Solving Pulley Problem with Newton's Laws: Calculating Acceleration of Bodies

[devanlevin]

In the below case, in dynamics, how do i solve this pulley problem using Newtons laws?
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what is the acceleration of each of the bodies?
the hanging body has a mass of 2kg
the lying body has a mass of 3kg

the cords and pulleys have no mass and the system has no friction.

i realize that the 2kg body needs to have half the acceleration of the 3kg, because of the manner in which it is connected to the pulley but how do i work out the exact acceleration??


what i tried to do was say the total mass is 5kg and the only force is the Mg(2kg*9.8)- but it is obvious that thiere is a bit more to it, then what i thought is making the total mass 7-(3 +2*2) but this doesn't make sense,

 

[physixguru]

First make a free body diagram.i.e. mark all the forces acting on each mass.
Also, show some attempt.

 

[devanlevin]

forces affecting the lying body
N1=29.4N
W1=MG=29.4N
T1=?

affeting the hanging body
W2=MG=19.6N
T2=?

no friction in the sysstem, as far as i can see there are no other forces

i don't know how to deal with the body hanging to the body, i see that its acceleration must be half of the other's but don't know how i can put this into my equations

using
SIGMAFx=MA
the only forces i have in x are W2, so i divided 19.6 by 5(total mass) but my acceleratioon doesn't come to the correct answer, i treated it like a simple pulley problem with 2 bodies on either sides of a pulley, connected directly to the cord of the pulley but i see that this cannot work

 

[physixguru]

T1 is equal to the weight of the hanging body.

 

[devanlevin]

are you sure?? according to the answer in the book T1 is equal to 8.4N whereas the weight of the hanging body in 19.6N

 

[physixguru]

It was a typo.It is common sense because the hanging body is held up by two wires so the tension doubles but differently.

 

[Doc Al]

forces affecting the lying body
N1=29.4N
W1=MG=29.4N
T1=?

affeting the hanging body
W2=MG=19.6N
T2=?

There's a single tension throughout the cord. Call it T.

Hint: When you analyze the hanging mass, treat the mass + pulley as a single system.

no friction in the sysstem, as far as i can see there are no other forces

i don't know how to deal with the body hanging to the body, i see that its acceleration must be half of the other's but don't know how i can put this into my equations

If you call the acceleration of the lying mass = a, what would you call the acceleration of the hanging mass?

using
SIGMAFx=MA
the only forces i have in x are W2, so i divided 19.6 by 5(total mass) but my acceleratioon doesn't come to the correct answer, i treated it like a simple pulley problem with 2 bodies on either sides of a pulley, connected directly to the cord of the pulley but i see that this cannot work

Apply Newton's 2nd law to each mass separately. You'll get two equations (and two unknowns) that you can then solve together.

T1 is equal to the weight of the hanging body.

Not so.