Question

A bullet of mass 6.00g is fired horizontally into a wooden block of mass 1.20kg resting on a horizontal surface. The coefficient of kinetic friction between block and surface is 0.160. The bullet remains embedded in the block, which is observed to slide a distance 0.200m along the surface before stopping. What is the initial speed of the bullet?

Answer 1

Concepts and reason

The concepts used to solve this problem is the work done due to friction force, conservation of energy, kinetic energy and conservation of momentum.

Initially, calculate the work done by the frictional force by substituting coefficient of kinetic friction between the block and surface and force exerted into a wooden block on the horizontal surface.

Then, using the conservation of energy, the work done is equal to the kinetic energy of the bullet and block system to find the velocity of the bullet and block system after the collision.

Finally, apply the conservation of momentum before and after collision by substituting mass and velocity for the bullet–block system, to find the initial speed of the bullet.

Fundamentals

The expression for the work done by the frictional force is,

$W=Fd $

Here, is work done, is the frictional force, and d is the slide distance of the bullet-block system.

The expression for the frictional force exerted on the horizontal surface is,

Here, is the coefficient of kinetic friction between block and surface and is the normal force.

The expression for the normal force acts on the bullet-block system is,

Here, is the acceleration due to gravity and is the mass.

The kinetic energy for the bullet-block system is,

Here, is the kinetic energy and is the speed of the bullet embedded in the block.

Since the principle of conservation of energy states that the work done is equal to the kinetic energy of the bullet-block system after collision.

$n=M $

According to the principle of conservation of momentum before and after collision,

Here, is the speed of the bullet that remains embedded in the block.

The expression for the work done by the frictional force is,

$W=Fd $

Substitute for , and for to find the W.

is the mass of the bullet and is the mass of the block,

The kinetic energy for the bullet-block system is,

According to the principle of conservation of energy,

$n=M $

Substitute for and for .

Rearrange the above expression for .

Substitute for, for , and for .

According to the principle of the conservation of momentum,

Rewrite the expression in terms of .

Substitute for , for , and for to find .

Ans:

The initial speed of the bullet is .