A ball of mass 200 g is dropped from a height 3 m above the ground onto a hard floor, and rebounds to a height of 2.2 m. If the ball is in contact with the floor for 0.002 s calculate the average force exerted by the floor on the ball

A ball of mass 1kg is dropped from a height of 7m and rebounds to a height of 4.5m. Calculate:

(I) its KE just before impact
(II) its initial rebound velocity and KE
(III) Account for the loss of KE on the impact.

V^2 = Vo^2 + 2g*h = 0 + 19.6*3 = 58.8

V = 7.67 m/s.

V^2 = Vo^2 + 2g*h = 0 @ max ht.
Vo^2 - 19.6*2.2 = 0
Vo^2 = 43.12
Vo = 6.57 m/s.

a = (-6.57-7.67)/0.002s = -7120 m/s^2.

F = m*a = 0.20 * (-7120) = -1424 N.

To calculate the average force exerted by the floor on the ball, we can use the impulse-momentum principle.

Impulse is defined as the change in momentum of an object, and it is equal to the force applied multiplied by the time interval over which the force is applied.

In this case, since the ball bounces off the floor, the impulse is equal to the change in momentum of the ball.

The impulse-momentum principle can be expressed as:

Impulse = Change in momentum

Therefore,

Force × Time = Change in momentum

Now, let's find the change in momentum of the ball.

The momentum of an object is given by the formula:

Momentum = Mass × Velocity

Before the ball hits the floor, its velocity can be found using the conservation of energy principle. The potential energy of the ball is converted into kinetic energy when it falls.

The potential energy of the ball at a height h is given by the formula:

Potential energy = Mass × Gravity × Height

The kinetic energy of the ball can be calculated using the formula:

Kinetic energy = 1/2 × Mass × Velocity^2

Since energy is conserved, the initial potential energy of the ball is equal to its final kinetic energy:

Mass × Gravity × Height = 1/2 × Mass × Velocity^2

Simplifying the equation, we get:

Velocity = √(2 × Gravity × Height)

Now that we know the initial velocity, we can calculate the momentum before the collision:

Initial momentum = Mass × Velocity_initial

After the ball rebounds to a height of 2.2m, the final velocity can be calculated using the same method:

Final momentum = Mass × Velocity_final

The change in momentum is given by:

Change in momentum = Final momentum - Initial momentum

Finally, by substituting the values into the equation:

Force × Time = Change in momentum

We can solve for the average force exerted by the floor on the ball.