a tennis ball has mass 0.045 kg and is hit at a speed of 120 km/h by the server. the opposing player hits the ball exactly back along the line of its trajectory giving the ball a new speed of 115 km/h. if the contact time between the racquet and the ball is 0.02s what is the average force on the tennis ball imparted by the opposing player?
Ft = change mv = mvf-mvi
Be careful with your signs. If you call the initial serve positive the return must be in the negative direction.
To find the average force on the tennis ball imparted by the opposing player, we can use Newton's second law of motion, which states that the force (F) is equal to the change in momentum (Δp) divided by the change in time (Δt).
Step 1: Convert the given speeds from km/h to m/s.
- Given initial speed (v1) = 120 km/h
- Given final speed (v2) = 115 km/h
Since 1 km/h = 1000 m/3600 s,
v1 = (120 km/h) * (1000 m/3600 s) = 33.3 m/s (approximately)
v2 = (115 km/h) * (1000 m/3600 s) = 31.9 m/s (approximately)
Step 2: Calculate the change in momentum (Δp).
The momentum (p) of an object is given by the product of its mass (m) and velocity (v): p = mv.
Initial momentum (p1) = (mass) * (initial velocity)
p1 = (0.045 kg) * (33.3 m/s) = 1.494 kg·m/s (approximately)
Final momentum (p2) = (mass) * (final velocity)
p2 = (0.045 kg) * (31.9 m/s) = 1.436 kg·m/s (approximately)
Change in momentum (Δp) = p2 - p1
Δp = 1.436 kg·m/s - 1.494 kg·m/s = -0.058 kg·m/s (approximately)
Note: The negative sign indicates a decrease in momentum.
Step 3: Calculate the average force by dividing the change in momentum by the contact time (Δt).
Given contact time (Δt) = 0.02 s
Average force (F) = Δp / Δt
F = (-0.058 kg·m/s) / (0.02 s)
Calculating this, we find that the average force on the tennis ball imparted by the opposing player is approximately -2.9 N (since the negative sign indicates that the force is in the opposite direction of motion).
To determine the average force imparted by the opposing player on the tennis ball, you can use Newton's second law of motion, which states that force is equal to the change in momentum over time. In this case, we'll calculate the change in momentum and then divide it by the contact time.
The momentum of an object is given by the product of its mass and velocity:
Momentum = mass x velocity
First, let's convert the given velocities from km/h to m/s:
120 km/h = (120 * 1000) / (60 * 60) m/s = 33.33 m/s
115 km/h = (115 * 1000) / (60 * 60) m/s = 31.94 m/s
Now we can calculate the initial momentum and final momentum:
Initial momentum = mass x initial velocity = 0.045 kg x 33.33 m/s = 1.49985 kg m/s
Final momentum = mass x final velocity = 0.045 kg x 31.94 m/s = 1.4373 kg m/s
Next, we can calculate the change in momentum:
Change in momentum = final momentum - initial momentum = 1.4373 kg m/s - 1.49985 kg m/s = -0.06255 kg m/s
Since the ball changes direction, the change in momentum is negative.
Finally, we can calculate the average force using Newton's second law:
Force = change in momentum / contact time = -0.06255 kg m/s / 0.02 s = -3.1275 N
The average force exerted by the opposing player on the tennis ball is approximately -3.1275 N. The negative sign indicates that the force is in the opposite direction of the initial velocity.