A meter rule AB of mass 0.2kg was balanced horizontally on a single support when loads of 0.1kg and 0.08kg were placed at a distance of 60cm and 90cm respectively from A. find the position of the support and the magnitude of the downward force?
To find the position of the support and the magnitude of the downward force, we can use the principle of moments. The principle states that for an object in rotational equilibrium, the sum of the clockwise moments about any point is equal to the sum of the anticlockwise moments about the same point.
Let's assume that the support is at a distance 'x' from point A. By applying the principle of moments, we can write the equation:
(0.1 kg * 60 cm) + (0.08 kg * 90 cm) = (0.2 kg * x cm)
Now, let's solve this equation to find the value of 'x':
(0.1 kg * 60 cm) + (0.08 kg * 90 cm) = (0.2 kg * x cm)
6 kg.cm + 7.2 kg.cm = 0.2 kg * x cm
13.2 kg.cm = 0.2 kg * x cm
Divide both sides of the equation by 0.2 kg to isolate 'x':
(13.2 kg.cm) / 0.2 kg = x cm
66 cm = x
Therefore, the support should be placed at a distance of 66 cm from point A.
To find the magnitude of the downward force, we need to calculate the sum of the weights acting on the meter rule. The weight can be calculated using the formula:
Weight = mass * acceleration due to gravity
The total weight acting on the meter rule can be found by summing the weight of the 0.1 kg load, the 0.08 kg load, and the meter rule itself (0.2 kg).
Weight = (0.1 kg * 9.8 m/s^2) + (0.08 kg * 9.8 m/s^2) + (0.2 kg * 9.8 m/s^2)
Weight = 0.98 N + 0.784 N + 1.96 N
Weight = 3.724 N
Hence, the magnitude of the downward force acting on the meter rule is approximately 3.724 N.