he data below was recorded during an investigation of the relationship between potential energy and the mass and height of an object.
Height Data
When a 2 kg weight was lifted 3 meters above the floor, it had 58.8 Joules of potential energy.When a 2 kg weight was lifted 6 meters above the floor, its potential energy doubled.
Mass Data
When a 3 kg weight was lifted 2 meters above the floor, it had 58.8 Joules of potential energy.When a 6 kg weight was lifted 2 meters above the floor, its potential energy doubled.
Which of the following graphs BEST represents the relationship between potential energy and the mass and height of an object?
*
1 point
A
B
C
D
The correct answer cannot be determined without the options for the graphs A, B, C, and D. Please include the options for a more accurate response.
To determine the best graph that represents the relationship between potential energy and mass and height, let's analyze the given data.
From the height data, we can see that when the mass is constant at 2 kg, the potential energy increases from 58.8 Joules when the height is 3 meters, to double that value (117.6 Joules) when the height is doubled to 6 meters. This indicates that the potential energy is directly proportional to the height when the mass is constant.
Likewise, from the mass data, we can observe that when the height is constant at 2 meters, the potential energy remains constant at 58.8 Joules regardless of the mass. However, when the mass is doubled from 3 kg to 6 kg, the potential energy also doubles to 117.6 Joules. This implies that the potential energy is directly proportional to the mass when the height is kept constant.
Based on this analysis, we can conclude that the relationship between potential energy, mass, and height can be explained by two independent factors: potential energy is directly proportional to the height when the mass is constant, and potential energy is directly proportional to the mass when the height is constant.
Now, let's evaluate the given graphs (A, B, C, and D) to find the one that represents these relationships accurately:
- Graph A accurately shows a linear relationship between potential energy and height when the mass is constant. However, it does not show any relationship between potential energy and mass when the height is constant, so it does not represent the given data adequately.
- Graph B represents the given data accurately. It shows a linear relationship between potential energy and height when the mass is constant (as the height increases, the potential energy also increases proportionally). Additionally, it shows no relationship between potential energy and mass when the height is constant (the potential energy remains constant).
- Graph C shows a linear relationship between potential energy and mass when the height is constant (doubling the mass doubles the potential energy). However, it does not represent the relationship between potential energy and height accurately when the mass is constant, as the potential energy remains constant regardless of the height.
- Graph D does not represent the given data accurately. It shows a linear relationship between potential energy and height when the mass is constant, which is correct. However, it does not show any relationship between potential energy and mass when the height is constant, so it does not represent the given data adequately.
Therefore, the graph that BEST represents the relationship between potential energy and mass and height of an object is B.
To determine which graph best represents the relationship between potential energy and the mass and height of an object, we can analyze the given data.
From the height data, we can observe that when the height is doubled, the potential energy also doubles while keeping the mass constant (2 kg weight). This indicates that potential energy varies directly with the height. Therefore, the graph should be a linear relationship with an upward slope.
From the mass data, we can observe that when the mass is doubled, the potential energy also doubles while keeping the height constant (2 meters). This indicates that potential energy varies directly with the mass. Therefore, the graph should be a linear relationship with an upward slope.
Considering both pieces of information, the graph that represents the relationship between potential energy and the mass and height of an object would be graph C.