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In an experiment to investigate the relationship between the acceleration of a body and the force applied to it, a student recorded the following data - Leaving Cert Physics - Question 1 - 2010
Question 1
In an experiment to investigate the relationship between the acceleration of a body and the force applied to it, a student recorded the following data. | F/N | 0.20... show full transcript
Worked Solution & Example Answer:In an experiment to investigate the relationship between the acceleration of a body and the force applied to it, a student recorded the following data - Leaving Cert Physics - Question 1 - 2010
Step 1
Describe the steps involved in measuring the acceleration of the body.
Answer
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Measure the initial velocity: Start by calculating the initial velocity of the object or trolley using a motion sensor or similar apparatus.
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Calculate the velocity/speed: Measure the velocity or speed again after a specified time interval t (e.g., 1 second later).
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Determine time intervals: Calculate the time interval from the initial to final velocities by using the distance between light gates divided by the time taken.
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Apply the relevant formula: Use the kinematic equation, such as the following, to find the acceleration:
where v is the final velocity, u is the initial velocity, and t is the time taken.
Step 2
Using the recorded data, plot a graph to show the relationship between the acceleration of the body and the force applied to it.
Answer
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Label axes correctly: Label the x-axis as 'Force (N)' and the y-axis as 'Acceleration (m/s²)'.
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Plot points: Plot the points represented by the recorded data accurately on the graph.
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Draw a line of best fit: Connect the points with a straight line to illustrate the relationship.
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Analyze distribution: Ensure the points are well distributed, indicating a clear relationship between acceleration and force.
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State the relationship: The graph should reflect the relationship that acceleration is proportional to the applied force (i.e., ).
Step 3
What does your graph tell you about this relationship?
Answer
The graph illustrates a linear relationship between the acceleration of the body and the force applied to it. This means that as the force increases, the acceleration also increases proportionally. The slope of the graph represents the mass of the body according to Newton's second law, which can be expressed as:
This reinforces the idea that acceleration is directly proportional to the net force acting on the body and inversely proportional to its mass.
Step 4
Using your graph, find the mass of the body.
Answer
Using the slope obtained from the graph, which is calculated from:
You can plug in the values corresponding to any point on the line. For example, if the force is 1.00 N and the corresponding acceleration is 0.45 m/s², the mass can be calculated as:
Step 5
On a trial run of this experiment, a student found that the graph did not go through the origin. Suggest a reason for this and describe how the apparatus should be adjusted, so that the graph would go through the origin.
Answer
One reason the graph might not go through the origin could be due to friction between the body and the surface. This frictional force creates a resistance that affects the initial acceleration when no force is applied, resulting in a non-zero intercept.
To adjust the apparatus so that the graph goes through the origin, it is necessary to minimize this frictional force. This can be done by elevating the track or slope to reduce contact with the surface, or by using a low-friction track for the trolley. This adjustment allows for a more accurate measurement of the acceleration directly proportional to the applied force.