Solved Examples of Applying Newton's Second Law

📚 Quick Study Guide

• 🍎 Newton's Second Law: The acceleration of an object is directly proportional to the net force acting on the object, is in the same direction as the net force, and is inversely proportional to the mass of the object.
• 🔢 Formula: $F = ma$, where:
  • $F$ is the net force acting on the object (in Newtons, N)
  • $m$ is the mass of the object (in kilograms, kg)
  • $a$ is the acceleration of the object (in meters per second squared, m/s²)
• 📐 Units: Ensure all quantities are in SI units (kg, m, s) before applying the formula.
• 💡 Problem Solving Tips:
  • Draw a free-body diagram to visualize forces.
  • Resolve forces into components along x and y axes.
  • Apply $F = ma$ separately for each axis.
• 🏋️‍♀️ Weight: The force of gravity acting on an object: $W = mg$, where $g$ is the acceleration due to gravity (approximately $9.8 m/s^2$ on Earth).

🧪 Practice Quiz

1. A 2 kg block is pulled across a frictionless surface with a force of 10 N. What is the acceleration of the block?
   1. 2 m/s²
   2. 5 m/s²
   3. 10 m/s²
   4. 20 m/s²
2. A net force of 20 N is applied to an object, causing it to accelerate at 4 m/s². What is the mass of the object?
   1. 4 kg
   2. 5 kg
   3. 8 kg
   4. 10 kg
3. A 5 kg object is subjected to two forces: 15 N to the right and 5 N to the left. What is the net force acting on the object?
   1. 5 N to the left
   2. 10 N to the right
   3. 20 N to the right
   4. 25 N to the left
4. A 3 kg ball is dropped from a height. What is the force of gravity acting on the ball (assume g = 9.8 m/s²)?
   1. 9.8 N
   2. 19.6 N
   3. 29.4 N
   4. 39.2 N
5. An object with a mass of 8 kg accelerates at 3 m/s². What is the net force acting on it?
   1. 5 N
   2. 11 N
   3. 24 N
   4. 32 N
6. A car of mass 1000 kg accelerates from 0 to 20 m/s in 10 seconds. What is the net force acting on the car?
   1. 1000 N
   2. 2000 N
   3. 3000 N
   4. 4000 N
7. A force of 50 N is applied to an object, which experiences an acceleration of 2.5 m/s². What is the mass of the object?
   1. 10 kg
   2. 20 kg
   3. 125 kg
   4. 200 kg