A solid cylinder rolls up an inclined plane of angle of inclination 30°. At the bottom of the inclined plane the centre of mass of the cylinder

Question

A solid cylinder rolls up an inclined plane of angle of inclination 30°. At the bottom of the inclined plane the centre of mass of the cylinder

A solid cylinder rolls up an inclined plane of angle of inclination 30°. At the bottom of the inclined plane the centre of mass of the cylinder has a speed of 5 m/s.

(a) How far will the cylinder go up the plane?

(b) How long will it take to return to the bottom?

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Salim Ahmed Kawsar · Answer 1 · Feb 05, 2023 15:29:48

Inclination angle (∅)= 30°
Speed of centre of mass (v)= 5m/s

(A) acceleration of the cylinder rolling up the inclined plane is
Given by the formula,
a = -gsin∅/(1 + k²/r²)
Where K = radius of gyration
Moment of inertia of cylinder = (1/2)mr²
K² = r²/2

a = -gsin30°/(1 + 1/2)
= -9.8/3 m/s²

Using equation of motion,
V² = U² + 2aS
0 = (5)² + 2(-9.8/3)×S
S = 25×3/2×9.8 = 3.83 m

Time taken to return the bottom = t
S = ut + (1/2)at²
3.83 = 0 + 1/2(9.8/3)t²
t = 1.53 sec

A solid cylinder rolls up an inclined plane of angle of inclination 30°. At the bottom of the inclined plane the centre of mass of the cylinder

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