# Why does the mass of an object on a frictionless surface matter?

I'm given a physics problem about a climber hanging over a cliff and attached by rope to a rock on level, frictionless ice. The goal is to find the acceleration of the pair. After working out the net forces, the books says that for the rock,

$T = m_ra$, where $T$ is the tension in the rope, since the sum of the forces is equal to mass times acceleration and the net force on the rock is just the tension force.

and for the climber,

$-T + m_cg = m_ca$

So, combining the two, the book gives:

$a = \frac{m_cg}{m_c + m_r}$

I can make sense of the equations, but I don't understand why they work. If there is no friction, then I would think the rock would just move effortlessly across the ice and not detract from the climber's downward acceleration. At the same time, if the climber were in freefall, that would mean the rope tension is 0, which wouldn't be possible if the climber is attached to the rock.

I feel like I'm missing something obvious here..

edit: the picture in the book is similar to:

• The rock is frictionless but still has inertia. Is that what you are asking? – CuriousOne May 1 '15 at 6:36
• @CuriousOne, Ooh right, inertia. There's the obvious thing I was missing. Thanks! – mowwwalker May 1 '15 at 6:38