Two forces of magnitude 50 N, as shown in the figure below, act on a cylinder of
ID: 2020523 • Letter: T
Question
Two forces of magnitude 50 N, as shown in the figure below, act on a cylinder of radius 4 m and mass 6.25 kg. The cylinder, which is initially at rest, sits on a frictionless surface. After 1 second, the velocity and angular velocity of the cylinder in m/s and rad/s are respectively
A mass m = 4.0 kg is connected, as shown, by a light cord to a mass M = 6.0 kg, which slides on a smooth horizontal surface. The pulley rotates about a frictionless axle and has a radius R = 0.12 m and a moment of inertia I = 0.090 kg × m2. The cord does not slip on the pulley. What is the magnitude of the acceleration of m?
2.4 m/s2 2.8 m/s2 3.2 m/s2 4.2 m/s2 1.7 m/s2Explanation / Answer
1) since the forces are acting in opposite direction and are equal in magnitude
v=0 m/s
consider angular forces acting on the body through centre of solid cylinder
I of solid cylinder = MR2/2
since the lowermost force is passing through centre the due to the force is 0
50 * 4 = 6.25* 16 /2
= 4rad/s2
f = i + t
f= 4rad/s
option 2
2)consider the acceleration of system of the two blocks = a
for anticlockwise rotation
a = r
T1 (tension due to mass M ) = -Ma =- 6a
T2 - mg = ma
T2 = 40+4a
I = R (T1 - T2)
0.09 a = 0.12 * 0.12 (-6a - 40- 4a)
0.09a = 0.0144(-10a-40)
6.25a=(-10a-40)
16.25a =- 40
a = 40/16.25 =- 2.46m/s2
acceleration of the blocks is 2.46 m/s2 towards right and downwards
option 1
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