As you catch a 0.14-kg ball it accelerates at -320 m/s^2 and comes to rest in your hand.

Описание: As you catch a 0.14-kg ball it accelerates at -320 m/s^2 and comes to rest in your hand. What force does the ball exert on your hand?

Problem:
As you catch a 0.14-kg ball, it accelerates at -320 m/s² and comes to rest in your hand. What force does the ball exert on your hand?

Step 1: Identify the forces involved
Mass of the ball (m):
m = 0.14 kg

Acceleration of the ball (a):
a = -320 m/s² (negative because the ball is decelerating)

Step 2: Use Newton's second law to find the force exerted on the ball
Newton's second law states that the force is equal to the mass times the acceleration:

\[
F = m * a
\]

Substitute the known values:

\[
F = 0.14 \, \text{kg} * (-320 \, \text{m/s}^2)
\]

\[
F = -44.8 \, \text{N}
\]

The negative sign indicates that the force exerted on the ball is in the opposite direction of its motion (i.e., the force exerted by the hand is upward while the ball was falling downward).

Step 3: Determine the force the ball exerts on the hand
By Newton’s third law, the force the ball exerts on your hand is equal in magnitude but opposite in direction to the force the hand exerts on the ball. Therefore, the force the ball exerts on your hand is *44.8 N* in the downward direction.

Answer:
The force the ball exerts on your hand is *44.8 N* downward