Question

a player hits a billiard ball of mass 500 g by an impluse of 100N/s find the speed attained by the ball and the average force applied on the ball if the time of impact was 6 ms​

Answer 1

Given :

Mass of the ball = 500g = 0.5 kg

Impluse = 100 N/s

Initial velocity = zero.

Time taken = 5 ms = 5 × 10¯³ s

To Find :

The speed attained by the ball and the average force applied on the ball if the time of impact was 6 ms

Solution :

We know that the Impluse is equal to the change of mementum that is,

$\sf I = \Delta P = mv_f - mv_i$

by substituting the values in the formula,

$\dashrightarrow \sf I = mv_f - mv_i$

$\dashrightarrow \sf 100 = (0.5)(v_f) - (0.5)(0)$

$\dashrightarrow \sf 100 = 0.5v_f$

$\dashrightarrow \sf v_f = \dfrac{100}{0.5}$

$\dashrightarrow \sf v_f = 200 \: {ms}^{ - 1}$

Thus, the speed attained by the ball is 200 m/s.

we know that,

$\sf Average \: force = \dfrac{I}{t}$

Bu substituting the values,

$\dashrightarrow \sf F_{avg}= \dfrac{I}{t}$

$\dashrightarrow \sf F_{avg}= \dfrac{100}{5 \times {10}^{ - 3} }$

$\dashrightarrow \sf F_{avg}= \dfrac{20}{ {10}^{ - 3} }$

$\dashrightarrow \sf F_{avg}= 20 \times {10}^{3}$

$\dashrightarrow \sf F_{avg}= 20000 \: N$

Thus, the average force of the ball is 20,000 N.