How Do You Calculate the Linear Acceleration and Impact Velocity of a Load?

[brooker2009uk]

Homework Statement

was wondering if anybody here does mech engineering and if so can they point me in the right direction of this question please.


Figure 1 below shows a drum of mass of 50kg and radius 350mm. The drum can be assumed to be a uniform solid cylinder. A rope of negligible mass is wrapped around the drum and is attached to a load of 15kg which is held 2.4m above the ground initially. Determine:
• the linear acceleration of the 15kg load when the brake preventing the drum from rotating is released and
• the velocity with which the 15kg load will impact the ground with.

(Assume the acceleration due to gravity is 9.8 m/s2.)

Homework Equations

q = qo + wo t + (1/2)a t2
w2 = wo
2 + 2 a q

to start, i am not looking the answer and i just want someone to please show me how to get the linear acceleration

thanks

 

[tiny-tim]

welcome to pf!

hi brooker2009uk! welcome to pf!

(btw, this is a fairly standard dynamics problem also, so you'll get answered sooner if you post future questions like this in the physics homework forum )

you'll need F = ma for the load, and τ = Iα for the drum …

(and also the rolling constraint, a = rα)

call the tension "T" …

what do you get? ​

 

[brooker2009uk]

thank you, that is getting the torque but i need an equation to get the linear acceleration of the load when the brake is released

 

[tiny-tim]

thank you, that is getting the torque but i need an equation to get the linear acceleration of the load when the brake is released

yes, that's F = ma !

get on with it! ​