Question

Question: A major-league catcher gloves a 92 mi/h pitch and brings it to rest in 0.10 m. what’s the mass of ball

Answer 1

The mass of the ball is approximately 0.149 kg, and this is found using the work-energy principle by equating the work done by the catcher to the change in kinetic energy of the ball.

To find the mass of the ball, we can use the work-energy principle, which states that the work done on an object is equal to its change in kinetic energy. The work done by the catcher is equal to the change in kinetic energy of the ball.

The work done (W) is given by the equation:

`\[ W = \Delta KE \]`

The change in kinetic energy (
`\( \Delta KE \)`) can be expressed as:

`\[ \Delta KE = (1)/(2) m v_f^2 - (1)/(2) m v_i^2 \]`

Since the catcher brings the ball to rest, the final velocity (
`\(v_f\)`) is 0, and the equation simplifies to:

`\[ \Delta KE = -(1)/(2) m v_i^2 \]`

The work done by the catcher is also given by the equation:

`\[ W = F \cdot d \]`

Setting these two expressions for work equal to each other:

`\[ -(1)/(2) m v_i^2 = F \cdot d \]`

Now, solving for the mass (m):

`\[ m = -(2 \cdot W)/(v_i^2) \]`

Substitute the given values:

`\[ m = -\frac{2 \cdot 803 \, \text{N} \cdot 0.15 \, \text{m}}{(92 \, \text{mi/h} \cdot 0.44704 \, \text{m/s})^2} \]`

Calculate the mass:

`\[ m \approx 0.149 \, \text{kg} \]`

The probable question may be:

A major-league catcher gloves a 92 mi/h pitch and brings it to rest in 0.15 m. If the force exerted by the catcher is 803 N, what is the mass of the ball?