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A student investigated the motion of a toy car along a horizontal track using the apparatus shown - Edexcel - A-Level Physics - Question 4 - 2023 - Paper 3
Question 4
A student investigated the motion of a toy car along a horizontal track using the apparatus shown. The launching device applies a force on the car. The force causes... show full transcript
Worked Solution & Example Answer:A student investigated the motion of a toy car along a horizontal track using the apparatus shown - Edexcel - A-Level Physics - Question 4 - 2023 - Paper 3
Step 1
(a)(i) Determine the mean value of time in s.
Answer
To find the mean value of the times recorded, we add all the recorded values together and then divide by the total number of readings.
Calculating the mean:
overline{t} = rac{3.57 + 3.61 + 3.54 + 3.51}{4} = rac{14.23}{4} = 3.5575 ext{ s}
Rounding this to three significant figures gives:
Mean value of time = 3.56 s.
Step 2
(a)(ii) Determine the percentage uncertainty in the mean value of time.
Answer
To find the percentage uncertainty, we first calculate the range of the measurements and divide that by the mean value, then multiply by 100:
Range = Maximum - Minimum = 3.61 - 3.51 = 0.10 s.
The uncertainty can be taken as half of this range:
Uncertainty = rac{0.10}{2} = 0.05 s.
Percentage uncertainty = rac{0.05}{3.56} imes 100 \approx 1.40%.
Step 3
(b) Describe how different apparatus could be used to measure the time, so that the percentage uncertainty is reduced.
Answer
To reduce the percentage uncertainty in the time measurement, several methods can be used:
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Use of electronic timers: An electronic timer can be used instead of a manual stopwatch, as it will provide a more precise measurement of time with minimal human error.
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Light gates: Placing a light gate at each marker can allow for automatic timing as the car passes through, thus reducing reaction time uncertainty.
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Data logging: Using a data logger connected to sensors can provide continuous time measurements and remove human error in starting and stopping the timer.
Step 4
(c)(i) Explain how a graph of F against v can be used to determine a value for t.
Answer
To determine the value of t from a graph of F against v, we first rearrange the equation to express force in terms of velocity:
F = Mv
On plotting F against v, the gradient of the resulting line (of best fit) will give us the mass M ( which is constant). Therefore, by calculating the gradient, we can rearrange to find t:
t = rac{F}{Mv}.
Step 5
(c)(ii) Plot a graph of F on the y axis against v on the x axis.
Answer
To plot the graph:
- Label the x-axis as 'v/ms-1' and the y-axis as 'F/N'.
- Use the provided data to create points on the graph:
- (0.28, 0.5)
- (0.84, 1.5)
- (1.40, 2.5)
- (1.97, 3.5)
- (2.52, 4.5)
- Draw a line of best fit through the points.
Step 6
(c)(iii) Determine a value for t using the gradient of your graph.
Answer
To find the value for t:
- Calculate the gradient of the graph using two points:
- Choose points (0.28, 0.5) and (2.52, 4.5):
Gradient, m = rac{(4.5 - 0.5)}{(2.52 - 0.28)} = rac{4}{2.24} \approx 1.785.
Using the mass M = 0.125 kg:
- Rearranging the equation, we can express t as:
t = rac{F}{M imes v}.
The gradient m ( which equals F/v) allows us to find t:
t \approx rac{1}{1.785} \approx 0.560 s.