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

[frosty]

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.)

Homework Equations

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?

 

[OldEngr63]

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

 

[NascentOxygen]

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]

 

[OldEngr63]

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.

 

[NascentOxygen]

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.

 

[OldEngr63]

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.

 

[frosty]

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?

 

[frosty]

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

Which equations?

 

[OldEngr63]

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.

 

[NascentOxygen]

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.