In Figure the incline is frictionless and the string passes through the center o

Question

In Figure the incline is frictionless and the string passes through the center of mass of the block and the bucket. The pulley has a moment of inertia I and radius R. (a) Find the net torque acting on the system (about the center of the pulley. (b)Write an expression for the total angular momentum of the system about the center of the pulley. Assume the objects are moving with a speed v. (c) Find the acceleration of the bucket by using your results for Parts (a) and (b) and by setting the net torque equal to the rate of change of the system's angular momentun. nt:

Explanation / Answer

(A) Net torqeu = m1 g sin(theta) R - m2 g R

  
torque = g R ( m1 sin(theta) - m2 )

(B) angular momentum , L = (r x F)

L = m1 v R + m2 v R + I w and w = v / R

L = v R (m1 + m2 + (I / R^2))

(C) torque = dL/dt

g R ( m1 sin(theta) - m2 ) = (m1 + m2 + (I / R^2)) R dv/dt

and dv/dt = a

a = g (m1 sin(theta) - m2 ) / (m1 + m2 + (I/R^2))

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

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