Question

A block of mass 5 kg is placed on a frictionless surface and pushed with a force of 20 N at an angle of 30° to the horizontal. What is the acceleration of the block?

• A. 3.46 m/s²
• B. 4.00 m/s²
• C. 3.00 m/s²
• D. 2.31 m/s²

Hint:

For forces at an angle, resolve into horizontal and vertical components; only the horizontal component affects acceleration on a frictionless surface.

Answer 1

The Correct Option is A

To find the block's acceleration:

1. Frictionless surface: horizontal force component causes acceleration.
2. Given: \( F = 20 \, \text{N} \), \( \theta = 30^\circ \), \( m = 5 \, \text{kg} \).
3. Calculate horizontal force: \[ F_x = F \cos \theta = 20 \times \cos 30^\circ. \]
4. Since \( \cos 30^\circ = \frac{\sqrt{3}}{2} \approx 0.866 \): \[ F_x = 20 \times 0.866 \approx 17.32 \, \text{N}. \]
5. Apply Newton's second law: \( a = \frac{F_x}{m} \). \[ a = \frac{17.32}{5} \approx 3.464 \, \text{m/s}^2. \]
6. Round to two decimal places: \[ 3.464 \approx 3.46 \, \text{m/s}^2. \]
7. Answer matches option (A).

Correct answer: \[ \boxed{3.46 \, \text{m/s}^2} \]