Question

alan launches a ball of clay into the air using a catapult. he calculates its kinetic energy to be 9.0 j. then he tears it in half and forms a ball that has half the mass. he launches the smaller ball into the air at the same speed. what is the kinetic energy of the smaller ball?
○ 3.0 j
○ 9.0 j
○ 4.5 j
○ 18.0 j

a student stretches a rubber band and then releases it. what happens to the potential energy stored in the system?
○ it increases as the rubber band snaps back
○ it remains constant throughout the motion
○ it converts to kinetic energy as the rubber band moves
○ it disappears completely

Explanation:

First Question (Kinetic Energy of the Smaller Ball)

Step1: Recall Kinetic Energy Formula

The formula for kinetic energy is $KE = \frac{1}{2}mv^2$, where $m$ is mass and $v$ is speed.

Step2: Analyze Initial and Final Mass

Initially, $KE_1=\frac{1}{2}m_1v_1^2 = 9.0\ J$. After tearing, $m_2=\frac{1}{2}m_1$ and $v_2 = v_1$ (same speed).

Step3: Calculate New Kinetic Energy

Substitute $m_2$ into the formula: $KE_2=\frac{1}{2}m_2v_2^2=\frac{1}{2}(\frac{1}{2}m_1)v_1^2=\frac{1}{2}(\frac{1}{2}m_1v_1^2\times2)$? Wait, no. Wait, $KE_1=\frac{1}{2}m_1v_1^2$, so $KE_2=\frac{1}{2}(\frac{m_1}{2})v_1^2=\frac{1}{2}(\frac{1}{2}m_1v_1^2)=\frac{1}{2}KE_1$. Since $KE_1 = 9.0\ J$, then $KE_2=\frac{9.0}{2}=4.5\ J$.

When a rubber band is stretched, it has elastic potential energy. When released, the potential energy is converted into kinetic energy as the rubber band moves (snaps back). Energy is conserved, so it doesn't increase, remain constant, or disappear.

Answer:

4.5 J (Option: 4.5 J)

Second Question (Potential Energy of Stretched Rubber Band)