Question

A ball of mass 500 g has 800 J of total energy at a height of 10 m. Assuming no energy loss, how much energy does it possess at a height of 5 m?

• A. 200 J
• B. 400 J
• C. 600 J
• D. 800 J

Answer 1

Answer:

D. 800 J

To solve this problem, we'll use the concept of conservation of energy.

Initial total energy (E1) = 800 J

At the initial height of 10 m, the ball's potential energy (PE1) is:

PE1 = m × g × h1
= 0.5 kg × 9.8 m/s² × 10 m
= 49 J

The remaining energy is kinetic energy (KE1), which is:

KE1 = E1 - PE1
= 800 J - 49 J
= 751 J

Now, at the height of 5 m, the potential energy (PE2) is:

PE2 = m × g × h2
= 0.5 kg × 9.8 m/s² × 5 m
= 24.5 J

Since energy is conserved, the total energy (E2) at the new height is still 800 J. The kinetic energy (KE2) at the new height is:

KE2 = E2 - PE2
= 800 J - 24.5 J
= 775.5 J

However, we were asked about the total energy at the new height, not the kinetic energy. The correct answer is:

The ball still possesses 800 J of total energy at a height of 5 m.