Torque Calculations with Pulleys

Torque Calculations with Pulleys

Review Newtons Second Law. Pulley on horizontal surfaceGiven a mass of14 kg on a horizontal table. It is attached by a rope over a pulley to a mass of26 kg which hangs vertically. = 0.1. What is the acceleration?

A = 6 m/s2FT= 98 NAtwood machine reviewGiven mass 1 is 90 kg and mass 2 is 50 kg, what is the acceleration?

A = 2.8 m/s2FT = 630 NIncline Plane with pulleyGiven = 25 an incline has a mass of 20kg placed upon it. It is attached by a rope over a pulley to a mass of 30kg which hangs vertically. The coefficient of friction is 0.2. The acceleration will be

A = 3.5 m/s2FT = 189 NExample

Consider a hanging mass wrapped around aMASSIVE pulley. The hanging mass hasweight, mg, the mass of the pulley is mp, theradius is R, and the moment of inertia about itscenter of mass Icm = 1/2mpR2. (assuming thepulley is a uniform disk). Determine theacceleration of the hanging mass.

Pulleys with massHOW TO: STEPS TO GUIDE THINKING1. Draw free body diagrams for the masses and the pulley.2. Write an equation for Net force for each masss acceleration.3. Write an equation for Net Torque for the pulley. 4. In the torque equation, eliminate and sub a/r.5. Combine the equations to eliminate T(tension) and be left with unknown a. 6. Solve for a. Ex. 1A 1.53 kg mass hangs on a rope wrapped around a disk-shaped pulley of mass 7.07 kg and radius 66 cm. What is the linear acceleration of the hanging mass?

A = 2.96 m/s2Ex. 2

A = 2.9 m/s2Ex. 3

A = 7.35 m/s2