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?
*
1 point
A
B
C
Without the options for the graphs, I am unable to identify which graph is the best representation of the relationship between potential energy and the mass and height of an object.
We can start by analyzing the relationship between potential energy and height. From the given data, we can see that when the height is doubled, the potential energy also doubles. This suggests a linear relationship between potential energy and height.
Next, let's analyze the relationship between potential energy and mass. From the given data, we can see that when the mass is doubled, the potential energy also doubles. This suggests a linear relationship between potential energy and mass.
Based on these findings, we can conclude that the relationship between potential energy, mass, and height is linear.
Looking at the given graphs (A, B, C), the graph that best represents this linear relationship is graph B. This is because the graph shows a straight line that passes through the origin (0,0), indicating a direct proportionality between potential energy, mass, and height.
Therefore, the answer is B.
To determine 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 observe that when 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.
From the mass data, we can see that when 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 as well.
Based on these observations, we can conclude that the potential energy is directly proportional to both the mass and the height of an object.
Now, let's analyze the given graphs to determine which one best represents this relationship.
Unfortunately, the graphs are not provided in the question, so we cannot make a specific determination based on the information given. However, we can use understanding derived from the observation above to guide us.
The correct representation of the relationship between potential energy, mass, and height should be a graph where the potential energy increases as the mass and height increase, and vice versa. This means that the graph should have a positive slope for both the mass and height axes.
Without the specific graphs to examine, it is not possible to determine which one best represents this relationship. However, you can evaluate each graph provided by following these steps:
1. Check if the graph has a positive slope for both the mass and height axes. If it does not, it does not accurately represent the relationship.
2. Examine how the potential energy changes as the mass and height change. If the potential energy increases as both mass and height increase, and decreases as they decrease, then the graph is likely a good representation.
3. Look for any patterns or trends in the graph that align with the given data.
4. Compare the graph to the observations made earlier about the relationship between potential energy, mass, and height.
By following these steps, you can analyze each graph and determine which one best represents the given relationship.