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Consider a cylinder of mass M resting on a rough horizontal rug that is pulled out from under it with acceleration ' ' perpendicular to the axis of the cylinder. What is at point P? It is assumed that the cylinder does not slip.

Rolling motion

A

B
Ma

C

D

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For no slipping at


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Solve the equations (2) and (3)

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Texts: 1. Motion of a Vibrating Mass-Spring System A spring is attached to a solid wall on one end and a mass of M kilograms on the other. If the mass begins to move horizontally along the axis of the spring, it will continue to do so for some time. The nature of the motion depends on a number of factors, such as the tightness of the spring, the amount of mass, whether there is friction between the mass and the surface, or between the mass and the medium (say air) in which it slides, and whether there are any other forces F(t) acting on the mass. Suppose that x (in meters) is the position of the mass relative to the equilibrium position - the position that it would occupy were the spring unstretched and uncompressed. According to Hooke’s law, when a spring is stretched (or compressed), the force exerted by the spring to restore itself to an unstretched position is proportional to the amount of stretch (or compression) in the spring, with the proportionality constant k called the spring constant. The position x is a function of time t, assuming that t = 0 is the instant at which the motion begins. A straightforward force balance yields the equation of motion for the position x, given by M(d^2x/dt^2) + β(dx/dt) + kx = F(t), where β(dx/dt) represents the damping force, a force opposing motion whose magnitude is proportional to the velocity of the mass, dx/dt, with β being the damping constant. A 100-gram mass is suspended vertically from a spring with a constant of 40 Newtons per meter, is pulled 2 centimeters below its equilibrium position, and is given an upward velocity of 10 meters per second.
  1. Determine the position of the mass as a function of time.
  2. To simplify further analysis, write the solution x(t) as x(t) = Asin(αt + φ). Determine A, α, and φ.
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Question Text
Consider a cylinder of mass M resting on a rough horizontal rug that is pulled out from under it with acceleration ' ' perpendicular to the axis of the cylinder. What is at point P? It is assumed that the cylinder does not slip.


Updated OnApr 18, 2023
TopicSystem of Particles and Rotational Motion
SubjectPhysics
ClassClass 11
Answer TypeText solution:1 Video solution: 1
Upvotes179
Avg. Video Duration17 min