To determine the relationship between the potential energy of Gerald's toy truck and the total mass of the truck with weights, we can use the formula for gravitational potential energy (PE):
\[ \text{PE} = m \cdot g \cdot h \]
Where:
- \( m \) is the mass in kilograms,
- \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \)),
- \( h \) is the height in meters (in this case, 0.30 meters).
In this scenario, since the height \( h \) is constant at 0.30 meters and \( g \) is also a constant, the potential energy is directly proportional to the mass (\( m \)). Therefore, as Gerald adds more weight to the truck, the potential energy will increase linearly with mass.
This relationship can be represented in a graph as a straight line starting from the origin (0,0) with a positive slope. The x-axis would represent the mass of the truck (in kilograms) and the y-axis would represent the potential energy (in joules).
Based on this information, the graph that best shows the relationship between the potential energy of the truck at its starting position and the total mass of the weighted truck would be a straight line starting at the origin and increasing linearly.
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