To determine the relationship between potential energy (PE), mass (m), and height (h), we can use the formula for gravitational potential energy:
\[ PE = mgh \]
where \( g \) is the acceleration due to gravity (approximately \( 9.8 , \text{m/s}^2 \)).
From the provided data:
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For the 2 kg weight:
- At a height of 3 meters: \[ PE = 2 \times 9.8 \times 3 = 58.8 , \text{Joules} \]
- At a height of 6 meters, its potential energy doubles: \[ PE_{6m} = 2 \times 9.8 \times 6 = 117.6 , \text{Joules} \]
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For the 3 kg weight:
- At a height of 2 meters: \[ PE = 3 \times 9.8 \times 2 = 58.8 , \text{Joules} \]
- For the 6 kg weight lifted to 2 meters, the potential energy doubles: \[ PE_{3kg} = 6 \times 9.8 \times 2 = 117.6 , \text{Joules} \]
Thus, from the data, we observe that:
- Doubling the height \( (3m \to 6m) \) for a constant mass results in the potential energy also doubling.
- Doubling the mass \( (3kg \to 6kg) \) while keeping the height constant also doubles the potential energy.
This clearly shows a linear relationship between both mass and height with potential energy.
In terms of graph representation:
- Potential energy should be on the y-axis.
- Mass can be on one x-axis, while height can be on another axis, potentially showing two lines indicating that both variables have a direct positive linear relation to potential energy.
To visualize this accurately, look for a graph with linear slopes indicating these dependencies, such as lines increasing steeply for increased height or mass.
Therefore, the graph that best represents the relationship between potential energy, mass, and height would be one that shows this linear relationship growing with both increasing mass and height. However, since there is insufficient detail on the available graph options, look for any option that indicates a positive slope curving upwards consistently with both x-axes showing mass and height.
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