Question

A 2 kg object is hanging vertically from a rope. The tension in the rope is 15 N. What is the acceleration of the object? (Assume \( g = 9.8 \, \text{m/s}^2 \))

• A. \( 1.0 \, \text{m/s}^2 \)
• B. \( 2.0 \, \text{m/s}^2 \)
• C. \( 0.5 \, \text{m/s}^2 \)
• D. \( 3.0 \, \text{m/s}^2 \)

Hint:

If the tension in a rope is less than the weight of an object, the object will experience a downward acceleration.

Answer 1

The Correct Option is A

The net force on the object is the difference between the tension and the weight of the object: \[ F_{\text{net}} = T - mg \] Where: - \( T = 15 \, \text{N} \) is the tension in the rope, - \( m = 2 \, \text{kg} \) is the mass of the object, - \( g = 9.8 \, \text{m/s}^2 \) is the acceleration due to gravity. The weight of the object is: \[ mg = 2 \times 9.8 = 19.6 \, \text{N} \] Now calculate the net force: \[ F_{\text{net}} = 15 \, \text{N} - 19.6 \, \text{N} = -4.6 \, \text{N} \] The negative sign indicates that the object is accelerating downward. Using Newton's second law: \[ a = \frac{F_{\text{net}}}{m} = \frac{-4.6}{2} = -2.3 \, \text{m/s}^2 \] Thus, the acceleration of the object is \( 2.3 \, \text{m/s}^2 \) downward.