Solving Mass m2 Acceleration on a 30° Slope

[temaire]

Homework Statement

A mass, m2, on a 30$$^{o}$$ slope is connected to another mass, m1, by a light string that passes over a frictionless pulley, as shown. The two masses are equal, the slope is smooth, and the acceleration due to gravity is g.
What is the scalar equation for mass m2, that correctly shows the relationship between the acceleration, a, of the mass and the tension in the string, FT?

http://img220.imageshack.us/img220/4884/inclinexx4.png​

Homework Equations

F = ma
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The Attempt at a Solution

I got sin 30$$^{o}$$ = $$m_{1}$$g - FT/$$m_{2}$$a - $$m_{2}$$g. However, this is wrong. The answer is supposed to be FT - m2g sin30$$^{o}$$ = m2a.

Can someone show me where I went wrong please?

 

[Chi Meson]

What two unbalanced forces are on m2?

what is the acceleration of m2 due to the net unbalanced force on m2?

 

[ogb p]

I would first commend the student for attempting to solve the problem and using relevant equations. However, there seems to be a misunderstanding of the concepts involved. Let me clarify the solution for you.

Firstly, we need to understand that the two masses, m1 and m2, are connected by a light string. This means that the tension in the string, FT, is the same for both masses. This is because the string is not stretched or compressed and therefore has the same force acting on both sides.

Secondly, we need to consider the forces acting on mass m2. These are the weight of m2 (m2g) acting downwards and the tension in the string (FT) acting upwards. The angle between the weight and the slope is 30°, so we can use trigonometry to find the component of m2g acting parallel to the slope, which is m2g sin 30°.

Now, using Newton's second law, we can write the following equation for mass m2:

ΣF = m2a

Where ΣF is the sum of all the forces acting on m2. This can be written as:

FT - m2g sin 30° = m2a

This is the correct scalar equation for mass m2, which shows the relationship between the acceleration, a, and the tension in the string, FT. I hope this helps clarify the solution for you. Remember to always carefully consider the forces acting on an object and use relevant equations to solve problems in physics.