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

Input Data:

• Object Mass: \( m = 2 \, \text{kg} \)
• Rope Tension: \( T = 15 \, \text{N} \)
• Gravitational Acceleration: \( g = 9.8 \, \text{m/s}^2 \)

Procedure:

Step 1: Apply Newton's Second Law

The net force (\( F_{\text{net}} \)) on the object is the difference between the upward tension (\( T \)) and the downward gravitational force (\( mg \)): \[ F_{\text{net}} = T - mg \] Newton's second law states that the net force equals mass times acceleration (\( ma \)): \[ F_{\text{net}} = ma \]

Step 2: Formulate the Acceleration Equation

Equating the two expressions for net force: \[ T - mg = ma \] Substitute the given values: \[ 15 - (2 \times 9.8) = 2a \] Perform the calculation: \[ 15 - 19.6 = 2a \] \[ -4.6 = 2a \]

Step 3: Calculate the Acceleration

Solve for \( a \): \[ a = \frac{-4.6}{2} = -2.3 \, \text{m/s}^2 \] The negative acceleration signifies downward motion. The magnitude of the acceleration is: \[ \boxed{2.3 \, \text{m/s}^2} \]