A mass 5.8 kg is attached to a light cord, which is wound around a pulley. The p

Question

A mass 5.8 kg is attached to a light cord,
which is wound around a pulley. The pulley
is a uniform solid cylinder of radius 7 cm and
mass 2.2 kg.
A) The acceleration of gravity is 9.8 m/s^2 .
What is the magnitude of the net torque on
the system about the point on the axis at the
center of the pulley?
Answer in units of Nm.
B)When the mass has a speed v = 39 m/s, the
pulley has an angular speed =v/R.
Determine the magnitude of the total an-
gular momentum of the system about a point
on the axis at the center of the pulley?
Answer in units of kgm^2/s.

C) Using the fact that =dL and your result from the previous section, calculate the magnitude of acceleration of the mass. Answer in units of m/s^2.

Explanation / Answer

a) Torque = Force * Distance Torque = mg*R Torque = (5.8 * 9.81 * .07)=3.98 Nm For direction, look at the diagram (and remember the right hand rule) b) L = I*w w = v/R I = (1/2)(M)(R^2) + mR^2 (here we are treating the block as a particle orbiting around the axis O) L = (M/2 + m)*R*V L = (2.2/2 + 5.8)*.07*V=0.483 c) Torque = dL/dt since L = (I*V/R) T = (I*A/R) we have torque from part a) and we have I/R from part b) so (T*R/I) = A A = (answer from part a / answer from part b)

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