To evaluate which two line graphs would be correct according to the provided table of results, we need to analyze how potential energy (PE) changes with respect to mass and height.
Potential energy can be calculated using the formula:
\[ \text{PE} = mgh \]
where \( m \) is mass (in kg), \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \)), and \( h \) is height (in m).
From the table provided, the potential energy is already given for different combinations of mass and height:
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As the height increases (keeping mass constant at 10 kg), potential energy increases:
- From height 5 m to 10 m (PE increases from 490 J to 980 J)
- From height 10 m to 15 m (PE increases from 980 J to 1,470 J)
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As the mass increases (keeping height constant at 10 m), potential energy also increases:
- From 10 kg to 20 kg (PE increases from 980 J to 1,960 J)
- From 20 kg to 30 kg (PE increases from 1,960 J to 2,940 J)
- From 30 kg to 40 kg (PE increases from 2,940 J to 3,920 J)
Therefore, potential energy increases with both an increase in height and mass.
Two correct line graphs would show:
- A line graph showing potential energy vs. height, with points representing heights 5 m, 10 m, and 15 m, showing an upward trend.
- A line graph showing potential energy vs. mass, with points representing masses 10 kg, 20 kg, 30 kg, and 40 kg, also showing an upward trend.
You can choose line graphs that illustrate these relationships for your response. If specific graphical options were provided to visualize, you would select the ones showing positive linear relationships for both scenarios.
1 answer