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?
The graph that best represents the relationship between potential energy and the mass and height of an object would be a linear equation, since the potential energy doubles when either the mass or the height is doubled.
One possible graph that represents this relationship is a linear graph with potential energy on the y-axis and either mass or height on the x-axis. The line on the graph would have a positive slope, indicating that potential energy increases with mass or height.
However, without the specific options provided, it is not possible to determine the best graph.
Based on the given information, let's analyze the relationship between potential energy and mass, as well as between potential energy and height.
1. Mass Relationship:
- When a 3 kg weight was lifted 2 meters, it had 58.8 Joules of potential energy.
- When a 6 kg weight was lifted 2 meters, its potential energy doubled.
From these observations, we can conclude that the potential energy is directly proportional to the mass when the height is constant.
2. Height Relationship:
- When a 2 kg weight was lifted 3 meters, it had 58.8 Joules of potential energy.
- When a 2 kg weight was lifted 6 meters, its potential energy doubled.
From these observations, we can conclude that the potential energy is directly proportional to the height when the mass is constant.
Based on the analysis above, we can conclude that the potential energy is directly proportional to both mass and height.
Considering this relationship, the graph that would best represent the relationship between potential energy and mass and height would show both variables on the axes. It would likely be a 3-dimensional graph with potential energy on the vertical axis, mass on one horizontal axis, and height on the other horizontal axis. With only the given options to consider, it is not possible to determine which graph would best represent this relationship without further information or visual representation of the options.
To determine which graph best represents the relationship between potential energy and the mass and height of an object, we need to analyze the given data and look for any patterns or trends.
From the height data, we can see that when the mass is fixed at 2 kg and the height is doubled from 3 meters to 6 meters, the potential energy also doubles. This indicates that the potential energy is directly proportional to the height when mass is constant.
Next, from the mass data, we can observe that when the height is fixed at 2 meters and the mass is doubled from 3 kg to 6 kg, the potential energy also doubles. This suggests that the potential energy is directly proportional to the mass when height is constant.
Based on these observations, we can conclude that potential energy is influenced by both mass and height, and it is directly proportional to both variables.
Therefore, the best graph that represents the relationship between potential energy and mass and height of an object would be a 2D scatter plot with potential energy on the y-axis and both mass and height on the x-axis. Each data point would represent a specific combination of mass and height, and a trend line or curve can be drawn to show the direct proportional relationship with both variables.