In the same system, what is the tension in the rope?

In the same system, what is the tension in the rope?

• A. 19.6 N
• B. 29.4 N
• C. 58.8 N
• D. 9.8 N

Answer: (A)

In this setup, the rope has the same tension throughout and both masses accelerate together. Use Newton’s second law for each mass. For the block on the table, the only horizontal force is the rope’s tension, so T = m1 a. For the hanging mass, gravity pulls down and the rope pulls up, so m2 g − T = m2 a. Combine these: from T = m1 a we get a = T/m1. Substitute into the second equation: m2 g − T = m2 (T/m1). Solve for T: m2 g = T (1 + m2/m1) ⇒ T = (m1 m2 g) / (m1 + m2). Plug in m1 = 3 kg, m2 = 6 kg, g = 9.8 m/s²: T = (3 × 6 × 9.8) / (3 + 6) = 18 × 9.8 / 9 = 19.6 N. The rope’s tension is 19.6 N, which is smaller than the hanging mass’s weight (58.8 N) because part of the weight accelerates the system.

In this setup, the rope has the same tension throughout and both masses accelerate together. Use Newton’s second law for each mass.

For the block on the table, the only horizontal force is the rope’s tension, so T = m1 a.

For the hanging mass, gravity pulls down and the rope pulls up, so m2 g − T = m2 a.

Combine these: from T = m1 a we get a = T/m1. Substitute into the second equation:

m2 g − T = m2 (T/m1).

Solve for T: m2 g = T (1 + m2/m1) ⇒ T = (m1 m2 g) / (m1 + m2).

Plug in m1 = 3 kg, m2 = 6 kg, g = 9.8 m/s²:

T = (3 × 6 × 9.8) / (3 + 6) = 18 × 9.8 / 9 = 19.6 N.

The rope’s tension is 19.6 N, which is smaller than the hanging mass’s weight (58.8 N) because part of the weight accelerates the system.