Question

When serving a tennis ball, a player hits the ball when its velocity is zero (at the highest point of a vertical toss). The racquet exerts a force of 540 N on the ball for 5.00 ms, giving it a final velocity of 45.0 m/s. Using these data, find the mass (in grams) of the ball.

Answer 1

Answer:

60 grams

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity

m = Mass

F = Force

Impulse

$J=Ft$

$J=m(v-u)\\\Rightarrow Ft=m(v-u)\\\Rightarrow m=\frac{Ft}{v-u}\\\Rightarrow m=\frac{540\times 5\times 10^{-3}}{45-0}\\\Rightarrow m=0.06\ kg=60\ g$

Mass of the tennis ball is 60 grams

or

$v=u+at\\\Rightarrow a=\frac{v-u}{t}\\\Rightarrow a=\frac{45-0}{0.005}\\\Rightarrow a=9000\ m/s^2$

$F=ma\\\Rightarrow m=\frac{F}{a}\\\Rightarrow m=\frac{540}{9000}\\\Rightarrow m=60\ grams$

Answer 2

The mass of the ball (in grams) in which the racquet exerts a force of 540 N for 5 ms is 60 grams

Data obtained from the question

• Initial velocity (u) = 0 m/s
• Final velocity (v) = 45 m/s
• Time (t) = 5 ms = 5×10¯³ s
• Force (F) = 540 N

• Mass (m) =?

How to determine the mass of the ball

The mass of the ball can be obtained as follow:

F = m(v –u) / t

540 = m(45 – 0) / 5×10¯³

540 = m(45) / 5×10¯³

540 = 45m / 5×10¯³

Cross multiply

45m = 540 × 5×10¯³

Divide both side by 45

m = (540 × 5×10¯³) / 45

m = 0.06 Kg

Multiply by 1000 to express in Kg

m = 0.06 × 1000

m = 60 g

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