Why Is Calculating Tension in a Frictionless Pulley System Confusing?

[johnsonandrew]

Newton's Laws Problem--confused

This has been frustrating me:

Problem:

The pulley in the figure is essentially weightless and frictionless. Suppose someone holds on to m=10.0 kg and accelerates it upward at 4.905 m/s/s. What will then be the tension in the rope given that M=10.0 kg?

Attempt:

The sum of the forces on m = Ftension + Fhand - Fgravity = ma
The sum of the forces on M = Ftension - Fgravity = Ma

I said Fhand= m * upward acceleration

I tried solving for 'a' on both equations, then set them equal to each other to solve for Ftension. This gave me a ridiculous answer, and I'm pretty sure I didn't screw up my math. I must have set it up wrong? Please help!

 

[Vijay Bhatnagar]

Acceleration of M will also be 4.9 m/s2. Apply F = Ma to get tension. F = Mg - T.

 

[learningphysics]

Don't assume what Fhand is... you only know that m accelerates upwards at 4.905m/s^2, therefore the other mass accelerates downwards at 4.905m/s^2

you should get 2 equations with 2 unknowns (Fhand and tension). solve for the tension. careful about signs and directions... remember one mass accelerates upwards, the other accelerates downwards.