Tension question

[premed1001]

question

answer

i understand the equation for the mass on the right Fnet=2T-mg

i don't understand the equation for the mass on the left. mg=T+m2a
shouldnt it be Fnet=mg-T? since T is the only upwards acting force on it? where does the m2a come from?

thanks

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[premed1001]

Anyone?

 

[studentofsdn]

I'm thinking the m2a comes from the fact that you have 2 tension forces contributing to acceleration downwards for mass on the left. The answer description is pretty confusing in regards to that acceleration. If you do the problem with the way you suggested, the answers are spread out enough for you to still get the right answer, so I wouldn't worry about it.

 

[premed1001]

I'm thinking the m2a comes from the fact that you have 2 tension forces contributing to acceleration downwards for mass on the left. The answer description is pretty confusing in regards to that acceleration. If you do the problem with the way you suggested, the answers are spread out enough for you to still get the right answer, so I wouldn't worry about it.

but then how does Fnet = m2a?

 

[studentofsdn]

I don't know if this is the right way of thinking, but there are 2 upward tension forces on the right side in the direction of overall acceleration, unlike 1 tension force in the regular version of this problem. Maybe because of this, they are multiplying what would be Fnet = ma in the regular version of this problem, by 2 for the second tension force.

 

[premed1001]

I don't know if this is the right way of thinking, but there are 2 upward tension forces on the right side in the direction of overall acceleration, unlike 1 tension force in the regular version of this problem. Maybe because of this, they are multiplying what would be Fnet = ma in the regular version of this problem, by 2 for the second tension force.

It doesn't make sense to me. From the perspective of the mass on the left there are only 2 forces acting on it.
Mg and T.

Fnet=mg-T
Fnet+T=mg
MA+T=mg ?

It makes absolutely no sense to me Fnet=2MA????

 

[sniderwes]

nvm

 

[premed1001]

Bump

 

[butters221]

The purpose of a pulley is to reduce the force necessary to move the object at the other end. You should be able to see that when the block on the left changes position by distance x, the block on the right will change position by distance x/2. So the pulley allows a trade-off - less force required to change the position of the block on the right, at the cost of having to pull the left block a greater distance. This has to happen to conserve energy. If we pull the block on the right upwards 1m and it weighs 1kg, then we increased the potential energy by 10J (work = force*distance). We can apply this equation to the block on the left as well, but since we are using a pulley, distance is doubled and force is halved to ensure the same amount of work is done on each side. If the blocks were connected without pulleys, then the tension in the line would simply be equal to mass*gravity because neither block would be moving. Since the right block has 2 ropes on the top, each of these ropes has an upwards force equal to the tension, leading the upwards force on the right block to be 2T. This overcomes the force due to gravity on the right block and therefore causes both blocks to move. Since both blocks are moving we need to include mass*acceleration for each. Since the above explanation requires the left block to move twice as far as the right block, the acceleration of the left block must have twice the acceleration of the right block.
Therefore:
The equation for the block on the left is: m2a = mg - T (mg is the downward force, tension being upwards force subtracts from this force, we are left with the downward force (m2a) that represents what will be making the block move down)
The equation for the block on the right is: ma = 2T - mg (tension is the upward force, mg is the downward force that subtracts from this force, we are left with an upward force that represents what will make the right block move up)
Rearrange one of the equations for acceleration, plug that in for the other equation, and solve for T.
Book answer is correct.