Rotational/Linear motion & friction

[Nick_L]

Homework Statement

A 2.4 kg block rests on a 30° slope and is attached by a string of negligible mass to a solid drum of mass 0.80 kg and radius 5.0 cm, as shown in Fig. 10.29. When released, the block accelerates down the slope at 1.2 m/s2. What is the coefficient of friction between block and slope?

Homework Equations

F_f=mu*N

a=alpha*r

Torque=I*alpha

The Attempt at a Solution

Ok the first thing I did was draw a free-body diagram of the block and the drum. I have F_net=mg-Tension-mu*F_normal then and set Tension=torque and got T=1/2*M_drum*a and put that back into the original equation and solved for mu, but I didn't get the right answer. Is this even the right way to do this?

 

[tiny-tim]

Welcome to PF!

Hi Nick_L! Welcome to PF!

A 2.4 kg block rests on a 30° slope and is attached by a string of negligible mass to a solid drum of mass 0.80 kg and radius 5.0 cm, as shown in Fig. 10.29. When released, the block accelerates down the slope at 1.2 m/s2. What is the coefficient of friction between block and slope?

I don't get it … what's the drum doing?

is it rotating on a fixed horizontal axis, with the string unwinding, or on a fixed vertical axis, or is it sliding down the hill on its base?

 

[Nick_L]

Here is the picture associated with the problem

 

[tiny-tim]

ok … rotating on a fixed horizontal axis, presumably with a frictionless axle, and with the string unwinding …

so use the work-energy theorem … work done = energy lost, using the mass of the object and the moment of inertia of the drum

 

[Nick_L]

Ok so I would have F_friction*dcos(30)=1/2*mass_box*v²+1/2I*omega²? If that's right it makes sense, but how would I find displacement or velocity when I only have the acceleration?

 

[tiny-tim]

Ok so I would have F_friction*dcos(30)=1/2*mass_box*v²+1/2I*omega²? If that's right it makes sense, but how would I find displacement or velocity when I only have the acceleration?

(you left out gravity)

sorry, I missed the acceleration …

in that case, just use F = ma and torque = Iα and slug it out!

 

[Nick_L]

Alright, thanks for the help