The picture shows Gerald's toy truck, which he can fill with weights, and the track it will travel on.

Question

Gerald puts a weight in the truck and releases it from the starting position, at a height of 0.30 meters. He does this again for each of the weights, releasing the truck from the same position each time. He makes the chart below to keep track of each test.

Which of the following graphs best shows the relationship between the potential energy (in joules) of the truck at its starting position and the total mass (in kilograms) of the weighted truck?

A. A straight line going upwards, the x axis says Mass (kg) while the y axis says Potential Energy (J).

B. A curve going upward yet gets steep, the axis stays the same.

C. A straight line going downward, the axis stays the same.

D. A curve going upward but is less steep than the previous, the axis stays the same.

Answer 1

The potential energy (PE) of an object can be calculated using the formula:

\[ PE = m \cdot g \cdot h \]

where:

• \( PE \) is the potential energy in joules,
• \( m \) is the mass in kilograms,
• \( g \) is the acceleration due to gravity (approximately \( 9.81 , m/s^2 \)),
• \( h \) is the height in meters.

In this case, Gerald is placing weights in the truck and releasing it from the same height (0.30 meters). As he adds more mass, the potential energy will increase linearly with mass, since both \( g \) and \( h \) remain constant.

Therefore, the graph that best represents the relationship between potential energy and total mass would be a straight line going upwards, indicating that potential energy increases proportionally with mass.

The answer is:

A. A straight line going upwards, the x axis says Mass (kg) while the y axis says Potential Energy (J).