Question

A 14.0-g wad of sticky clay is hurled horizontally at a 120-g wooden block initially at rest on a horizontal surface. The clay sticks to the block. After impact, the block slides 7.50 m before coming to rest. If the coefficient of friction between block and surface is 0.650, what was the speed of the clay immediately before impact?

Answer 1

Concepts and reason

The main concepts required to solve this problem are the law of conservation of momentum, velocity, friction and acceleration due to gravity.

Initially, write the equation of motion for the position and the equation for the law of conservation of momentum. Use these equations and calculate the speed of the sticky clay immediately before the impact.

Fundamentals

Use the following equation of motion.

Here, u is the initial speed, v is the final speed, a is the acceleration and s is the displacement.

The equation for the law of momentum conservation for inelastic collision is,

Here, is the mass of first object, is the initial speed of the first object, is the mass of the target object, is the initial velocity of the target object and is the final speed of the combined masses of the two objects after the collision.

Let the speed of the combined mass of the sticky clay and wooden block just after the collision be v.

Use the following kinematic equation for the system of sticky clay and wooden block after the collision.

…… (1)

Here, v is the speed of the combined mass of the sticky clay and wooden block just after the collision, v’ is the final speed of the block which comes to rest, a is the acceleration of the block and s is the distance travelled by the block.

As the final speed of the block comes to rest, the final speed of the block is 0, that is,

The acceleration of the block as the block moves under the frictional surface is,

$811-=D $

Here, is the coefficient of friction and g is the acceleration due to gravity.

Substitute for a in above equation (1).

…… (2)

Rearrange the above equation (1) for v.

…… (3)

Substitute 0 for , 0.65 for , for , and for s in above equation (3).

Let the speed of the sticky clay immediately before the impact be .

Use the law of the conservation of momentum as follows,

…… (4)

Here, is the mass of the sticky clay, is the initial speed of the sticky clay, is the mass of the wooden block, is the initial speed of the wooden block and v is the speed of the combined mass of the sticky clay and wooden block just before the impact.

.

The initial speed of the wooden block is zero as the wooden block is at rest initially, that is,

Rearrange the above equation (4).

Substitute for , for , for , and for in above equation.

Ans:

The speed of the sticky clay immediately before the impact is 93.5 m/s.