8. The 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?
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1 point
A
B
C
D
Without the option of seeing the graphs and their corresponding representations, it is not possible to determine which graph BEST represents the relationship between potential energy and the mass and height of an object.
8. The 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.
what would the graph for this look llike
Based on the given data, we can make the following observations:
1. When the height is doubled (from 3 meters to 6 meters) for a 2 kg weight, the potential energy doubles.
2. When the mass is doubled (from 3 kg to 6 kg) for a 2 meters height, the potential energy doubles.
From these observations, we can infer that potential energy is directly proportional to both mass and height.
Therefore, the graph representing the relationship between potential energy and mass and height of an object would show a linear relationship with both variables. As mass and height increase, potential energy will also increase. The graph would start at the origin (0,0) and have a positive slope.
To determine the best graph that represents the relationship between potential energy and the mass and height of an object, we need to analyze the given data.
From the height data, we can see that when the height was increased from 3 meters to 6 meters, the potential energy doubled. This means that there is a linear relationship between height and potential energy.
From the mass data, we can see that when the mass was doubled from 3 kg to 6 kg, the potential energy also doubled. This suggests that there is a linear relationship between mass and potential energy as well.
Based on these observations, we can conclude that both height and mass have a direct and linear relationship with potential energy. We can therefore eliminate graphs that do not show any direct or linear relationship.
To further clarify, let's refer to the given graphs:
A: This graph shows a curved relationship between mass and potential energy, which does not match the linear relationship observed in the data. We can eliminate this option.
B: This graph shows a direct and linear relationship between both mass and height with potential energy. It accurately represents the information provided in the data, and thus, is a strong candidate.
C: This graph shows an inverse relationship between mass and potential energy, which contradicts the data. We can eliminate this option.
D: This graph shows a linear relationship between height and potential energy, but an inverse relationship between mass and potential energy. This is inconsistent with the data. We can eliminate this option.
Therefore, the best graph that represents the relationship between potential energy and the mass and height of an object is option B.