Lesson Notes By Weeks and Term v4 - SHS 2
KINEMATICS
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KINEMATICS
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Subject: Physics
Class: SHS 2
Term: 1st Term
Week: 11
Grade code: 2.1.3.LI.3
Strand code: 1
Sub-strand code: 3
Content standard code: 2.1.3.CS.1
Indicator code: 2.1.3.LI.3
Theme: MECHANICS AND MATTER
Subtheme: KINEMATICS
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In our daily lives, we see vehicles making turns all the time – at roundabouts like the Ako Adjei Interchange in Accra, on the winding roads to Aburi, or even on the sharp curves of the new interchanges. Have you ever wondered why you feel pushed to the side when a car turns? Or why some sharp curves on major highways like the N1 are tilted inwards? This is not by accident; it is pure physics at work! Today, we will explore the forces that allow a car to safely navigate a curve. We will learn why a car might skid if it goes too fast on a flat road and how civil engineers use a clever technique called "banking" to make our roads safer.
Part 1: Motion on a Flat Curve and Skidding
Let us first consider a car moving around a flat, circular path, like a roundabout. The Essential Force: For any object to move in a circle, it needs a force constantly pulling it towards the centre of the circle. This force is called the centripetal force (F_c). It is given by the formula: `F_c = mv²/r`, where 'm' is the mass, 'v' is the speed, and 'r' is the radius of the circle. Source of the Force: On a flat road, what provides this centripetal force? It is the static friction (f_s) between the car's tyres and the road surface. This frictional force is directed towards the centre of the turn. The Condition for a Safe Turn: To make the turn without slipping, the required centripetal force must be less than or equal to the maximum available static friction. Required Force: `F_c = mv²/r` Available Force: `f_s(max) = μ_s * N`, where `μ_s` is the coefficient of static friction and `N` is the normal reaction force. On a flat road, the normal reaction `N` is equal to the weight of the car, `mg`. So, `f_s(max) = μ_s * mg`. What is Skidding? Skidding occurs when the speed of the vehicle is so high that the required centripetal force (`mv²/r`) becomes greater than the maximum available frictional force (`μ_s * mg`). The tyres lose their grip, and the car slides outwards, away from the centre of the curve, often leading to an accident.