When catching a baseball, a catcher's glove moves by 11 cm along the line of motion of the ball. If the baseball exerts a force of 407 N on the glove, how much work is done by the ball?
Use this equation that you should already know:
Force x Distance = Work
The distance must be in meters if you want the work to be in Joules (N-m).
To find the work done by the ball, we can use the formula:
Work = Force × Distance × cosθ
Where:
- Force is the amount of force exerted by the ball on the glove (407 N).
- Distance is the distance the glove moves in the direction of the force (11 cm).
- θ is the angle between the force vector and the direction of motion (which is 0 degrees since the glove moves along the line of motion of the ball).
Now, let's plug in the values into the formula:
Work = 407 N × 11 cm × cos(0°)
Before we continue, we need to convert the distance from centimeters to meters and the angle from degrees to radians:
1 cm = 0.01 m (conversion factor)
θ = 0° × π/180° ≈ 0 radians
Work = 407 N × 0.11 m × cos(0 radians)
Since cos(0 radians) = 1, this simplifies to:
Work = 407 N × 0.11 m × 1
Finally, we can calculate the work:
Work = 44.77 Joules
Therefore, the work done by the ball is approximately 44.77 Joules.