Final answer:
To determine the mass of the volleyball, the impulse formula and the change in velocity are used. The calculation involves dividing the given impulse by the change in velocity, resulting in a mass of 0.270 kg for the volleyball.
Step-by-step explanation:
To find the mass of the volleyball, we use the concept of impulse, which is the product of the force applied to an object and the time interval during which it is applied. Impulse can also be understood as the change in momentum of the object. The formula to calculate impulse (I) is:
I = Δp = m • Δv
Where Δp is the change in momentum, m is the mass of the object, and Δv is the change in velocity. Since momentum, p, is equal to mass times velocity (p = m • v), the change in momentum can be calculated by finding the difference in initial and final momentum values:
Δp = m • v_final - m • v_initial
We are given that the impulse delivered to the ball is -7.7 kg • m/s and the change in velocity is from 5.2 m/s to -23.3 m/s. Mathematically, this is represented as:
-7.7 kg • m/s = m • (-23.3 m/s) - m • (5.2 m/s)
This simplifies to:
-7.7 kg • m/s = -m • 28.5 m/s
Dividing both sides by -28.5 m/s yields the mass of the volleyball:
m = 7.7 kg • m/s / 28.5 m/s
After performing the division, the mass of the volleyball is found to be:
m = 0.270 kg