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

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

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