Calculating Tension Force for Different Masses

[bentrinh]

Homework Statement

The following is for a lab report. We had a couple pulleys set up, with a weight on one side, and a weight on the other side. We timed how long it took for it to fall and figured out the acceleration was .891 m/s$$^{2}$$
http://img682.imageshack.us/img682/5316/uploadyt.jpg
I need to calculate the Force of tension for 50.0g mass, and the Force of tension for 60.0g mass. Gravity is 9.80 m/s$$^{2}$$

Homework Equations

F$$_{tension} + F_{weight}$$ = mass * acceleration

The Attempt at a Solution

Deriving...
F$$_{tension} + F_{weight}$$ = mass * acceleration
F$$_{tension}$$ = mass * acceleration - F$$_{weight}$$

F$$_{weight}$$ = mass * gravity
F$$_{tension}$$ = (mass * acceleration) - (mass * gravity)
F$$_{tension}$$ = (mass * .891 m/s$$_{2}$$) + (mass * -9.80 m/s$$_{2}$$)

Solving for 50.0g...
50.0g = .0500kg
F$$_{tension}$$ = (.0500kg * .891 m/s$$_{2}$$) - (0.0500kg * -9.80 m/s$$_{2}$$)
F$$_{tension}$$ = .535 N

Solving for 60.0g...
60.0g = .0600kg
F$$_{tension}$$ = (.0600kg * .891 m/s$$_{2}$$) - (0.0600kg * -9.80 m/s$$_{2}$$)
F$$_{tension}$$ = .641 N

However, apparently, one of the tension forces should be negative. I'm stumped at this point. Sorry if it seems to be a very basic mistake, but my teacher doesn't always explain things clearly, and all my classmates are equally confused at this point.

 

[diazona]

However, apparently, one of the tension forces should be negative.

You've defined the upward direction to be positive, and downward negative, right? I assume that's why you set g to a negative value. (Which is perfectly fine) In that case, both the tension forces should be positive because they're both pointing upward.

Tension is normally given as a positive value, anyway, since we consider it to be the amount of force pulling pieces of the string together. A negative tension, to my mind, would mean that the string should spontaneously blow itself apart.

 

[kerimek]

Your approach and calculations are correct. The negative sign in the tension force for the 60.0g mass is due to the direction of the force. Since the acceleration is downward, the tension force will be in the opposite direction (upward). This is why it is represented as a negative value.

To clarify, the negative sign does not indicate a negative or "wrong" value, but rather a direction. In this case, it means that the tension force is acting in the opposite direction of the weight force.

Hope this helps!