Solving Physics Homework: Find Acceleration & Tension

[Husker70]

Homework Statement

A 5.00-kg object placed on a frictionless, horizontal table is connected to a cable that
passes over a pulley and then is fastened to a hangng 9.00-kg object. Find the acceleration of the two objects and the tension in the string.

Homework Equations

I am using Net Force = (m2)-1/2(m1)(g)
a = force/total mass

The Attempt at a Solution

I am using Net Force = (m2)-1/2(m1)(g) = (9.00)-1/2(5.00)(9.8) = 63.7N
I used 1/2 of m1 because if the were hanging like on an atwood machine it
would be -m1. Since this is horizontal surface would this be correct?
I then divided the force(63.7N) by Total Mass 14.0-kg to get 4.55m/s2
They both should be travling at the same acceleration, I believe
I'm working on the tension.
Am I starting this right?
Thanks,
Kevin

 

[alphysicist]

Hi Husker70,

Homework Statement

A 5.00-kg object placed on a frictionless, horizontal table is connected to a cable that
passes over a pulley and then is fastened to a hangng 9.00-kg object. Find the acceleration of the two objects and the tension in the string.

Homework Equations

I am using Net Force = (m2)-1/2(m1)(g)
a = force/total mass

The Attempt at a Solution

I am using Net Force = (m2)-1/2(m1)(g) = (9.00)-1/2(5.00)(9.8) = 63.7N
I used 1/2 of m1 because if the were hanging like on an atwood machine it
would be -m1. Since this is horizontal surface would this be correct?

I do not believe this is correct. Rather than try doing this in one step, I would suggest you draw a free body diagram for each of the objects. Then you can write down Newton's law in the vertical direction for the hanging object and in the horizontal direction for the object on the table; with two equations and two unknowns here you can solve for both unknowns. What do you get?

I then divided the force(63.7N) by Total Mass 14.0-kg to get 4.55m/s2
They both should be travling at the same acceleration, I believe

Yes, they will have the same acceleration here.