Lesson Notes By Weeks and Term v5 - Grade 11

Lesson Video

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Performance objectives

• Apply Newton's Second Law (Fnet = ma) to solve problems.
• Calculate static and kinetic frictional force.
• Solve problems involving objects on inclined planes.
• Distinguish between static and kinetic friction.
• Draw accurate free-body diagrams for various scenarios.

Lesson summary

This week, we delve deeper into Newton's Laws of Motion, building upon the foundational knowledge from previous grades. Understanding these laws is crucial for explaining and predicting the motion of objects, from cars on our roads to the trajectory of a cricket ball. These principles govern everything from the everyday act of walking to the design of safer vehicles and bridges. A solid grasp of Newton's Laws is not just about passing exams; it's about understanding the physical world around us and opening doors to careers in engineering, physics, and other STEM fields that are vital for South Africa's development. The application of these laws will be the focus of the week.

Lesson notes

2.1 Newton's Second Law: Fnet = ma Newton's Second Law states that the net force (Fnet) acting on an object is directly proportional to the object's mass (m) and its acceleration (a). In simpler terms, the greater the force acting on an object, the greater its acceleration. The greater the object's mass, the smaller its acceleration for the same force.

Fnet: The net force is the vector sum of all forces acting on the object. This means you need to consider the direction of each force and add them accordingly. If forces are in opposite directions, you subtract them. m: Mass is a measure of an object's inertia, its resistance to changes in motion. Measured in kilograms (kg). a: Acceleration is the rate of change of velocity. Measured in meters per second squared (m/s²).

Important: Fnet and a are vectors, meaning they have both magnitude and direction. The direction of the acceleration is always the same as the direction of the net force. 2.2 Friction Friction is a force that opposes motion between two surfaces in contact.

There are two main types of friction: Static Friction (fs): This force prevents an object from starting to move. It's a variable force that increases to match the applied force, up to a maximum value.

The maximum static friction is given by: `fs(max) = μs N` `μs` is the coefficient of static friction (a dimensionless number). `N` is the normal force (the force exerted by a surface perpendicular to the object resting on it).

Kinetic Friction (fk): This force opposes the motion of an object that is already moving. It's generally constant.

The kinetic friction is given by: `fk = μk N` `μk` is the coefficient of kinetic friction (a dimensionless number). `N` is the normal force.

Key Point: The coefficient of static friction (μs) is usually greater than the coefficient of kinetic friction (μk). This means it takes more force to start an object moving than to keep it moving. 2.3 Inclined Planes An inclined plane is a flat surface tilted at an angle to the horizontal. When an object is on an inclined plane, the force of gravity (weight) needs to be resolved into two components: Weight component parallel to the plane (Wparallel or Wx): This component causes the object to accelerate down the plane. `Wx = W sin(θ) = mg * sin(θ)` where θ is the angle of the incline. Weight component perpendicular to the plane (Wperpendicular or Wy): This component is balanced by the normal force. `Wy = W cos(θ) = mg * cos(θ)` 2.4 Free-Body Diagrams A free-body diagram is a visual representation of all the forces acting on an object. It's essential for solving problems involving Newton's Laws.

Here's how to draw one: Represent the object as a dot or a box. Draw arrows representing each force acting on the object. The length of the arrow should be proportional to the magnitude of the force. Label each force clearly (e.g., Fg for gravity, FT for tension, FN for normal force, Ff for friction). Indicate the coordinate system (x and y axes). This is particularly important for inclined planes.

Worked example

Example 1: Object on a Horizontal Surface

A 5 kg box is pulled across a horizontal surface with a force of 20 N at an angle of 30° above the horizontal. The coefficient of kinetic friction between the box and the surface is 0.

2. Calculate the acceleration of the box.

Solution:

Draw a free-body diagram:

Fg (weight) downwards

FN (normal force) upwards

FA (applied force) at 30° above the horizontal

Ff (kinetic friction) opposing the motion

Resolve the applied force into horizontal (FAx) and vertical (FAy) components:

FAx = FA cos(30°) = 20 N * cos(30°) ≈ 17.32 N

FAy = FA sin(30°) = 20 N * sin(30°) = 10 N

Calculate the normal force:

Since the box is not accelerating vertically, FN + FAy = Fg

FN = Fg - FAy = (5 kg 9.8 m/s²) - 10 N = 49 N - 10 N = 39 N

Calculate the kinetic friction force:

Ff = μk N = 0.2 * 39 N = 7.8 N

Calculate the net force in the horizontal direction:

Fnetx = FAx - Ff = 17.32 N - 7.8 N = 9.52 N

Apply Newton's Second Law to find the acceleration:

Fnetx = ma

a = Fnetx / m = 9.52 N / 5 kg ≈ 1.90 m/s²

Example 2: Object on an Inclined Plane