To determine which two line graphs are correct according to the table of results, we need to analyze the relationship between the variables: mass, height, and potential energy.
Line graph 1: Potential Energy vs. Mass
In this graph, we plot the potential energy on the y-axis and mass on the x-axis.
Line graph 2: Potential Energy vs. Height
In this graph, we plot the potential energy on the y-axis and height on the x-axis.
Now, let's compare the values in the table and determine which line graphs accurately represent the relationship between the variables.
From the table:
For object 1:
Mass = 10 kg
Height = 5 m
Potential Energy = 490 J
For object 2:
Mass = 10 kg
Height = 10 m
Potential Energy = 980 J
For object 3:
Mass = 10 kg
Height = 15 m
Potential Energy = 1,470 J
For object 4:
Mass = 20 kg
Height = 10 m
Potential Energy = 1,960 J
For object 5:
Mass = 30 kg
Height = 10 m
Potential Energy = 2,940 J
For object 6:
Mass = 40 kg
Height = 10 m
Potential Energy = 3,920 J
Based on these values:
In line graph 1, as mass increases, potential energy increases. This is shown by object 1 having a lower potential energy (490 J) compared to object 2 (980 J). However, object 2 has the same mass as object 1, but its potential energy is higher.
In line graph 2, as height increases, potential energy increases. This is shown by object 1 having a lower potential energy (490 J) compared to object 3 (1,470 J). However, object 3 has the same height as object 1, but its potential energy is higher.
Therefore, both line graphs accurately represent the relationship between the variables according to the table of results.