a uniform rod of length2m a uniform rod of 2 metres and mass 5 kg is lying on a horizontal surface the work done in raising one end of the road with the other m into contact with the surface until the road makes an angle 30 degree with the horizontal is
Answers
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Therefore the work done in raising the rod until it makes an angle of 30° with the ground is 25 Joule.
Given:
Length = L = 2 m
Mass of the rod = m = 5 kg
The angle made by the rod with the ground = θ = 30°
To Find:
Work done in raising the rod to make an angle of 30° with the ground =?
Solution:
This simple question can be solved by this simple approach.
Given that,
Length = L = 2 m
Mass of the rod = m = 5 kg
Weight of the rod = Wt = mg = 5 × 9.81 = 49.05
Where g = acceleration due to gravity.
The rod is lifted till it makes a 30° of angle with the ground.
Raising the rod to make an angle of 30° with the ground is the Work Done against gravity.
Work done against gravity = Potential Energy of the rod
⇒ Work done =W = mgh
Where h = height raised by the center of gravity of the rod. = L sinθ / 2
Hence Work done = W = Wt L sinθ / 2
⇒ W = 49.05 × 2 × sin 30° / 2 = 24.425 ≈ 25
Therefore the work done in raising the rod until it makes an angle of 30° with the ground is 25 Joule.
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