Question
A student drops six different objects.
object mass (kg) hight (m) potential energy (j)
1 10 5 490
2 10 10 980
3 10 15 1,470
4 20 10 1,960
5 30 10 2,940
6 40 10 3,920
show TWO line graphs are correct according to the table of results?
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.
To determine which two line graphs are correct according to the table of results, we need to plot the data points and analyze the trends. Let's plot the data points for each object's potential energy against its height:
Graph 1:
x-axis: Height (m)
y-axis: Potential Energy (J)
Data Points:
Object 1: (5, 490)
Object 2: (10, 980)
Object 3: (15, 1470)
Object 4: (10, 1960)
Object 5: (10, 2940)
Object 6: (10, 3920)
Graph 2:
x-axis: Height (m)
y-axis: Potential Energy (J)
Data Points:
Object 1: (5, 490)
Object 2: (10, 980)
Object 3: (15, 1470)
Object 4: (10, 1960)
Object 5: (10, 2940)
Object 6: (10, 3920)
Now let's analyze the trends in each graph:
Graph 1:
In this graph, the potential energy increases as the height increases for objects 1, 2, and 3. However, for objects 4, 5, and 6, the potential energy remains constant at different heights. This means that the potential energy is not directly proportional to the height for these objects.
Graph 2:
In this graph, the potential energy increases as the height increases for all objects. This means that the potential energy is directly proportional to the height for all objects.
Based on our analysis, Graph 2 is the correct representation of the relationship between potential energy and height for all objects. Therefore, Graph 2 is definitely correct. However, Graph 1 is incorrect as it does not accurately represent the relationship between potential energy and height for objects 4, 5, and 6.