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. \( 2.3 \, \text{m/s}^2 \)
• 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

Given:

• Mass of the object: \( m = 2 \, \text{kg} \)
• Tension in the rope: \( T = 15 \, \text{N} \)
• Acceleration due to gravity: \( g = 9.8 \, \text{m/s}^2 \)

Step 1: Use Newton's Second Law of Motion

The net force acting on the object is the difference between the tension in the rope and the gravitational force: \[ F_{\text{net}} = T - mg \] where: - \( T \) is the tension in the rope, - \( mg \) is the gravitational force acting on the object. The net force causes the object to accelerate, so according to Newton’s second law: \[ F_{\text{net}} = ma \] where: - \( a \) is the acceleration of the object, - \( m \) is the mass of the object.

Step 2: Set up the equation for acceleration

Combining the equations for \( F_{\text{net}} \) and \( ma \): \[ T - mg = ma \] Substituting the known values: \[ 15 - (2 \times 9.8) = 2a \] \[ 15 - 19.6 = 2a \] \[ -4.6 = 2a \]

Step 3: Solve for acceleration

\[ a = \frac{-4.6}{2} = -2.3 \, \text{m/s}^2 \] The negative sign indicates that the object is accelerating downward, but the magnitude of the acceleration is: \[ \boxed{2.3 \, \text{m/s}^2} \]