How Do You Calculate the Mass of a Pulley in a Physics Problem?

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To calculate the mass of a pulley in a physics problem involving two blocks and a rope, one must consider the torque acting on the pulley and its angular acceleration. The downward acceleration of the 44.0 kg block is half of the acceleration due to gravity, indicating that the tension in the rope differs on each side of the pulley. The relevant formulas include the relationship between linear acceleration, mass, and gravity, as well as the rotational inertia of a solid cylindrical disk. By determining the torque and angular acceleration, one can derive the mass of the pulley. Understanding these concepts is crucial for solving the problem effectively.
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Hi people again, sorry to not have done extensive searching in the forum for a problem like this but I need some help ASAP.

By means of a rope whose mass is negligible, two blocks are suspended over a pulley, as the drawing shows. The pulley can be treated as a uniform solid cylindrical disk. The downward acceleration of the 44.0 kg block is observed to be exactly one-half the acceleration due to gravity. Noting that the tension in the rope is not the same on each side of the pulley, find the mass of the pulley.


Thank you guys!
 

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I am not sure which formula to use to find the mass of the pulley since the accelartion is

a=m2-m1/m1+m2 * gravity that would give me the accel if it was a massless pulley.

any help appreciated.
 
I can't see your graph... but i think i can guess how its look like
since you are new here, just want to let you know our rule here does not allow me giving you the full solution... I can only give you some hints and you got to work out the problem yourself

hints:
1. what is the touqe acting on the pulley?
2. what is the angular acceleration for the pulley
3. after you have the above numbers and the rotational inertial for a disk, you should able to figure out what the mass is...
 
alright thanks got the problem!
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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