A uniform metre rule of mass 150g is pivoted freely at 0 cm mark.What force applied vertically upwards at the 60 cm mark is needed to maintain the rule horizontally?
i din't get answer
show the workings
how to find
which is the answer
this is a class 2 lever
the weight of the rule acts at its center of mass
f * 60 = (.15 g) * 50 ... g is gravitational acceleration ... 9.8 m/s^2
To answer this question, we need to consider the principle of rotational equilibrium.
Rotational equilibrium occurs when the sum of the clockwise moments is equal to the sum of the anticlockwise moments. In this case, the metre rule is balanced horizontally, so the sum of the clockwise moments is equal to the sum of the anticlockwise moments.
Let's break down the problem step by step:
1. Identify the forces and distances:
- The force applied vertically upwards at the 60 cm mark is the force we need to find (let's call it F).
- The weight of the metre rule acts vertically downwards at the center of gravity, which is at the 50 cm mark (since the ruler is uniform). We can calculate the weight using the formula W = mg, where m is the mass of the metre rule and g is the acceleration due to gravity.
- The distance between the weight and the pivot point (0 cm mark) is 50 cm.
- The distance between the applied force (F) and the pivot point is 10 cm (60 cm - 50 cm).
2. Calculate the moments:
- The moment of a force is the force multiplied by the distance from the pivot point.
- The anticlockwise moment is given by the weight of the metre rule: M₁ = W * 50 cm.
- The clockwise moment is given by the applied force: M₂ = F * 10 cm.
3. Set up the equation for rotational equilibrium:
- In rotational equilibrium, the sum of the clockwise moments is equal to the sum of the anticlockwise moments: M₁ = M₂.
- Substituting the moments calculated in step 2, we get:
W * 50 cm = F * 10 cm.
4. Solve for F:
- Rearranging the equation, we have:
F = (W * 50 cm) / 10 cm.
- Substitute the given values: W = mass * gravitational acceleration = 150 g * 9.8 m/s².
- Convert grams to kilograms: 150 g = 0.15 kg.
- Calculate F using the formula: F = (0.15 kg * 9.8 m/s² * 50 cm) / 10 cm.
5. Calculate the final answer:
- Perform the calculation using appropriate units: F = (0.15 kg * 9.8 m/s² * 50 * 0.01 m) / (10 * 0.01 m).
- Simplifying the equation, we find: F = 0.735 N (approximately).
Therefore, a force of approximately 0.735 N applied vertically upwards at the 60 cm mark is needed to maintain the metre rule horizontally.