A 0.3 kg tennis ball is travelling west with a speed of 4 m/s and bounces off a wall. After bouncing, the ball is travelling east at 2 m/s. The tennis ball was in contact with the wall for 0.004 seconds.
a) What is the initial and final momentum of the ball?
b) What is the direction and magnitude of the force the ball experienced due to the wall?
c) What is the direction and magnitude of the force the wall experienced due to the ball?
To solve these questions, we can use the principle of conservation of momentum, which states that the total momentum before an event is equal to the total momentum after the event, assuming no external forces act on the system.
a) Initial momentum (before the bounce):
P_initial = m * v_initial
P_initial = 0.3 kg * 4 m/s
P_initial = 1.2 kg⋅m/s
Final momentum (after the bounce):
P_final = m * v_final
P_final = 0.3 kg * (-2 m/s) (note that we use a negative sign since the ball is now moving in the opposite direction)
P_final = -0.6 kg⋅m/s
b) To find the direction and magnitude of the force experienced by the ball due to the wall, we can use the impulse-momentum theorem, which states that the impulse (change in momentum) experienced by an object is equal to the force applied multiplied by the time interval over which the force acts.
Impulse = F * Δt
The impulse experienced by the ball during the bounce can be calculated as follows:
Impulse = P_final - P_initial
Impulse = (-0.6 kg⋅m/s) - (1.2 kg⋅m/s)
Impulse = -1.8 kg⋅m/s
Since the time of contact with the wall is given as 0.004 seconds, we can calculate the force as:
Force = Impulse / Δt
Force = (-1.8 kg⋅m/s) / (0.004 s)
Force = -450 N
The negative sign indicates that the force acted in the opposite direction to the ball's initial momentum, which is east. Therefore, the ball experienced a force of magnitude 450 N directed west.
c) According to Newton's third law of motion, for every action, there is an equal and opposite reaction. Thus, the force experienced by the wall due to the ball is of the same magnitude but opposite in direction to the force experienced by the ball. Therefore, the wall experiences a force of magnitude 450 N directed east.
To answer these questions, we can use the principles of conservation of momentum and Newton's third law of motion.
a) The initial momentum of the ball is given by:
Initial momentum = mass x initial velocity
Initial momentum = 0.3 kg x 4 m/s
Initial momentum = 1.2 kg·m/s
The final momentum of the ball is given by:
Final momentum = mass x final velocity
Final momentum = 0.3 kg x (-2 m/s) (since the direction is reversed)
Final momentum = -0.6 kg·m/s
b) The change in momentum experienced by the ball can be calculated using the formula:
Change in momentum = Final momentum - Initial momentum
Change in momentum = -0.6 kg·m/s - 1.2 kg·m/s
Change in momentum = -1.8 kg·m/s
The time of contact is given as 0.004 seconds.
Using the definition of force:
Force = Change in momentum / time
Force = (-1.8 kg·m/s) / (0.004 s)
Force = -450 N
The negative sign indicates that the force is exerted in the opposite direction to the initial motion of the ball. So, the force experienced by the ball due to the wall is 450 Newtons and is directed eastward.
c) According to Newton's third law of motion, for every action, there is an equal and opposite reaction. This means that the force the wall experiences due to the ball is also 450 Newtons but directed westward.
In summary:
a) The initial momentum of the ball is 1.2 kg·m/s, and the final momentum is -0.6 kg·m/s.
b) The force the ball experiences due to the wall is 450 Newtons, directed eastward.
c) The force the wall experiences due to the ball is 450 Newtons, directed westward.