A ball of mass 200g strikes a rigid wall normally at the speed of 25m/s and bounces with the same speed. Time of contact of the ball with the wall is 1s. calculate the change in momentum and the force exerted by the ball on the wall?
Force * time = momentum change
The momentum change is 10 kg*m/s
(twice the incident momentum)
To calculate the change in momentum, we can use the formula:
Change in momentum = Final momentum - Initial momentum
The initial momentum of the ball can be calculated using the formula:
Initial momentum = mass × initial velocity
Given:
Mass of the ball (m) = 200g = 0.2kg
Initial velocity (u) = 25m/s
Initial momentum = 0.2kg × 25m/s
So, the initial momentum of the ball is:
Initial momentum = 5kg·m/s
Since the ball bounces back with the same speed, the final velocity (v) will be -25m/s (negative sign indicates the opposite direction).
The final momentum can be calculated as:
Final momentum = mass × final velocity
Final momentum = 0.2kg × (-25m/s)
So, the final momentum of the ball is:
Final momentum = -5kg·m/s
Now, we can calculate the change in momentum:
Change in momentum = Final momentum - Initial momentum
= (-5kg·m/s) - (5kg·m/s)
= -10kg·m/s
Therefore, the change in momentum is -10kg·m/s.
To calculate the force exerted by the ball on the wall, we can use Newton's second law of motion:
Force = Change in momentum / Time of contact
Given:
Time of contact (Δt) = 1s
Force = (-10kg·m/s) / 1s
= -10N
The negative sign indicates that the force is acting in the opposite direction of the initial motion.
Therefore, the force exerted by the ball on the wall is -10N.
To calculate the change in momentum, we can use the formula:
Change in momentum = Final momentum - Initial momentum
The initial momentum can be found using the formula:
Initial momentum = mass * initial velocity
The final momentum can be found using the formula:
Final momentum = mass * final velocity
Given:
mass (m) = 200g = 0.2kg
Initial velocity (u) = 25m/s
Final velocity (v) = 25m/s (as the ball bounces with the same speed)
Converting the mass to kilograms, we have:
mass (m) = 0.2kg
Calculating initial momentum:
Initial momentum = mass * initial velocity
Initial momentum = 0.2kg * 25m/s
Calculating final momentum:
Final momentum = mass * final velocity
Final momentum = 0.2kg * 25m/s
Now, we can calculate the change in momentum:
Change in momentum = Final momentum - Initial momentum
The force exerted by the ball on the wall can be calculated using the impulse-momentum equation:
Force = Change in momentum / time
Given:
Time of contact (t) = 1s
Now we can calculate the change in momentum and the force exerted by the ball on the wall using the values we have.