A simple problem using newton's laws?

Question

I just came back to studying physics after a month break, and I'm starting to get my feet wet again. I've come across a problem which I just cannot figure out. Two boxes are connected with a length of rope connecting the top of the bottom box to the bottom of the top box. There is also a rope coming out of the top of the top box. Each box is 10 kg, the mass of the strings is negligible. The boxes are accelerated upwards at 5 m/s^2. I need to find the tension in both strings.

Now, I know I should use F = ma (F = 10*5 = 50?), but I also need to incorporate g = 9.8 m/s^2... How do I do this problem? Again, I apologize for the triviality of the problem.

Answer 1

Ok represent both boxes by a point for each and connect the point with a line. Draw a line from the top point going up. This line represents the rope pulling up.

Now for the top box the forces acting are a force pulling up, the weight of the box pulling down, and the tension of the bottom rope pulling up. So,

ma = T - mg -T2 where T is the force pulling up and T2 is the rope from the bottom pulling down

The bottom box has a force T2 acting up and gravity pulling down. So for teh second box

ma = T2 - mg

a is the same for both boxes. Now solving for T2 in second equation

T2 = m(a+g)

Going to the first equation

ma = T - mg - T2 = T - mg - m(a+g) = T - 2mg - ma

2ma = T-2mg

T = 2m*(a+g)

Answer 2

acceleration is 5 + 9.8 m/s^2 = 14.8m/s^2
for the bottom box the 'weight' is 10kg x 14.8 =148N which is the tension in the string between the boxes.
for the higher string the tension is the weight of both boxes, or 2 x 148

Answer 3

the tension on the top string is 296 newtons
14.8 m/s^2 * 20 kg
the tension on the bottom string is 148 newtons
14.8 m/s^2 * 10 kg

Answer 4

0 tension since both boxes are moving and being accelerated at the same speed.