A 200g tennis ball approaches a racket at 20m/s, is in contact with the racket for 0.008s, and the ball rebounds at 4m/s. Find the average force that the racket exerted on the ball.
Change of the linear momentum of the ball is
Δp= mv1-(-mv2) =m(v1+v2) =0.2(20+4) =4.8 kg•m•s^-1
Newton’s 2 Law
F=Δp/Δt =4.8/0.008=600 N
To find the average force exerted by the racket on the tennis ball, we can apply Newton's second law of motion, which states that the force exerted on an object is equal to the rate of change of its momentum. The momentum of an object can be calculated by multiplying its mass by its velocity.
The equation can be written as:
Force = (Change in momentum) / (Time)
1. Calculate the initial momentum of the tennis ball:
Initial momentum = mass * initial velocity
= 0.2 kg * 20 m/s
= 4 kg·m/s
2. Calculate the final momentum of the tennis ball:
Final momentum = mass * final velocity
= 0.2 kg * (-4 m/s) (rebound velocity is in the opposite direction)
= -0.8 kg·m/s
3. Calculate the change in momentum:
Change in momentum = final momentum - initial momentum
= -0.8 kg·m/s - 4 kg·m/s
= -4.8 kg·m/s
4. Calculate the average force exerted by the racket on the tennis ball:
Force = change in momentum / time
= -4.8 kg·m/s / 0.008 s
= -600 N
Therefore, the average force exerted by the racket on the tennis ball is 600 Newtons, in the opposite direction of the ball's initial motion.
To find the average force exerted by the racket on the ball, we can use Newton's second law of motion, which states that the force exerted on an object is equal to the rate of change of its momentum. The momentum of an object is the product of its mass and velocity.
Step 1: Calculate the initial momentum of the ball.
The initial momentum (p_initial) of the ball can be calculated using the formula:
p_initial = m * v_initial
where m is the mass of the ball (200g = 0.2kg) and v_initial is the initial velocity of the ball (20m/s).
p_initial = 0.2kg * 20m/s
p_initial = 4 kg⋅m/s
Step 2: Calculate the final momentum of the ball.
The final momentum (p_final) of the ball can be calculated using the formula:
p_final = m * v_final
where v_final is the final velocity of the ball (4m/s).
p_final = 0.2kg * 4m/s
p_final = 0.8 kg⋅m/s
Step 3: Calculate the change in momentum.
The change in momentum (Δp) can be calculated as:
Δp = p_final - p_initial
Δp = 0.8 kg⋅m/s - 4 kg⋅m/s
Δp = -3.2 kg⋅m/s
Step 4: Calculate the average force.
The average force (F_avg) can be calculated as:
F_avg = Δp / Δt
where Δt is the time interval during which the force is applied (0.008s).
F_avg = -3.2 kg⋅m/s / 0.008s
F_avg = -400 N
Thus, the average force exerted by the racket on the ball is -400 Newtons. The negative sign indicates that the force is in the opposite direction to the initial momentum of the ball.