When serving a tennis ball, the player hits it when its velocity is zero (at the highest point of a vertical toss). The racket exerts a force of 560 N on the ball for 5.00 ms, giving it a final velocity of 45.0 m/s. Using these data, find the mass of the ball.
F = m a = (change in momentum/ change in time)
560 = m (45 - 0) / 5 *10^-3
560 = 45,000 m /5 = 9,000 m
m = .0622 Kg = 62.2 grams
To find the mass of the ball, we can use Newton's second law of motion, which states that the force applied to an object is equal to the mass of the object multiplied by its acceleration.
Given:
Force (F) = 560 N
Time (t) = 5.00 ms = 0.005 s
Final Velocity (v) = 45.0 m/s
We know that the acceleration of the ball is given by the change in velocity divided by the change in time.
Acceleration (a) = (final velocity - initial velocity) / time
Initial velocity (u) = 0 m/s (since it is at rest at the highest toss point)
Using the equation:
a = (v - u) / t
a = (45.0 m/s - 0 m/s) / 0.005 s
a = 9000 m/s^2
Now, we can find the mass (m) of the ball using Newton's second law:
F = m * a
560 N = m * 9000 m/s^2
Rearranging the equation to solve for mass:
m = F / a
m = 560 N / 9000 m/s^2
m ≈ 0.0622 kg
Therefore, the mass of the ball is approximately 0.0622 kg.
To find the mass of the ball, we can use the equation that relates force, mass, and acceleration:
F = ma
In this case, we know the force exerted on the ball by the racket (F = 560 N) and the time interval during which the force is applied (t = 5.00 ms = 0.005 s). We also know the final velocity of the ball (v = 45.0 m/s).
First, let's convert the time to seconds:
t = 0.005 s
Now, let's rearrange the equation to solve for mass (m):
F = ma
m = F / a
To calculate the acceleration (a), we can use the equation that relates velocity, time, and acceleration:
v = u + at
Considering that the initial velocity (u) is zero, we can simplify the equation to:
v = at
Rearranging the equation to solve for acceleration, we get:
a = v / t
Now, we can substitute the values we know into this equation:
a = 45.0 m/s / 0.005 s
Simplifying, we find:
a = 9000 m/s²
Now, let's substitute the values into the equation to find the mass:
m = 560 N / 9000 m/s²
m ≈ 0.0622 kg
Therefore, the mass of the ball is approximately 0.0622 kg.