Systems of Particles and Rotational Motion
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Question : 31
Total: 33
A cylinder of mass 10 kg and radius 15 cm is rolling perfectly on a plane of inclination 30°. The coefficient of static friction µ s = 0.25
(a) How much is the force of friction acting on the cylinder?
(b) What is the work done against frictionduring rolling?
(c) If the inclination θ of the plane is increased, at what value of θ does the cylinder begin to skid, and not roll perfectly?
(a) How much is the force of friction acting on the cylinder?
(b) What is the work done against frictionduring rolling?
(c) If the inclination θ of the plane is increased, at what value of θ does the cylinder begin to skid, and not roll perfectly?
Solution:
Mass of cylinder M = 10 k g R = 0.15 m θ = 30 ° µ s = 0.25
(a) Force of friction on the cylinder is given by
F =
m g sin θ
=
× 10 × 9.8 × sin 30 °
=
× 10 × 9.8 ×
= 16.3 N
(b) During rolling the point of contact is at rest. Therefore, work done against friction is zero.
(c) The cylinder skids (does not roll) when
µ s =
tan θ
tan θ = 3 µ s = 3 × 0.25 = 0.75
⇒ θ = 36.87 ° ≈ 37 °
(a) Force of friction on the cylinder is given by
(b) During rolling the point of contact is at rest. Therefore, work done against friction is zero.
(c) The cylinder skids (does not roll) when
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