Calculating Mass and Tension of Stone Suspended from Pulley

[oldspice1212]

A stone is suspended from the free end of a wire that is wrapped around the outer rim of a pulley, as shown in the figure. The pulley is a uniform disk with mass 11.3kg and radius 49.0cm and turns on frictionless bearings. You measure that the stone travels a distance 12.3m during a time interval of 2.50s starting from rest.

1. Find the mass of the stone.

2. Find the tension in the wire.Free fall acceleration = 9.80 m/s^2

Figure: http://tinyurl.com/cpht4rr

I'm not to sure what formula to use for this?

 

[oldspice1212]

EDIT: Working on it atm, I'll see what I get first.

 

[ehild]

Is the stone or the pulley in free fall?

Hint: draw the free body diagram first.

ehild

 

[oldspice1212]

It's for both of them atm I'm using
S=Ut+1/2at^2
then I will apply Newtons second law mg - T = ma
hopefully this will get me the mass.

 

[oldspice1212]

Ok so I got S = 0 +1/2 (9.8m/s^2)(2.5s)^2 which gave me 30.625
30.625/ 12.3 = 2.489...m/s^2

I manipulated Newtons second law to get T = 1/2M*a
T = 1/2(11.3kg)(2.48...m/s^2)
T = 14.067N

\SigmaF=mg-T=ma
mg-ma = T = m(g-a)
m= T/(g-a)
14N/(9.8m/s^2-2.4...m/s^2) = 1.92kg

How does this look?Mhm got it wrong, not sure where the mistake is though.

 

[ehild]

The stone accelerates with a and s= 1/2 at², why do you calculate with g?

What about the pulley? Does it move?

ehild?

 

[oldspice1212]

Yes it says "take free fall acceleration to be 9.80 m/s^2"

 

[ehild]

It is the free-fall acceleration, but is not the acceleration of the stone. Calculate the acceleration again.

ehild

 

[oldspice1212]

Dope! Haha thanks for that, I got 3.936 m/s^2 meaning the tension is 22.2384 N.
Therefore the mass comes out to be...3.79 kg.

Thanks a lot! :P

 

[ehild]

That is better

ehild