Detailed Notes on Newton's Second Law of Motion

Newton's Second Law of Motion

Learning Intentions

• Explain the relationship between mass and acceleration.
• Use the second law of motion triangle to calculate force, mass, or acceleration.

Success Criteria

• Describe how unbalanced forces acting on an object can cause it to accelerate or decelerate.
• State Newton’s second law of motion and explain this law using appropriate examples.
• Calculate the net (unbalanced) force acting on an object.
• Manipulate the formula $(F=ma)$ appropriately to determine the unknown variable.
• Use Newton’s second law to connect the mass and weight of an object.

Newton's Second Law of Motion

• The net force on an object is equal to the object's mass multiplied by its acceleration.
• Formula: $F = ma$
  • $F$ is the net force, measured in Newtons (N).
  • $m$ is the mass, measured in kilograms (kg).
  • $a$ is the acceleration, measured in metres per second per second (m/s²).

Worked Example 1

• Problem: A net force causes a mass of 10 kg to accelerate at 2 m/s². Calculate the magnitude of the net force.
  • Given: $m = 10 \text{ kg}$, $a = 2 \text{ m/s}^2$
  • Using $F = ma$:
    • $F = (10 \text{ kg}) (2 \text{ m/s}^2) = 20 \text{ N}$
  • The magnitude of the net force is 20 N.

Worked Example 2

• Problem: A cyclist and a bike with a mass of 90 kg is moving forward with a total thrust force of 400 N, and the total drag force from air resistance and friction is 300 N backwards. Calculate the acceleration of the cyclist.
  • Given: $m = 90 \text{ kg}$, $F<em>{\text{thrust}} = 400 \text{ N}$, $F</em>{\text{drag}} = 300 \text{ N}$
  • The net force is the difference between the thrust force and the drag force:
    • $F<em>{\text{net}} = F</em>{\text{thrust}} - F_{\text{drag}} = 400 \text{ N} - 300 \text{ N} = 100 \text{ N}$
  • Using $F = ma$ to find acceleration:
    • $a = \frac{F}{m} = \frac{100 \text{ N}}{90 \text{ kg}} = 1.11 \text{ m/s}^2$
  • The acceleration of the cyclist is 1.11 m/s².

Mass vs. Weight

• In Physics, weight is a force, not a mass.
• Weight is the force from gravity acting on an object, measured in Newtons (N).
• Weight can be calculated using the formula:
  • $W = mg$
    • $W$ is weight.
    • $m$ is mass.
    • $g$ is gravitational acceleration.

Remember and Understand

• Define the term ‘weight force’.
• Describe what happens to a moving object if it is acted on by a net force in the same direction as its motion.
• Describe what happens to a moving object if it is acted on by a net force in the opposite direction to its motion.

Apply and Analyze

• Compare the acceleration of a bus full of passengers to that of an empty bus, if the same net force was used.
• Explain why a bike slows down on a level road when the rider stops pedaling.
• A net force causes a mass of 10 kg to accelerate at 2 m/s². Calculate the magnitude of the net force.

Evaluate and Create

• Create a poster that explains why trucks need a greater stopping distance than cars.