Tension Pull problem w/friction

[cocomoj]

Please Help! Tension Pull problem w/friction

Hello all, I am having a bit of trouble on this for some reason.

On a horizontal plane, a 10kg box and a 20kg box are tied together by a rope, and the 20kg box is being pulled by another rope with a force of 200N. The coefficient of friction is 0.500

1. What is the acceleration of the blocks?
2. What is the tension in the rope connecting the boxes?
3. What is the change in KE?
4. What is the change in thermal/internal energy of the block/floor
system?

I know the answers to the questions, but need to know how to find them, especially question #2.

Thanks in advance,
Jason

 

[cocomoj]

I got as far as drawing the two free body diagrams. In box one and two I had figured friction force for them, but could not figure the tension force for them, so then I could not find the acceleration.

 

[cocomoj]

On box 1 (10kg) I got these values for the forces:

Weight(downward)= (0,-98)
Normal(upward)= (0,98)
Tension(to the right)= (?,0)
Friction(to the left)= (-49,0)

On box 2 (20kg) I got these values for the forces:

Weight(downward)= (0,-196)
Normal(upward)= (0,196)
Pull(to the right)= (200,0)
Tension(to the left)= (?,0)
Friction(to the left)= (-98,0)

To find the sum of the forces for the equation Fsum = ma I need the tension right? My question is how do I find it?

 

[cocomoj]

Oh yeah I forgot to put in the original equation that the 200N pull moves the blocks from rest over a distance of 2 meters.

 

[cocomoj]

Could someone please steer me in the right direction? I don't want anyone to do my work for me, I want to do it all, but my book is not explaining this concept to me.

Thanks,
Jason

 

[gnome]

First, look at the two blocks + the interconnecting rope as a single unit. This let's you ignore the unknown tension and solve for the acceleration A of the combined system.

Once you've done that, what do you know about a₁ and a₂ as compared to A?

Knowing a₁ and a₂ let's you look at each block individually and solve for the net force acting on the individual block, and using that you can find the tension in the connecting rope.

 

[cocomoj]

Thank You gnome, I finally figured it out. Not combining the two really threw me off. Thanks again.