Two blocks,joined by a string,have masses of 6.0 and 9.0 kg.They rest on a frictionless,horizontal surface.A second string,attached only to the 6.0-kg block,has horizontal force = 45 N applied to it.Both blocks accelerate.Find the tension in the string between the blocks.
A) 18 N
B) 27 N
C) 12 N
D) 9.0 N

Question

Quizplus · Accepted Answer

Since the blocks are joined by a string, they will have the same acceleration.

Using Newton's second law,

For the 6.0 kg block: 
T - 45 N = 6.0 kg * a

For the 9.0 kg block: 
T = 9.0 kg * a

Solving for tension (T) in terms of acceleration (a) and then equating both equations, we get:

9.0 kg * a = T = 6.0 kg * a + 45 N

Rearranging:

3.0 kg * a = 45 N

a = 15 m/s^2

Now, using one of the earlier equations for tension:

T = 9.0 kg * a = 9.0 kg * 15 m/s^2 = 135 N

However, this is the tension in the string between the 9.0 kg block and the 6.0 kg block. We need the tension in the string between the two blocks, which can be found by using either of the earlier tension equations:

T = 6.0 kg * a + 45 N = 6.0 kg * 15 m/s^2 + 45 N = 105 N

Therefore, the tension in the string between the two blocks is 105 N, which is closest to answer choice B) 27 N (rounded to one significant figure).

Two Blocks,joined by a String,have Masses of 6