3.1 Describe the difference between the distances used to calculate moment and work. (2)
The distance used to calculate moment is the perpendicular distance from the pivot point (or axis of rotation) to the line of action of the force (the weight of the crate, in this case). This distance determines the effectiveness of the force in producing rotational motion.
In contrast, the distance used to calculate work is the linear distance moved in the direction of the applied force. For lifting the crate, this is the vertical distance it is lifted, which directly relates to how much energy is expended in overcoming the gravitational force.
3.2 Calculate the work done to lift the crate. (2)
The work done (W) can be calculated using the formula:
\[
W = F \times d
\]
where \( F \) is the force (weight of the crate) and \( d \) is the distance lifted.
Given:
- Weight of the crate \( F = 11,500 , \text{N} \)
- Distance lifted \( d = 2.60 , \text{m} \)
So,
\[
W = 11,500 , \text{N} \times 2.60 , \text{m}
\]
\[
W = 29,900 , \text{J}
\]
3.3 Calculate the distance d. (2)
The moment (M) caused by the weight of the crate can be calculated using the formula:
\[
M = F \times d
\]
where \( F \) is the force (weight of the crate) and \( d \) is the distance from the pivot.
Given:
- Moment \( M = 13,800 , \text{Nm} \)
- Weight of the crate \( F = 11,500 , \text{N} \)
Rearranging the formula to solve for \( d \):
\[
d = \frac{M}{F}
\]
Substituting the values:
\[
d = \frac{13,800 , \text{Nm}}{11,500 , \text{N}}
\]
\[
d \approx 1.20 , \text{m}
\]
4. Plan an experiment to investigate whether the length of a string affects the period of a pendulum.
How the Investigation would be Carried Out:
-
Setup the Apparatus:
- Use the retort stand to hang the solid mass piece (50 g or 100 g) from the thin string. Attach the string at the top of the stand, leaving it free to swing as a pendulum.
-
Vary the Length of the String:
- Measure different lengths of string using the metre ruler (for example, 10 cm, 20 cm, 30 cm, up to the maximum length of 130 cm) and cut the string to these lengths. Ensure that each length is measured accurately.
-
Conduct the Experiment:
- For each length, pull the pendulum to a small angle (not exceeding 15 degrees) and release it. Use the stopwatch to measure the time it takes for the pendulum to complete a specified number of oscillations (for example, 10 oscillations).
- Record the time taken for each length of string.
-
Repeat for Accuracy:
- Repeat the measurements multiple times for each length and take the average time for more reliable results.
Measurements to be Taken:
- Length of the string (in cm or m).
- Time taken for a set number of oscillations (e.g., 10 oscillations).
- Calculate the period of each length (divide the total time by the number of oscillations).
Key Variables to be Controlled:
- The mass of the pendulum (ensure the same mass is used throughout).
- The initial angle at which the pendulum is released (should be kept small and consistent).
- Environmental factors such as air resistance, temperature, etc. (perform the experiment in a controlled environment).
Table to Show Readings:
| Length of String (cm) | Time for 10 Oscillations (s) | Average Period (s) | |-----------------------|------------------------------|---------------------| | 10 | | | | 20 | | | | 30 | | | | 40 | | | | ... | | | | 130 | | |
How the Readings would be Used to Reach a Conclusion:
- Analyze the average period for each length of string and create a graph of the period (y-axis) against the length of the string (x-axis).
- Look for trends (e.g., whether the period increases or decreases with increasing string length).
- Use the data to determine if there is a direct relationship between the string length and the period of the pendulum, confirming or refuting the proposed hypothesis.
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