Question

A ball with a mass of 0.25 kg hits a gym ceiling with a force of 78.0 n. what happens next?

a. the ball accelerates downward with a force of 80.5 n.
b. the ball accelerates downward with a force of 78.0 n.
c. the ball accelerates downward with a force of 2.45 n.
d. it depends on the height of the ceiling.

Answer 1

After the ball hits the ceiling with a force of 78.0 N, it experiences a net force of 75.5 N downward due to the impact force minus its weight, causing it to accelerate downward.

Step-by-step explanation:

When a ball with a mass of 0.25 kg hits the gym ceiling with a force of 78.0 N, the force exerted on the ceiling by the ball is equal and opposite to the force exerted on the ball by the ceiling, according to Newton's third law of motion. Right after the impact, the ball will experience a net force in the downward direction which will cause it to accelerate downward. This net force can be calculated by subtracting the weight of the ball from the applied force. The weight of the ball, which is the force due to gravity, is the mass of the ball times the acceleration due to gravity (0.25 kg * 9.8 m/s² = 2.45 N). Thus, the net force on the ball after hitting the ceiling would be 78.0 N - 2.45 N = 75.5 N downward. Therefore, the correct answer to what happens to the ball next is that it accelerates downward with a force of 75.5 N.

Answer 2

a. The ball accelerates downward with a force of 80.5 N. This is a rather badly worded question since the answer depends upon whether or not the impact with the gym ceiling was elastic or non-elastic. With an elastic collision, the ball will accelerate downward with it's original force plus the acceleration due to gravity. With a non-elastic collision (the energy in the ball being used to damage the ceiling of the gym), then the initial energy the ball has would be expended while causing damage to the gym ceiling and then the ball would accelerate downward solely due to the force of gravity. In either case, we need to take into consideration the force of gravity. So multiply the mass of the ball by the gravitational acceleration, giving F = 0.25 kg * 9.8 m/s^2 = 2.45 kg*m/s^2 = 2.45 N Since the initial force is 78.0 newtons, let's add them 78.0 N + 2.45 N = 80.45 N and after rounding to 3 figures, gives 80.5 N So we have a possible answer of 2.45N or 80.5N depending upon if the collision is elastic or not. And unfortunately, both possible answers are available. Since no mention of the ceiling being damaged is made in the question, and to be honest a 100% non-elastic collision is highly unlikely, I will assume the collision is elastic, so the answer is "a".