How Is Acceleration Calculated in a Frictionless Pulley System?

[mst3kjunkie]

The system shown in the figure is accelerating. Asume that there is no friction anywhere in the system and that the mass of the string can be neglected. The values of the masses are:

m1=5.00 kg
m2=8.00 kg

Determine the acceleration of the system.

Figure and work done so far shown here:
http://img104.imageshack.us/img104/6218/pulleyproblemop3.th.png

Where do I go from here? How do I solve for the acceleration?

 

[mst3kjunkie]

solved. ( ten character minimum )

 

[kyle8921]

To solve for the acceleration of the system, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. In this case, we have two masses (m1 and m2) connected by a string passing over a pulley, so we need to consider the forces acting on each mass separately.

For m1, the only force acting on it is the tension in the string, which is pulling it upwards. We can write this as:

T - m1g = m1a

Where T is the tension in the string, m1g is the weight of m1 (mass multiplied by acceleration due to gravity), and a is the acceleration of the system.

For m2, we have two forces acting on it - the tension in the string pulling upwards and its weight pulling downwards. We can write this as:

m2g - T = m2a

Combining these two equations, we get:

T = m1a + m1g

m2g - T = m2a

Substituting the value of T from the first equation into the second equation, we get:

m2g - (m1a + m1g) = m2a

Now, we can solve for a:

m2g - m1a - m1g = m2a

m2g - m1g = m2a + m1a

m2g - m1g = (m2 + m1)a

a = (m2g - m1g) / (m2 + m1)

Plugging in the values of m1 and m2, and using the acceleration due to gravity (g = 9.8 m/s^2), we get:

a = (8*9.8 - 5*9.8) / (8 + 5) = 3.27 m/s^2

Therefore, the acceleration of the system is 3.27 m/s^2.