(II) A wooden block is cut into two pieces, one with three times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit .When the firecracker explodes inside, the two blocks separate and slide apart. What is the ratio of distances each block travels?

Solution 38P:

We have to find the ratio of distance travelled by each block when the firecracker in the reassembled block explode and the blocks was separated.

Step 1 of 4</p>

Concept:

Law of conservation of linear momentum: When no external force acts on the system, then the final momentum of the system is equal to their initial momentum.

Frictional force always acts on the surface of the bodies in contact whenever their is

relative motion between between the two bodies.

Kinetic Energy: The energy possess by the body by virtue of its motion is known as kinetic energy of the body.

Work-Energy Theorem: The change in kinetic energy of the body is equal to the amount of work done.

Step 2 of 4</p>

Let the mass of the lighter block be , therefore mass of the heavier block would be .

Let the speed of the lighter and heavier blocks be and respectively, after explosion.

Let the coefficient of the kinetic friction be .

Before explosion, the reassembled blocks was at rest, therefore initial momentum of the system was zero. As the explosion takes place due to internal forces and external forces was absent, therefore according to law of conservation of linear momentum,

…(1)

The negative sign implies that both the blocks move in opposite direction after the explosion.

Step 3 of 4</p>

As both the blocks are performing horizontal motion, therefore, the magnitude of the frictional force acting against the lighter block trying to slow its down and eventually stops it is,

…(2)

Similarly, the magnitude of the frictional force acting against the heavier block trying to slow its down and eventually stops it is,

…(3)

Let and be the distance travelled by the lighter and heavier blocks respectively before coming to rest. Therefore,

Work done by frictional force Change in kinetic energy of the block