Final answer:
The correct answers are: a) 4.41 J, b) Increases, c) 7.35 m/s, which correspond to the work done by gravity on the ball, the increase in kinetic energy as it falls, and the velocity of the ball after falling 2.5 meters, respectively.
Step-by-step explanation:
The question is about determining the work done by gravity, changes in kinetic energy, and the final velocity of a falling ball using the principles of physics, specifically the work-energy theorem. To find these quantities, we use the formula for the work done by gravity (Work = force x displacement) and the principle of conservation of energy. The force of gravity is given by the weight of the object (mass times the acceleration due to gravity).
a) To find the work done by the force of gravity, we multiply the weight of the ball (mass times gravitational acceleration, 0.180 kg × 9.81 m/s²) by the displacement in the direction of the force (2.5 m). Therefore, the work done by gravity is Work = 0.180 kg × 9.81 m/s² × 2.5 m = 4.41 J. Since the force of gravity is doing the work, and the direction of the force is the same as the displacement, the sign is positive, confirming choice c) from the options.
b) Over the interval from rest until the ball hits the ground, the kinetic energy of the ball increases as its velocity increases due to acceleration by gravity. Initially, the ball has no kinetic energy, but as it falls, its kinetic energy increases, which corresponds to option d) for the kinetic energy change.
c) To determine the final velocity, we use the kinetic energy equation: Kinetic Energy (K) = 1/2 × mass × (velocity)². Since the kinetic energy is equal to the work done by gravity (assuming no other forces like air resistance are involved), we set them equal to each other and solve for the velocity:
1/2 × mass × (velocity)² = 4.41 J, from which we can calculate the velocity to be 7.35 m/s after falling 2.5 m, confirming option d).