Lesson Notes By Weeks and Term v5 - Grade 11

Lesson Video

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Performance objectives

• Define and apply Newton's First, Second, and Third Laws.
• Calculate static and kinetic friction forces.
• Analyze problems with objects connected by strings.
• Draw correct free-body diagrams.
• Apply Newton's Laws to systems in equilibrium.

Lesson summary

This week, we delve deeper into Newton's Laws of Motion, building upon what we've learned previously. Mastering these laws is crucial, as they form the bedrock of understanding how objects move and interact. From the simple act of walking to the complex engineering of vehicles and structures, Newton's Laws are at play. In a South African context, understanding these principles is vital for fields like civil engineering (designing safe bridges and buildings), automotive engineering (improving vehicle safety and fuel efficiency), and even sports science (optimizing athletic performance).

Lesson notes

2.1 Newton's Laws: A Quick Recap Newton's First Law (Law of Inertia): An object will remain at rest or continue moving at a constant velocity unless acted upon by a net external force. Inertia is the tendency of an object to resist changes in its state of motion.

Newton's Second Law: The net force acting on an object is equal to the mass of the object multiplied by its acceleration: ∑F = ma. The acceleration is in the same direction as the net force.

Newton's Third Law: For every action, there is an equal and opposite reaction. If object A exerts a force on object B, then object B exerts an equal and opposite force on object A. 2.2 Friction Friction is a force that opposes motion between surfaces in contact.

Static Friction (Fs): The force that prevents an object from starting to move when a force is applied. It has a maximum value (Fs,max) which is proportional to the normal force (N) pressing the surfaces together: Fs ≤ μsN, where μs is the coefficient of static friction.

Example: Imagine a heavy crate on a concrete floor in a warehouse. You push it gently. It doesn't move. That's static friction holding it in place. As you push harder, static friction increases to match your push, up to a maximum value.

Kinetic Friction (Fk): The force that opposes the motion of an object that is already moving. It is also proportional to the normal force: Fk = μkN, where μk is the coefficient of kinetic friction. μk is usually less than μs.

Example: Once you manage to get that crate moving across the warehouse floor, there's still friction opposing its movement. This is kinetic friction. It's generally easier to keep something moving than to start it moving, which is why μk is usually less than μs.

Important Notes on Friction: Friction always opposes motion (or the tendency for motion). The coefficient of friction (μ) is a dimensionless number that depends on the nature of the surfaces in contact. A higher coefficient means more friction. Friction converts kinetic energy into thermal energy (heat). That's why rubbing your hands together makes them warm. 2.3 Objects Connected by Strings and Pulleys When objects are connected by strings or ropes passing over pulleys, the tension in the string is a crucial factor.

Tension (T): The force transmitted through a string, rope, cable, or wire when it is pulled tight by forces acting from opposite ends. We assume ideal strings (massless and inextensible) unless stated otherwise. In such cases, the tension is uniform throughout the string.

Pulleys: Ideal pulleys change the direction of the force but do not change the magnitude of the tension (again, assuming they are massless and frictionless). 2.4 Free-Body Diagrams A free-body diagram is a visual representation of all the forces acting on an object. This is crucial for applying Newton's Second Law correctly. Draw the object as a point. Represent each force as an arrow, with the tail of the arrow starting at the point representing the object. The length of the arrow should be proportional to the magnitude of the force. Label each force clearly (e.g., Fg for gravitational force, FT for tension, FN for normal force, Ff for friction). 2.5 Worked Examples Example 1: Crate on a Surface with Friction A 50 kg crate is pulled across a horizontal floor with a force of 200 N at an angle of 30° above the horizontal. The coefficient of kinetic friction between the crate and the floor is 0.

2. Calculate the acceleration of the crate.

Solution: Draw a free-body diagram. Draw the crate as a point. Show the applied force (F) at 30 degrees, the weight (Fg) downwards, the normal force (FN) upwards, and the kinetic friction (Fk) to the left. Resolve the applied force into horizontal and vertical components. Fx = F cos(30°) = 200 N cos(30°) = 173.2 N Fy = F sin(30°) = 200 N sin(30°) = 100 N Calculate the weight of the crate. Fg = mg = 50 kg 9.8 m/s² = 490 N Calculate the normal force. Since the crate is not accelerating vertically, the sum of the vertical forces is zero. FN + Fy - Fg = 0 FN = Fg - Fy = 490 N - 100 N = 390 N Calculate the kinetic friction force. Fk = μkN = 0.2 390 N = 78 N Apply Newton's Second Law in the horizontal direction. ∑Fx = ma Fx - Fk = ma 173.2 N - 78 N = 50 kg a 95.2 N = 50 kg a a = 95.2 N / 50 kg = 1.904 m/s² Therefore, the acceleration of the crate is 1.904 m/s² to the right.

Example 2: Two Objects Connected by a String Over a Pulley Two masses, m1 = 2 kg and m2 = 3 kg, are connected by a light string that passes over a frictionless pulley. The system is set up such that m2 hangs vertically and m1 is on a frictionless horizontal surface. Determine the acceleration of the system and the tension in the string.

Solution: Draw free-body diagrams for each mass.

For m1: Tension (T) to the right, weight (Fg1) downwards, normal force (FN) upwards.

For m2: Tension (T) upwards, weight (Fg2) downwards. Apply Newton's Second Law to each mass.