A cylinder (mass M, radius R) can rotate on a frictionless axle.On one side is a

Question

A cylinder (mass M, radius R) can rotate on a frictionless axle.On one side is a counterweight (mass m, on the rim). The other sideattaches to a spring with constant k. The pulley is displaced fromequilibrium and begins to oscillate. Assume very smalloscillations.

b.)        Sum the forces inhorizontal and vertical directions. The cylinder undergoes“pure rotation”, what should the net force componentsequal?

c.)        Find the nettorque. Identify the origin (pivot point) about which each torqueis calculated.

d.)        Findw2, the frequency of oscillation.

Explanation / Answer

a.)the free body diagram of the cylinder consists of normalforce n acting upwards and the weight of the cylinder and force dueto the spring acting downwards the forces acting on the attached mass are similarly thenormal force n' and the weight of the attached mass actingdownwards. b.)the forces in horizontal and vertical directions are Fx = 0 and Fy = (n + n') + (-w - w' - F) = 0 or n + n' = w + w' + F w is the weight of the cylinder,w' is the weight of theattached mass and F is the force acting on the spring therefore,the net force components are Fnet= w + w' + F = (m + m') * g + k * y y is the distance moved by the spring from the equilibriumposition during its vertical motion c.)the net torque is = Fnet * R = [(m + m') * g + k * y] *R the origin (pivot point) about which each torque is calculatedis the point where the mass m is attached to the cylinder. d.)the frequency of oscillation is w = (k/m + m')^(1/2)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.