Solving a Physics Puzzle: Calculating Rope Tension

[JayDub]

Hey there all of you.

I am doing some studying for my final for physics and i have come across this question. I thought it was easy but it is not working that way. The question is. A 4kg block (held by a block) is accelerating down at 3 m/s/s, what is the tension of the rope?

So I am thinking to do this:
Fnet = ma
T - Fg = ma
T = ma + mg
T = 4kg(-3m/s/s) + 4kg(-9.8m/s/s)
T = 51N

So I look at the answer and it is wrong, it says it is: 27N

So now I try making the opposite end negative.

Fnet = ma
Fg - T = ma
- T = ma - mg
T = -ma + mg
T = -4kg(-3m/s/s) + 4kg(-9.8m/s/s)
T = 27N

Now I am getting the right answer. However I can not get the correct answer doing the same question the other way, so my question is what am I doing wrong? Thank you.

 

[Delzac]

u need to draw the Free-body Diagram. Once drawn, u with find that the tension is in an upwards direction, the weight downwards.

since it is accelerating downwards, there is a netforce in the downwards direction. thus mg-T = ma allows acceleration downwards. ( this means mg>T)

However, T-mg = ma give a netforce in the upwards direction, the object is not accelerating in the upwards direction. ( this means T>mg, but is this true ? )

 

[JayDub]

I am sorry, I do not quite follow. Isn't the netforce up AND down?

 

[Delzac]

nope, Net force = Resultant force

A net force (also known as a resultant force) is a vector produced when two or more forces act upon a single object. It is calculated by adding the force vectors acting upon the object.

for example, i put a 10N object on a table what is te net force?

the object has a weight of 10N, and by Newton 3rd law, the table exert a 10N force on the object also.

the force exerted by table is in a upwards direction and the weight is in a downwards direction.

thus the net force is $$F_net = 10 - 10 = 0$$ thus the object is not accelerating, as a netforce will cause it to accelerate