# Dynamics Problem -- box accelerated horizontally via a mass & pulley system

• frosty
In summary: The tension is the constraint in the system that has to be satisfied. So you have to use the equations of motion of the blocks (F=ma) and the constraint (tension) to solve for the acceleration of the system as a whole.In summary, the conversation discusses the problem of finding the magnitude of acceleration of a 1.0 kg box on a horizontal frictionless surface, which has been accelerated by attaching a 1.5 kg mass to it. The conversation includes drawing a free body diagram, calculating the force of gravity on the 1.5 kg object, and discussing the equations of motion and kinematic constraints that need to be considered in solving the problem. The conversation emphasizes the importance of working through each step of the problem

## Homework Statement

A 1.0 kg box on a horizontal frictionless surface is accelerated by attaching a 1.5 kg mass as shown in the diagram. What is the magnitude of acceleration of the box?(Remember, both boxes accelerate.)

F = ma

## The Attempt at a Solution

I drew a free body diagram of all the forces on the system.

The only thing I can calculate from here is the force of gravity on the 1.5 kg object.
Fg = mg
Fg = (1.5 kg) (-9.81m/s^2)
Fg = -14.7 N

Where do I go from here?

Write the two equations of motion, one for each block and then impose the kinematic constraint existing between the two of them.

frosty said:
Where do I go from here?
You have a force of 14.7N accelerating a body of mass 2.5kg. You're almost done.

BTW, frosty ... http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif [Broken]

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NascentOxygen said:
You have a force of 14.7N accelerating a body of mass 2.5kg. You're almost done.

It is not a good practice to jump to the answer. Far better to work through the equations of motion, see how they can be combined to get the final answer. In more complicated situations, it is usually not possible to simply jump to the final calculation.

Chestermiller and PhanthomJay
OldEngr63 said:
It is not a good practice to jump to the answer. Far better to work through the equations of motion
Even better is to be adept at both---using short working when that is all that's required, such as for questions like this that you typically find on multiple-choice achievement tests, and using more thorough analysis when more parameters are sought.

An A grade student will be able to demonstrate how the result of one confirms the other.

NascentOxygen said:
Even better is to be adept at both---using short working when that is all that's required, such as for questions like this that you typically find on multiple-choice achievement tests, and using more thorough analysis when more parameters are sought.

Anyone requesting help on PF for a problem such as this is clearly a beginner. Beginners do not need encouragement to cut corners. They need to learn to work through every step of the problem, without skipping steps. Only then, after the whole idea is mastered will the, on their own, begin to skip steps.

As an engineering professor, I have seen far too many students who could "see" the answer to the simple problems, but they had no idea how to systematically approach a more complex problem. I think that they must have been previously taught by NacentOxygen.

NascentOxygen said:
You have a force of 14.7N accelerating a body of mass 2.5kg. You're almost done.

BTW, frosty ... http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif [Broken]
I got the answer but I don't see connection between the two. What about the tension on the 1.5 kg object why is that ignored?

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OldEngr63 said:
Write the two equations of motion, one for each block and then impose the kinematic constraint existing between the two of them.
Which equations?

Frosty, thank you for making my point with NacentOxygen so neatly. This is exactly why I said, you need to write the two equations of motion, one for each block, and then impose the kinematic constraint existing between the two of them.

Write F = m*a for each block, including in the force sums the tension in the cord that joins the two blocks. Then see if you can carry out the next step on your own.

frosty said:
I got the answer but I don't see connection between the two. What about the tension on the 1.5 kg object why is that ignored?
It's not ignored. That tension is what causes the blocks to move as one body, it causes the 1kg block to follow along.