Question

During a game the same batter swings at a ball thrown by the pitcher and hits a line drive. Just before the ball is hit it is traveling at a speed of 20.0 m/sm/s, and just after it is hit it is traveling in the opposite direction at a speed of 30.0 m/sm/s. What is the total work done on the baseball by the force exerted by the bat

Answer 1

Answer:

The total work done on the baseball by the bat is 36.25 J.

Explanation:

The mass of the baseball is missing which is equal to 0.145 kg.

Given:

Mass of the baseball (m) = 0.145 kg

Initial speed of the baseball (v₁) = 20.0 m/s

Final speed of the baseball (v₂) = 30.0 m/s

Total work done on the baseball by the force exerted by the bat is given using the work-energy theorem which states that the total work done is equal to the change in the kinetic energy of the baseball.

Kinetic energy of a body of mass 'm' and speed 'v' is given as:

$KE=\frac{1}{2}mv^2$

Therefore, the work done on the baseball is given as:

$Work=\Delta KE\\\\Work=\frac{1}{2}m(v_2^2-v_1^2)\\\\Work=\frac{1}{2}\times (0.145\ kg)((30.0\ m/s)^2-(20.0\ m/s)^2)\\\\Work=(0.0725)(900-400)\ kg.m^2/s^2\\\\Work=0.0725\times 500=36.25\ J$

Therefore, the total work done on the baseball by the bat is 36.25 J.