Question

A ball of mass 1 kg moving with a velocity of 8 metre per second rebounds after striking a wall calculate the change in momentum if the ball rebounds with the same speed also calculate the force if time of contact with wall is 0.1 second​

Answer 1

GIVEN :-

• Mass of ball ( m ) = 1 kg.
• Final velocity ( v ) = - 8 m/s [ Rebounds after striking the wall ]
• Initial velocity ( u ) = 8 m/s.
• Time ( T ) = 0.1 sec.

TO FIND :-

• The change in momentum.
• The Force applied by the wall.

SOLUTION :-

As we know that change in momentum is given by,

$\begin{gathered} \implies \displaystyle \sf \: \Delta p = mv - mu \\ \end{gathered} </p><p>$

$\begin{gathered} \implies \displaystyle \sf \: \Delta p =m(v - u) \\ \end{gathered}$

$\begin{gathered} \implies \displaystyle \sf \: \Delta p =1( - 8- 8) \\ \end{gathered}$

$\begin{gathered} \implies \displaystyle \sf \: \Delta p =1( - 16) \\ \end{gathered}$

$\begin{gathered} \implies \underline{ \boxed{ \displaystyle \sf \: \Delta p = - 16 \: kg.ms ^{ - 1} }} \\ \end{gathered}$

Hence the change in momentum if the ball rebounds with the same speed is -10 kg.m/s.

Now as we know that Force is given by,

$\begin{gathered}\implies \displaystyle \sf \: F = mass \times Acceleration \\ \end{gathered}$

Now as we know that ,

$Acceleration = ( v - u )/t,$

$\begin{gathered}\implies \displaystyle \sf \: F = 1\times \frac{v - u}{t} \\ \end{gathered} </p><p>$

$\begin{gathered}\implies \displaystyle \sf \: F = \frac{ - 8 - 8}{0.1} \\ \end{gathered} </p><p>$

$\begin{gathered}\implies \displaystyle \sf \: F = \frac{ - 16}{0.1} \\ \end{gathered}$

$\begin{gathered}\implies \underline{ \boxed{\displaystyle \sf \: F = - 160\: N}} \\ \end{gathered} </p><p>$

Hence The Force applied by the wall is -160 N which means that Force is applied on apposite direction.

Answer 2

Answer:

The initial momentum of the ball can be calculated using the formula:

Initial momentum = Mass * Velocity

Given that the mass of the ball is 1 kg and the velocity is 8 m/s, the initial momentum is:

Initial momentum = 1 kg * 8 m/s = 8 kg·m/s

Since the ball rebounds with the same speed, the final momentum after rebounding will be equal in magnitude but opposite in direction. Therefore, the change in momentum can be calculated as:

Change in momentum = Final momentum - Initial momentum

As the final momentum is equal in magnitude but opposite in direction, the final momentum can be expressed as:

Final momentum = - Initial momentum

Substituting the values, we have:

Change in momentum = (- Initial momentum) - Initial momentum

= -2 * Initial momentum

Substituting the value of the initial momentum, we get:

Change in momentum = -2 * 8 kg·m/s

= -16 kg·m/s

Therefore, the change in momentum is -16 kg·m/s.

To calculate the force exerted on the ball, we can use the formula:

Force = Change in momentum / Time of contact

Given that the time of contact with the wall is 0.1 seconds, we can calculate the force as:

Force = (-16 kg·m/s) / (0.1 s)

= -160 N

The negative sign indicates that the force is exerted in the opposite direction of the initial velocity of the ball.

Therefore, the force exerted on the ball is -160 Newtons.