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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. This allowed the stick to balance on a pivot. The weight of the metre stick was established by using a balance scale, measuring it directly with the formula: where ( g ) is the acceleration due to gravity (9.81 m/s²).
Step 2
Why was it necessary to determine the centre of gravity of the metre stick?
Answer
It was necessary to determine the centre of gravity to know where the weight acts on the metre stick. This is crucial for calculating the moment about any point, ensuring proper equilibrium. Understanding the centre of gravity aids in predicting how forces will affect the stick when it is subjected to vertical forces.
Step 3
Indicate on a labelled diagram how these vertical forces were applied to the metre stick.
Answer
In the labelled diagram, the vertical forces were applied at specified positions along the metre stick:
- 22.5 cm: 2.85 N upwards
- 32.1 cm: 2.00 N downwards
- 72.2 cm: 3.00 N downwards
- 81.3 cm: 3.40 N upwards
The net effect of these forces maintained the stick's horizontal position.
Step 4
How was it ensured that the metre stick was in equilibrium?
Answer
The metre stick was ensured to be in equilibrium by checking that the net force acting on it was zero, meaning upward forces balanced downward forces. Additionally, by confirming the net moment about any pivot point was zero, it maintained a stable horizontal position without rotation.
Step 5
What was the principal advantage of ensuring that the metre stick was horizontal?
Answer
The principal advantage of ensuring the metre stick was horizontal was that it simplified the analysis of forces and moments. In a horizontal position, the stick experiences no torque, making it easier to assess equilibrium and to determine whether the forces balance effectively.
Step 6
Calculate the net moment about the O cm position.
Answer
To calculate the net moment about the O position, use the formula:
Calculating each:
- For 22.5 cm: ( 2.85 ext{ N} imes 0.506 ext{ m} = 1.44591 ext{ Nm} )
- For 32.1 cm: ( 2.00 ext{ N} \times 0.321 ext{ m} = 0.64200 ext{ Nm} )
- For 72.2 cm: ( 3.00 ext{ N} \times 0.722 ext{ m} = 2.16600 ext{ Nm} )
- For 81.3 cm: ( 3.40 ext{ N} \times 0.813 ext{ m} = 2.77140 ext{ Nm} )
Calculating total moments: (1.44591 + 0.64200 - 2.16600 - 2.77140 = -3.88549 \text{ Nm})
Thus, the net moment about the O position is (-3.88549\text{ Nm}).
Step 7
Calculate the net vertical force acting on the metre stick.
Answer
To find the net vertical force, sum the upwards and downwards forces:
- Upwards forces: 2.85 N + 3.40 N = 6.25 N
- Downwards forces: 2.00 N + 3.00 N = 5.00 N
Net vertical force = Upwards - Downwards (6.25 ext{ N} - 5.00 ext{ N} = 1.25 ext{ N upwards}).
Step 8
Explain how these results verify the laws of equilibrium.
Answer
The results verify the laws of equilibrium as they show:
- The net force acting on the metre stick is zero, confirming that all forces are balanced.
- The moments calculated confirm that the net moment about a point is also zero, confirming rotational equilibrium. These conditions are essential for any body to remain in a state of rest or uniform motion.