# Inelastic Collision with friction

• scruffles
In summary, a ball of clay with mass 50 kg collides with a block with mass 100 kg on a frictional surface. The clay sticks to the block and the collision takes place in 1 dimension. With an initial velocity of 20 m/s and a coefficient of kinetic friction of 0.2, the block/clay system slides a distance of approximately 11.33 m before coming to a stop. This is calculated using the equations m1v1+m2v2=(m1+m2)vf and v_ave=(vi+vf)/2, and taking into account the rate of deceleration and average speed.
scruffles

## Homework Statement

A ball of clay collides with a block that sits on a frictional surface. If the collision proceeds in 1 dimension and the clay sticks to the block, how far does the block/clay system slide before coming to a stop? The clay has mass m = 50 kg, the block as mass M = 100 kg, the initial velocity of the clay is 20 m/s, and the coefficient of kinetic friction between the block and the surface is 0.2.

## Homework Equations

m1v1+m2v2=(m1+m2)vf
v_ave=(vi+vf)/2

## The Attempt at a Solution

50kg(20 m/s) + 100kg(0 m/s) = (50kg+100kg)vf
= 1000 kgm/s=150kgvf
= 6.66m/s = vf (speed of both objects after collision)

Rate of deceleration :
.2 x 9.8m/s^2 = 1.96 m/s^2

The velocity is 6.66 m / s, so the time it takes to stop is:
6.66 / 1.96 ~= 3.40 s

Average speed with linear deceleration is 1/2 initial speed or:

6.66 * 1/2 = 3.33 m/s

So the distance traveled is average speed times the time it took to stop:

3.33 m/s * 3.40 s ~ 11.33 m.

Did I do this right or wrong?

Hi scruffles,

ehild

Thanks!

## 1. What is an inelastic collision with friction?

An inelastic collision with friction is a type of collision between two objects in which kinetic energy is not conserved. This means that some of the initial kinetic energy is lost due to friction between the two objects. In this type of collision, the objects stick together after impact and continue to move as one combined object.

## 2. How does friction affect an inelastic collision?

Friction plays a crucial role in an inelastic collision. It causes some of the initial kinetic energy to be converted into heat, sound, and deformation of the objects. This results in a decrease in the overall kinetic energy of the system and a loss of momentum.

## 3. What factors affect the amount of friction in an inelastic collision?

The amount of friction in an inelastic collision depends on several factors, including the surface area of contact between the objects, the type of materials involved, and the speed at which the objects are moving. A larger surface area and higher speeds will result in more friction, while smoother surfaces and lower speeds will result in less friction.

## 4. How is the coefficient of restitution affected by friction in an inelastic collision?

The coefficient of restitution is a measure of the elasticity of a collision. In an inelastic collision with friction, the coefficient of restitution will always be less than 1 due to the loss of kinetic energy. The amount of friction will also affect the coefficient of restitution, with more friction resulting in a lower coefficient.

## 5. Can an inelastic collision with friction ever be perfectly elastic?

No, an inelastic collision with friction can never be perfectly elastic. This is because some of the initial kinetic energy is always lost due to friction, resulting in a decrease in the overall kinetic energy of the system. In a perfectly elastic collision, kinetic energy would be conserved, and there would be no loss of energy due to friction.

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