Based on the data in the table, we can analyze the relationships between mass, height, and potential energy in order to suggest two types of graphs.
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Potential Energy vs. Height for Constant Mass: We can plot potential energy on the y-axis and height on the x-axis for a constant mass (e.g., the objects with a mass of 10 kg). This will show a direct relationship between height and potential energy. The graph will be a linear function because potential energy (PE) is calculated using the formula: \[ PE = m \cdot g \cdot h \] where \( m \) is mass, \( g \) is acceleration due to gravity (approximately \( 9.8 , m/s^2 \)), and \( h \) is height.
For object 1, object 2, and object 3 (all of mass 10 kg), we have the following data points:
- (5, 490)
- (10, 980)
- (15, 1470)
The graph will show that as height increases, potential energy increases linearly.
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Potential Energy vs. Mass for Constant Height: Another graph can show potential energy on the y-axis and mass on the x-axis for a constant height (e.g., all objects dropped from 10 m). This will also be a linear relationship as potential energy depends directly on both mass and height.
We can plot this using object 2, object 4, and object 5, which are at a height of 10 m:
- Object 2: (10 kg, 980 J)
- Object 4: (20 kg, 1960 J)
- Object 5: (30 kg, 2940 J)
The graph will show that as mass increases, potential energy increases linearly.
In summary, the two types of graphs that can be supported by the data are:
- A graph of Potential Energy vs. Height for constant mass (e.g., 10 kg).
- A graph of Potential Energy vs. Mass for constant height (e.g., 10 m).