Example Consider a hanging mass wrapped around a MASSIVE pulley. The hanging mass has weight, mg, the mass of the pulley is m p, the radius is R, and the.

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Presentation transcript:

Example Consider a hanging mass wrapped around a MASSIVE pulley. The hanging mass has weight, mg, the mass of the pulley is m p, the radius is R, and the moment of inertia about its center of mass I cm = 1/2m p R 2. (assuming the pulley is a uniform disk). Determine the acceleration of the hanging mass. Let’s first look at the F.B.D.s for both the pulley and hanging mass mhgmhg T mpgmpg FNFN T

Example cont’ mhgmhg T a mpgmpg FNFN T

Example A trickier problem: Calculate the acceleration of the system: Assume m 1 is more massive than m 2 What you have to understand is that when the PULLEY is massive you cannot assume the tension is the same on both sides. Let’s first look at the F.B.D.s for both the pulley and the hanging masses. m1gm1g T1T1 m2gm2g T2T2 mpgmpg FNFN T2T2 T1T1

Example cont’ m1gm1g T1T1 m2gm2g T2T2 mpgmpg FNFN T2T2 T1T1

Example

Consider a hanging mass wrapped around a MASSIVE pulley. The hanging mass has weight, mg, the mass of the pulley is m p, the radius is R, and the moment of inertia about its center of mass I cm = 1/2m p R 2. (assuming the pulley is a uniform disk). Determine the acceleration of the hanging mass. Let’s first look at the F.B.D.s for both the pulley and hanging mass T

Example A trickier problem: Calculate the acceleration of the system: Assume m 1 is more massive than m 2 What you have to understand is that when the PULLEY is massive you cannot assume the tension is the same on both sides. Let’s first look at the F.B.D.s for both the pulley and the hanging masses.