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
A
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.
From the given 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.
From the given 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.
Based on this information, we can conclude that potential energy is directly proportional to height and mass.
Now, let's consider each option:
Option A:
- The graph shows potential energy increasing with both mass and height.
- This aligns with the given data and our conclusion that potential energy is directly proportional to mass and height.
Option B:
- The graph shows potential energy increasing only with mass and remaining constant with height.
- This does not align with the given data and our conclusion.
Option C:
- The graph shows potential energy increasing only with height and remaining constant with mass.
- This does not align with the given data and our conclusion.
Therefore, the graph that BEST represents the relationship between potential energy and the mass and height of an object is Option A.
To find the correct graph that represents the relationship between potential energy and mass and height, we can analyze the given information in the question.
First, let's consider the relationship between potential energy and height.
According to the data, when a 2 kg weight was lifted 3 meters above the floor, it had 58.8 Joules of potential energy. When the height was doubled to 6 meters, the potential energy also doubled. This indicates that the potential energy is directly proportional to the height.
Next, let's examine the relationship between potential energy and mass.
When a 3 kg weight was lifted 2 meters above the floor, it had 58.8 Joules of potential energy. When the mass was doubled to 6 kg, the potential energy also doubled. This shows that the potential energy is directly proportional to the mass.
Considering both relationships, we can conclude that potential energy is dependent on both mass and height. It is directly proportional to both the mass and the height.
Now, let's analyze the graphs A, B, and C to determine which one represents this relationship.
Graph A:
If we observe the graph A and compare the potential energy values at different heights and masses, we will see that they do not follow the described proportional relationship. The potential energy for different masses and heights does not increase in a consistent manner. Hence, Graph A is not the correct representation.
Graph B:
Upon analyzing the graph B, we can see that the potential energy values increase consistently as both the mass and height increase. This aligns with the proportional relationship described earlier. However, we need to compare it with Graph C to make a final decision.
Graph C:
When studying graph C, we can notice that the potential energy values increase in proportion to the mass and height. It follows the described pattern of direct proportionality for both variables.
Considering the explanations for each graph, we can conclude that **Graph C** BEST represents the relationship between potential energy and the mass and height of an object.