Solve Simple Force Question: Acceleration, Tension

[Sheneron]

[SOLVED] Simpe Force Question

Homework Statement

A 2.00 kg object placed on a frictionless, horizontal table is connected to a string that passes over a pulley and then is fastened to a hanging 7.00 kg object, as in Figure P5.24. Find the magnitude of the acceleration of the two objects and the tension in the string.

The Attempt at a Solution

I have a specific question about this problem that I came upon at the end. Here is how I solved it.

$$T = m_1a$$
$$-T + m_2g = m_2a$$
So two equations to uknowns, and here is what I got.
$$-m_1a + m_2g = m_2a$$
$$a = \frac{m_2g}{(m_1+m_2)}$$

So solving for a I got -7.62. The thing I have a question about is the negative on the acceleration. At the beginning of the problem I defined rightward and downward direction as positive and upward direction as negative. So if acceleration is a negative value does that not mean it is traveling up, since I defined up as negative? I know that it doesn't not, but I am confused it can be this way.

 

[alphysicist]

Hi Sheneron,

How did you get a negative answer? All the values (masses and g) are positive numbers.

Did you use g=-9.8? The value of g is a magnitude and therefore always a positive number; if we were talking about an object in free fall we would say that its acceleration is

$$a_y = -g$$

just to keep g a positive number.

 

[Sheneron]

Ah ok I see. thanks