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A pupil used the apparatus shown in the diagram to investigate the relationship between the force applied and the extension produced in the spring by that force - Junior Cycle Science - Question a - 2010
Question a
A pupil used the apparatus shown in the diagram to investigate the relationship between the force applied and the extension produced in the spring by that force. Poi... show full transcript
Worked Solution & Example Answer:A pupil used the apparatus shown in the diagram to investigate the relationship between the force applied and the extension produced in the spring by that force - Junior Cycle Science - Question a - 2010
Step 1
Calculate the total extension for each force
Answer
To calculate the total extension for each force, we take the difference between the scale reading and the initial position of the pointer (31.0 cm). Therefore:
- For 0 N: Total extension = 31.0 cm - 31.0 cm = 0 cm
- For 2 N: Total extension = 35.0 cm - 31.0 cm = 4 cm
- For 4 N: Total extension = 39.0 cm - 31.0 cm = 8 cm
- For 6 N: Total extension = 43.0 cm - 31.0 cm = 12 cm
- For 8 N: Total extension = 47.0 cm - 31.0 cm = 16 cm
- For 10 N: Total extension = 51.0 cm - 31.0 cm = 20 cm
Thus, the total extension values are:
| Force (N) | Total extension (cm) |
|---|---|
| 0 | 0 |
| 2 | 4 |
| 4 | 8 |
| 6 | 12 |
| 8 | 16 |
| 10 | 20 |
Step 2
Draw a graph of force against total extension
Answer
Plotting the graph involves marking the total extension on the x-axis and the corresponding force on the y-axis. Each pair of values from the table can be plotted as points, and a straight line can be drawn through them to show the relationship. The points would typically include:
- (0, 0)
- (4, 2)
- (8, 4)
- (12, 6)
- (16, 8)
- (20, 10)
Once plotted accurately, ensure that the line extends in both directions, ideally starting from the origin.
Step 3
What conclusion can be drawn from the graph regarding the relationship between the force applied to the spring and the extension produced by it?
Answer
The graph clearly illustrates that the extension produced in the spring is directly proportional to the applied force. As the force increases, the total extension increases uniformly, indicating a linear relationship. This suggests that for a given spring, the more force applied, the greater the extension observed, which is consistent with Hooke's Law.
Step 4
Use the graph to determine the weight of a stone that produced an extension of 14 cm in the spring.
Answer
To find the weight of the stone that caused an extension of 14 cm, locate 14 cm on the x-axis of the graph and draw a vertical line upwards until it intersects with the plotted line. Read the corresponding force value on the y-axis. Based on the linear trend observed in the graph, an extension of 14 cm approximately correlates to a force of around 7 N, as verified by the slope of the line.