Solve Two Pulleys Problem: Find Minimum Tension Needed

[zhenyazh]

Hi,
i am preparing for the test and have a problem with the following question.
a crate is pulled up using frictionless pulleys in the manner shown in the image attached.
the angle is teta=37 deg. the small pulley mass is m1=3.1 kg for the traveling pulley m2=6.9 kg. the mass of the crate is mc=54 kg.
what is the minimum tension with which the operator must pull on the cable which has negligible mass in order to slowly raise the crate.

as far as i understand i shlould use Newton's second law and write equation for the different objects. but this is exactly what i get confused with. i can't manage to write the correctly. can u help me with that?

thanks

 

[tiny-tim]

Hi zhenyazh!

(have a theta: θ )

… what is the minimum tension with which the operator must pull on the cable which has negligible mass in order to slowly raise the crate.

as far as i understand i shlould use Newton's second law …

Nooo … the question says "slowly raise the crate" …

when a question says that, it means that just enough force is used to move the object (since there's no friction, then that's the same as the force needed to hold the object stationary; if there was friction, you'd have to add some force to overcome the friction ) …

you can assume the acceleration is zero, and treat it as a case of static equilibirum …

so just get all the forces to balance.

 

[ZeroNowhere]

Of course, for the system to be lifted at a constant speed, it must be in equilibrium, as the above poster said while I was writing this. As such, you can simply equate the upwards and downwards forces. The upwards force will be 2T, as it is a moving pulley system, whereas the downwards force will equal mg, with m being the total mass being lifted (not all masses in the question are necessarily a part of this). You can figure it out from there.

 

[zhenyazh]

done.

thanks