Question

the following graph models the child-earth system’s kinetic energy (k) and gravitational potential energy (u_g) when the child is at the position shown in the image.
bar graph with k (400 j) and u_g (100 j)
which graph could represent the energy of the child-earth system when the child reaches the surface of the water?
assume frictional forces are small enough to ignore.
choose 1 answer.

Explanation:

Step1: Recall Energy Conservation

In a system with negligible friction, mechanical energy (sum of kinetic \( K \) and gravitational potential \( U_g \)) is conserved. So total energy \( E = K + U_g \) remains constant.

Step2: Calculate Initial Total Energy

From the graph, initial \( K = 400 \, \text{J} \), initial \( U_g = 100 \, \text{J} \). Total energy \( E = 400 + 100 = 500 \, \text{J} \).

Step3: Analyze Final Energy

When the child reaches the water, gravitational potential energy \( U_g \) decreases (height lowers), so kinetic energy \( K \) must increase such that \( K + U_g = 500 \, \text{J} \). For example, if \( U_g \) becomes \( 0 \, \text{J} \) (at water surface, assuming reference), \( K = 500 \, \text{J} \), but generally, the sum remains \( 500 \, \text{J} \), with \( U_g \) less than initial \( 100 \, \text{J} \) (if moving down) and \( K \) more than initial \( 400 \, \text{J} \), or adjusted such that their sum is \( 500 \, \text{J} \).

Answer:

The graph should show \( K + U_g = 500 \, \text{J} \) (e.g., \( K \) increased, \( U_g \) decreased, but total remains 500 J). A correct graph would have \( K + U_g = 500 \, \text{J} \), so if \( U_g \) is, say, \( 0 \), \( K = 500 \); or \( U_g = 50 \), \( K = 450 \), etc., as long as their sum is 500.