A 3 kg block on a horizontal frictionless table is connected to a 2 kg hanging mass via a massless string over a pulley. If the system starts from rest, what is the acceleration and the string tension?

A 3 kg block on a horizontal frictionless table is connected to a 2 kg hanging mass via a massless string over a pulley. If the system starts from rest, what is the acceleration and the string tension?

• A. a ≈ 2.0 m/s^2; T ≈ 8 N
• B. a ≈ 3.0 m/s^2; T ≈ 9 N
• C. a ≈ 3.92 m/s^2; T ≈ 11.8 N
• D. a ≈ 1.0 m/s^2; T ≈ 5 N

Answer: (C)

When two masses are connected by a massless string over a pulley with no friction, both masses share the same magnitude of acceleration. The tension in the string acts on the mass on the table to pull it toward the pulley, and the hanging mass experiences gravity pulling it downward minus the tension. Set up equations: - For the block on the table: T = m1 a. - For the hanging mass: m2 g − T = m2 a. Combine them by substituting T from the first into the second: m2 g − m1 a = m2 a ⇒ m2 g = (m1 + m2) a ⇒ a = m2 g /(m1 + m2). Plug in m1 = 3 kg, m2 = 2 kg, g ≈ 9.8 m/s^2: a = (2)(9.8) / (3 + 2) = 19.6 / 5 = 3.92 m/s^2. Tension from T = m1 a: T = 3 × 3.92 ≈ 11.76 N (about 11.8 N). So the system accelerates at about 3.92 m/s^2, and the string tension is about 11.8 N.

When two masses are connected by a massless string over a pulley with no friction, both masses share the same magnitude of acceleration. The tension in the string acts on the mass on the table to pull it toward the pulley, and the hanging mass experiences gravity pulling it downward minus the tension.

Set up equations:

• For the block on the table: T = m1 a.

• For the hanging mass: m2 g − T = m2 a.

Combine them by substituting T from the first into the second:

m2 g − m1 a = m2 a ⇒ m2 g = (m1 + m2) a ⇒ a = m2 g /(m1 + m2).

Plug in m1 = 3 kg, m2 = 2 kg, g ≈ 9.8 m/s^2:

a = (2)(9.8) / (3 + 2) = 19.6 / 5 = 3.92 m/s^2.

Tension from T = m1 a:

T = 3 × 3.92 ≈ 11.76 N (about 11.8 N).

So the system accelerates at about 3.92 m/s^2, and the string tension is about 11.8 N.