# Why is the acceleration not equal to 9.81 m/s^2

1. Apr 6, 2014

### rexorsist

1. The problem statement, all variables and given/known data

I'm doing a lab where there is a pulley system. A mass of 50g is attached to a string that goes through the pulley, which is then attached to a puck, on a frictionless air table. So when the mass is let go, the 50g pulls down the puck to the edge of the table.

So why isn't the acceleration of the puck = 9.81 m/s^2, knowing that the 50g mass is in free fall, pulling the puck?

I got an average acceleration of 33.69 cm/s^2.

Would I be correct to say that it's because the force of gravity would equal the acceleration of the puck? So I would multiply 0.05 kg by 981 cm/s^2 to get an answer of 49.05 cm/s (which would be the acceleration I should've gotten, instead of 33.69 cm/s^2). Is this at all correct? ...or am I completely off?

2. Apr 6, 2014

### paisiello2

You forgot to state the mass of the puck and the pulley.

The reason you will get a lower acceleration than g is that gravity only acts on the 50g mass to accelerate the system. But the total inertia of the system is the 50g mass plus the mass of the puck plus the mass of the pulley.

Last edited: Apr 6, 2014
3. Apr 6, 2014

### rexorsist

Thanks a lot!

But would I be correct to say that in order to find the mass of the puck, I could simply multiply 0.05 kg by 9.8 m/s^2 to get 0.49 N as a force, then divide it by my acceleration.

Or would that be the incorrect force?

My teacher is forcing us to find the mass by creating our own equation based on the pulley system.

Would my method be valid as well?

4. Apr 6, 2014

### dauto

There is no difference between your method and what the teacher is asking. The teacher wants you to use your method to find an equation. Pretend you don't know the hanging mass or what the local gravity is. Instead of using 50 g you use m and instead of using 9.81 you use g. Than you use algebra (which by the way is much easier than plugging in the numbers) to solve the problem.

5. Apr 6, 2014

### nasu

No, your method will not result in the mass of the puck.
Do as you teacher said. Write the equation (Newton's second law) for the system and you will see why. Guessing blindly is not the right way to learn physics.

6. Apr 6, 2014

### paisiello2

Start by doing a free body diagram for each mass and set up two equations of motion.

7. Apr 7, 2014

### rexorsist

How am I guessing blindly? I'm asking a question in order to correct a possible mistake, which is pretty natural when learning almost anything. Rather than telling me to see for myself, you can explain a concept I don't understand, because I've made the equation and still don't know why my method doesn't work (which I know is incorrect, but I don't understand why the force of gravity can't be applied as the net force of the puck).

8. Apr 7, 2014

### nasu

Well, you did not show the free body diagram or any equation.
You just asked if your series of arithmetical operations will provide the mass of the puck.
I answered that question (no) and I suggested a way to obtain the right answer.

If you did the diagram you should observe that the acceleration of the puck is due to the tension in the string and not to the weight of the 50g mass.
So the weight of the 50 g mass divided by the acceleration will not result in the mass of the puck.
But maybe I misunderstood you and you meant something else.

It is a good idea to show equations rather than describing operations in words. It will make what you mean much clearer.