Question

a student is trying to find the mass of a billiard ball while playing pool. the ball is moving at a velocity of 2.3m/s and has a kinetic energy of 0.45j. the students work is shown below; what did they do wrong? they forgot to square the velocity \\( \frac { ( 2.45 ) } { ( 2.3 ) } \\) what is the answer to the problem?

Explanation:

Step1: Recall the kinetic energy formula

The formula for kinetic energy is \( KE=\frac{1}{2}mv^{2} \), where \( KE\) is kinetic energy, \( m\) is mass, and \( v\) is velocity. We need to solve for \( m\), so we can rewrite the formula as \( m = \frac{2KE}{v^{2}}\).

Step2: Substitute the given values

Given \( KE = 0.45\space J\) and \( v=2.3\space m/s\). First, square the velocity: \( v^{2}=(2.3)^{2}=5.29\). Then substitute into the formula for \( m\): \( m=\frac{2\times0.45}{5.29}\).

Step3: Calculate the mass

\( 2\times0.45 = 0.9\). Then \( m=\frac{0.9}{5.29}\approx0.17\space kg\)

Answer:

\(0.17\space kg\)