Two blocks,joined by a string,have masses of 8.0 and 9.0 kg.They rest on a frictionless horizontal surface.A 2nd string,attached only to the 9.0-kg block,has horizontal force = 30 N applied to it.Both blocks accelerate.Find the tension in the string between the blocks.
A) 16 N
B) 2 N
C) 14 N
D) 64 N
E) 240 N

Question

Two blocks,joined by a string,have masses of 8.0 and 9.0 kg.They rest on a frictionless horizontal surface.A 2nd string,attached only to the 9.0-kg block,has horizontal force = 30 N applied to it.Both blocks accelerate.Find the tension in the string between the blocks.
A) 16 N
B) 2 N
C) 14 N
D) 64 N
E) ​240 N

Quizplus · Accepted Answer

Since the surface is frictionless, the force applied to the 9 kg block will cause it to accelerate, which in turn causes the 8 kg block to accelerate as well. To find the tension in the string, we need to use Newton's second law, which states that the net force on an object is equal to its mass times its acceleration. Let a be the acceleration of both blocks, then:
For the 9 kg block: 30 N - T = 9 kg * a
For the 8 kg block: T = 8 kg * a
where T is the tension in the string between the blocks. To solve for a, we can use the fact that both blocks have the same acceleration since they are connected by the same string, so:
30 N - T = (9 kg + 8 kg) * a
30 N - T = 17 kg * a
a = (30 N - T) / 17 kg
Substituting this into the equation for the tension in the string:
T = 8 kg * [(30 N - T) / 17 kg]
T = 240 N - (8/17)T
T = 240 N / (25/17)
T = 14.4 N
Therefore, the tension in the string between the blocks is approximately 14 N (choice C).

Two Blocks,joined by a String,have Masses of 8