What is the Tension in the String Connecting Two Blocks?

[caela]

Homework Statement

Hi guys! I need some help with a homework problem. Quoted from my book:

"A 4 kg block, which is tied to another block, is pulled to the right by a tension force T = 78N. The system accelerates to the right at 2 m/s/s. If the frictional force by the table on the 4 kg block is 20N, what is the tension in the string connecting the two blocks?"

Homework Equations

Block to the right = 4 kg
T from right block to the right = 78 N
a = 2 m/s/s
Friction force = 20 N

The Attempt at a Solution

So I have my free body diagram drawn. On the Y axis (N floor, box and W earth, box = 40 N) and the X axis (T 78 N, to the left I have no idea how to figure out).

Thanks so much for your help! :)

 

[PhanthomJay]

Homework Statement

Hi guys! I need some help with a homework problem. Quoted from my book:

"A 4 kg block, which is tied to another block, is pulled to the right by a tension force T = 78N. The system accelerates to the right at 2 m/s/s. If the frictional force by the table on the 4 kg block is 20N, what is the tension in the string connecting the two blocks?"

Homework Equations

Block to the right = 4 kg
T from right block to the right = 78 N
a = 2 m/s/s
Friction force = 20 N

The Attempt at a Solution

So I have my free body diagram drawn. On the Y axis (N floor, box and W earth, box = 40 N) and the X axis (T 78 N, to the left I have no idea how to figure out).

Thanks so much for your help! :)

Caela, welcome to PF!
On the X axis, you have T=78N acting to the right (given). Now in your free body diagram. you also should have a tension force (in the cable between the 2 blocks) and a friction force
(between the table and block) which both act to the left (tension forces always pull away from the object on which they act, and friction forces always oppose the direction of relative motion or pending motion between the two contact surfaces). So now set up your equation using Newton's 2nd law to solve for the tension in the string connecting the blocks.