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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 0.4... 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/Calculate Initial Velocity:
- Begin by recording the initial velocity of the body using suitable measuring equipment, such as a motion sensor or a stopwatch to time its travel from a rest position.
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Measure/Calculate Velocity/Speed Gain:
- After a set time interval, calculate the change in velocity. Record the speed gained at specific intervals and ensure this is timed with precision.
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Measure Interval and Distance:
- Measure the time interval between the initial and final velocities, often using light gates to ensure accuracy in measurements.
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Apply the Relevant Formula:
- Use the kinematic equation to relate acceleration, initial velocity, final velocity, and time, such as:
- From the velocities, calculate acceleration:
where ( v ) is final velocity, ( u ) is initial velocity, and ( t ) is time.
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Datalogging Method:
- Utilize a motion sensor with the body, document the process through a diagram. Start the experiment by selecting 'START' to release the body and 'STOP' once it reaches the designated point. Plot these values in a data graph for further analysis.
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 on Graph Paper:
- On your graph, the x-axis should represent the force (F in N), and the y-axis should represent the acceleration (a in m/s²).
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Plot the Data Points Correctly:
- Each force value paired with its corresponding acceleration value should be plotted accurately on the graph.
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Draw Straight Line Through Points:
- Analyze the plotted points and draw a line of best fit or straight line if appropriate.
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Review Graph Distribution:
- Ensure points are well-distributed along the line to reflect coherent data trends, demonstrating the relationship:
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Correct Statement/Equation Analysis:
- The relationship suggests that for forces applied, acceleration increases proportionally, confirming Newton's Second Law of Motion.
Step 3
Using your graph, find the mass of the body.
Answer
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Find the Slope of the Graph:
- From the plotted graph, calculate the slope using:
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Calculate Mass:
- According to Newton's Second Law, the relationship between mass (m), force (F), and acceleration (a) is given by:
Rearranging gives:
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Substitute the Values:
- Take values from the slope to find the mass of the body, e.g., if the slope is calculated as 2.32, then plug into the equation to estimate mass.
Step 4
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
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Reason for Not Passing Through Origin:
- The graph might not pass through the origin due to factors such as frictional forces acting on the body or a systematic error in measuring initial velocity.
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Adjustment of Apparatus:
- To rectify this, ensure that:
- All surfaces in contact are smooth to minimize friction.
- Use a more precise timing method or sensors to accurately measure starting velocities.
- Elevate the track/slope properly to reduce the initial frictional resistance when the body starts moving.
- To rectify this, ensure that: