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A student used a metre stick to investigate the laws of equilibrium for a set of co-planar forces - Leaving Cert Physics - Question 1 - 2022
Question 1
A student used a metre stick to investigate the laws of equilibrium for a set of co-planar forces. He found that the weight of the metre stick was 1.2 N and that its... show full transcript
Worked Solution & Example Answer:A student used a metre stick to investigate the laws of equilibrium for a set of co-planar forces - Leaving Cert Physics - Question 1 - 2022
Step 1
Describe how the student determined (a) the centre of gravity and (b) the weight of the metre stick.
Answer
The student determined the centre of gravity by:
- Suspending the metre stick from a thread or balancing it on a pivot until it came to rest.
- Weighing the metre stick using a scale to obtain its weight (1.2 N).
In essence, the balance point where the stick pivoted indicates the centre of gravity.
Step 2
Why was it necessary to determine the centre of gravity of the metre stick?
Answer
Determining the centre of gravity was crucial because it helps in calculating the moments acting on the stick. Knowing where the weight effectively acts allows for a clearer understanding of the equilibrium and moments produced when external forces are applied.
Step 3
Indicate on a labelled diagram how these vertical forces were applied to the metre stick.
Answer
The vertical forces were applied at specified positions along the metre stick: 2.85 N upwards at 22.5 cm, 2.00 N downwards at 32.1 cm, 3.00 N downwards at 72.2 cm, and 3.40 N upwards at 81.3 cm. A labelled diagram would show these forces at their respective positions with arrows indicating direction.
Step 4
How was it ensured that the metre stick was in equilibrium?
Answer
Equilibrium was ensured by balancing the forces acting on the metre stick such that the net force equaled zero and all moments about a point (in this case, the 0 cm position) summed to zero. This was likely checked by measuring and confirming that the stick remained horizontal.
Step 5
What was the principal advantage of ensuring that the metre stick was horizontal?
Answer
The principal advantage of keeping the metre stick horizontal is that it simplifies the analysis of forces and moments. A horizontal position means that the net torque about any point remains zero, making it easier to validate the laws of equilibrium.
Step 6
Calculate the net moment about the O cm position.
Answer
Using the distances from the O position, the net moment is calculated as follows:
Total moment from all forces = (2 x 0.321) + (1.2 x 0.506) + (3 x 0.722) - (2.85 x 0.225) + (3.4 x 0.831)
This results in a net moment of approximately 0.00975 N m, ensuring the correct direction and magnitude are considered.
Step 7
Step 8
Explain how these results verify the laws of equilibrium.
Answer
The laws of equilibrium are verified as:
- The net moment around the pivot point is zero, indicating rotational equilibrium.
- The net vertical force is also zero, confirming translational equilibrium, thus validating that all forces and moments acted to maintain the metre stick in a balanced state.