A body is in limiting equilibrium on a rough inclined plane at an angle of 30° with the horizontal. Calculate the acceleration with which the body will slide down when inclination of plane changed to 60°
Answers
Answer:
The acceleration will be g/√ 3
Explanation:
According to the problem initially the body is in equilibrium on a plane with an angle of 30° horizontal.
therefore the downwards force = m g sin θ
and the frictional force = μ m g cos θ
as the body is in equilibrium the downward force by the frictional force
Therefore,
m g sin θ = μ m g cos θ [ where θ = 30 °, m = mass of the body, g = acceleration for gravity, μ= friction coefficient]
μ = sin θ/ cos θ
= tan 30 °
= 1 /√ 3
Now when the body will slide down and making angle of 60°
we have net downward force on the body along the inclined plane
Therefore the net downward force, F = m g sin θ − μm g cos θ
Let the a is the acceleration o f the body,
a = F/m
= m g sin θ − μm g cos θ/m
= g(sin θ − μcos θ)
= g ( sin 60° - 1 /√ 3 cos 60°)
= g ( √ 3/2 - 1 /√ 3 x 1/2)
= g/2 (√ 3 - 1/√ 3)
= g/2 (3-1)/√ 3
= g/√ 3
Answer:
this is the answer
Explanation:
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