Question

When catching a fly-ball with your bare-hand during a baseball game, less damage to your hand occurs if you begin your catch with your hand extended toward the incoming ball so there's space to gradually pull your hand backward. In terms of impulse and momentum, explain why this is so.

Answer 1

Refer to the explanation below.

Step-by-step explanation:

When catching a fly ball with a bare hand, the goal is to reduce the force of the ball on the hand to prevent injury. This can be explained by the concepts of impulse and momentum.

Impulse is equal to the change in momentum of an object when a force is applied over time:

`\boxed{\left\begin{array}{ccc}\text{\underline{Impulse-Momentum Theorem:}}\\\\\vec I=\Delta\vec p =\vec F_(avg)\Delta t \\ \\ \text{Where:}\\\bullet \ \vec I \text{ represents the impulse}\\ \bullet \ \Delta \vec p \text{ represents the change in momentum}\\\bullet \ \vec F_(avg) \text{ represents the force applied}\\\bullet \ \Delta t\text{ represents the change in time}\end{array}\right}`

The momentum of the fly ball is its mass times its velocity as it moves towards your hand:

`\boxed{\left\begin{array}{ccc}\text{\underline{Momentum:}}\\\\\vec P=m\vec v\\\\\text{Where:}\\\bullet \ \vec P \ \text{is the momentum}\\\bullet \ m \ \text{represents the mass of the object}\\\bullet \ \vec v \ \text{represents the object's velocity}\end{array}\right}`

When the ball is caught, its momentum changes from this initial value to zero, as it comes to a stop in your hand.

If the ball is caught with the hand stationary and rigid, the time during which the stopping force acts is very short, and thus the force must be very large to stop the ball quickly. This large force is what can cause damage to the hand.

However, if you start with your hand extended and move it backward as you catch the ball, you increase the time over which the ball's momentum is brought to zero. According to the impulse-momentum theorem, impulse is the product of force and the time over which the force is applied. By increasing the time of contact during the catch, the average force exerted on the hand over the catch is reduced. This lower force results in less potential damage to your hand.

The backward motion of the hand effectively "cushions" the ball, spreading the ball's change in momentum over a longer period of time and reducing the peak force applied to the hand at any instant. This principle is why catching techniques in many sports involve moving the catching appendage backward at the moment of impact.