Problem 52P

In FIGURE, a block of mass m slides along a frictionless track with speed vm. It collides with a stationary block of mass M. Find an expression for the minimum value of vm that will allow the second block to circle the loop-the-loop without falling off if the collision is (a) perfectly inelastic or (b) perfectly elastic.

FIGURE

Solution 52 P:

Step 1 of 2:-

Here we have to find the minimum value of .

The mass of the block is m.

The initial speed is .

The stationary block mass is M.

For perfectly inelastic collision, the total energy and the momentum are conserved.

From the conservation of linear momentum,

-------------------(1)

The conservation of energy tells that,

-------------------(2)

Where .