Question

determining potential energy
complete these sentences.
if a bouncing ball has a total energy of 20 j and a kinetic energy of 5 j, the ball’s potential energy is ◊ j.
if the kinetic energy of the ball decreases, then the potential energy will ◊ .

Explanation:

First Sentence:

Step1: Recall total energy formula

The total mechanical energy \( E_{total} \) of a system is the sum of its kinetic energy \( E_k \) and potential energy \( E_p \), so \( E_{total}=E_k + E_p \).

Step2: Solve for potential energy

We know \( E_{total} = 20\space J \) and \( E_k = 5\space J \). Rearranging the formula to solve for \( E_p \), we get \( E_p=E_{total}-E_k \). Substituting the values, \( E_p = 20 - 5=15\space J \).

Second Sentence:

For a bouncing ball (assuming no non - conservative forces like air resistance are doing significant work), the total mechanical energy remains constant (law of conservation of mechanical energy). So if the kinetic energy (\( E_k \)) decreases, since \( E_{total}=E_k + E_p \) and \( E_{total} \) is constant, the potential energy (\( E_p \)) must increase to keep the sum constant.

Answer:

First blank: \( 15 \)
Second blank: increase