm/s. The momentum of the1kg mass is zero because it is stationary.

After the collision:

Pf = 10 kgm/s because momentum is conserved.

The final object has mass 6 kg, and kinetic energy½mv2 = Pf2/2m =[102/(2*6)]J = (100/12)J.

Now comes the second part:

The combined object with kinetic energy (100/12)J collides withthe spring.

All this kinetic energy is converted into elastic potentialenergy, ½kx2 as the spring is compressed.

(100/12)J = ½kx2 = 500x2. Solve for x.

Explanation / Answer

The hint is right, x = 0.129 m

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