Why Is the Acceleration Zero in a Frictionless Pulley System?

[ahhh_david]

Homework Statement

The pulley is essentially weightless and frictionless. If M₁= 10.0 kg and the second mass M₂ weighs 98.1 Newtons, what is the tension in the rope and the acceleration of M₁ ?

Homework Equations

F_T=mg
F=ma

F_T = tension
m=mass
g=gravity (9.81)
a=acceleration

The Attempt at a Solution

F_T=mg ---> F_T=(10)(9.81) = 98.1 Newtons

a= F_T / m
a= 98.1/10 = 9.81 m/s²The tension answer is right, but the acceleration should be 0. How would it be 0?
What am i doing wrong? Thanks.

 

[mark726]

Hello,

First of all, great job on solving for the tension in the rope using the formula FT=mg. However, there is a mistake in your calculation for the acceleration. The formula for acceleration is a=F/m, not a=FT/m. This is because acceleration is equal to the net force acting on an object divided by its mass.

In this case, the only force acting on M1 is the tension in the rope, which is equal to 98.1 Newtons. Therefore, the acceleration of M1 would be 98.1/10 = 9.81 m/s2, which is the same as the acceleration due to gravity. This means that M1 would be in equilibrium and not experience any acceleration.

I hope this helps clarify your doubts. Keep up the good work!