How to Calculate Forces and Acceleration of Boxes on a Frictionless Shelf?

[makerfeldt]

Homework Statement

A box of mass m2 = 3.7 kg rests on a frictionless horizontal shelf and is attached by strings to boxes of masses m1 = 1.2 kg and m3 = 2.1 kg as shown below. Both pulleys are frictionless and massless. The system is released from rest. After it is released, find the following.

The Attempt at a Solution

I found the relevant forces of gravity to be 18.62 on m1, and 27.44 on m3, but I have little clue of where to go from there. Any idea would be greatly appreciated.

 

[Simon Bridge]

Homework Statement

A box of mass m2 = 3.7 kg rests on a frictionless horizontal shelf and is attached by strings to boxes of masses m1 = 1.2 kg and m3 = 2.1 kg as shown below.

missing diagram?

Both pulleys are frictionless and massless. The system is released from rest. After it is released, find the following.

incomplete information.
Are m1 and m3 hanging off opposite sides of the shelf?

The Attempt at a Solution

I found the relevant forces of gravity to be 18.62 on m1, and 27.44 on m3, but I have little clue of where to go from there. Any idea would be greatly appreciated.

Draw a free-body diagram for each box and apply Newton's laws: ƩF=ma

 

[makerfeldt]

My apologies; the boxes m1 and m3 are indeed hanging off opposite sides of the shelf.

 

[Simon Bridge]

OK - so did you draw a free body diagram for each box?

 

[Nickie]

I would first clarify the problem by stating the assumptions and conditions given. It is stated that the shelf is frictionless, the pulleys are frictionless and massless, and the system is released from rest. This means that there are no external forces acting on the system, and the only forces involved are the gravitational forces between the boxes.

Next, I would approach the problem by using Newton's laws of motion. Since the system is released from rest, the initial acceleration of the system is 0 m/s^2. Using the equation F=ma, we can calculate the net force acting on the system. In this case, the net force is equal to the sum of the gravitational forces acting on the boxes.

Once we have calculated the net force, we can use Newton's second law, F=ma, to find the acceleration of the system. Since all the masses are connected by strings, they will all have the same acceleration.

Finally, we can use the equation of motion, s=ut+1/2at^2, to find the displacement of the boxes after a certain amount of time. We can also use this equation to find the velocities of the boxes at any given time.

In summary, to solve this problem, we need to use Newton's laws of motion and the equations of motion to calculate the net force, acceleration, and displacement of the boxes on the frictionless shelf. It is important to keep in mind the assumptions and conditions given in the problem and to use appropriate units and calculations to ensure accuracy.