solve for the amount of force exerted on an 8-kg ball rolling at 2m/s when it bumps into a pillow and stops in 0.5s. how mush force does the pillow exert on the ball?
To solve for the amount of force exerted on the ball, we can use Newton's second law of motion, which states that force (F) equals mass (m) multiplied by acceleration (a). In this case, since the ball stops moving, the acceleration can be calculated using the formula:
a = (final velocity - initial velocity) / time
Given:
Mass of the ball (m) = 8 kg
Initial velocity (u) = 2 m/s
Final velocity (v) = 0 m/s (since the ball stops)
Time taken (t) = 0.5 s
First, we calculate the acceleration (a):
a = (v - u) / t
a = (0 - 2) / 0.5
a = -2 / 0.5
a = -4 m/s^2 (negative sign indicates deceleration)
Next, we can calculate the force exerted on the ball using Newton's second law:
F = m * a
F = 8 kg * (-4 m/s^2)
F = -32 N
The force exerted on the ball is -32 Newtons. The negative sign indicates that the force opposes the motion of the ball.
Now, to find the force exerted by the pillow on the ball, we need to consider Newton's third law of motion, which states that every action has an equal and opposite reaction. Therefore, the force exerted by the ball on the pillow must be equal in magnitude but opposite in direction to the force exerted by the pillow on the ball.
Hence, the force exerted by the pillow on the ball is +32 Newtons. The positive sign indicates that the force is acting in the opposite direction of the ball's motion.