NJC Unit 2 Forces and Moments

National Junior College Science Department | Physics 1 2. Forces & Moments Content Page 2.1 Types of forces ................................ ................................ ................................ .....................3 2.1.1 What is a force? ................................ ................................ ................................ ...........3 2.1.2 Contact forces ................................ ................................ ................................ .............4 2.1.3 Fields of forces ................................ ................................ ................................ ............6 2.1.4 Hooke’s law ................................ ................................ ................................ .................7 Compressive and tensile force ................................ ................................ .............................7 Hooke’s law ................................ ................................ ................................ .........................8 2.2 Drawing force diagrams ................................ ................................ ................................ .15 2.3 Moment and Torque ................................ ................................ ................................ ......20 2.3.1 Moment of a force ................................ ................................ ................................ ......20 2.3.2 Torque of a Couple ................................ ................................ ................................ ....24 2.4 Translational and rotational equilibrium ................................ ................................ .........28 2.4.1 Principle of moments ................................ ................................ ................................ .28 2.4.2 Centre of gravity ................................ ................................ ................................ ........29 2.4.3 Equilibrium ................................ ................................ ................................ .................30 2.5 Upthrust (H2 Physics only) ................................ ................................ ........................38

National Junior College Science Department | Physics 2 Learning Objectives 2.1 Types of forces (a) Describe the forces on a mass, charge and current -carrying conductor in gravitational, electric and magnetic fields, as appropriate. (b) H2: Show a qualitative understanding of forces including normal force, frictional force, buoyant force (upthrust), and viscous force, e.g. air resistance (knowledge of the concepts of coefficients of friction and viscosity is not required). H1: Show a qualitative understanding of forces including normal force, frictional force and viscous force, e.g. air resistance (knowled ge of the concepts of coefficients of friction and viscosity is not required). (c) Recall and apply Hooke’s law ( 𝐹 = 𝑘𝑥, where k is the force constant) to new situations or to solve related problems. 2.2 Moment and torque (d) Define and apply the moment of a force and the torque of a couple. (e) Show an understanding that a couple is a pair of forces which tends to produce rotation only. (f) Show an understanding that the weight of a body1 may be taken as acting at a single point known as its centre of gravity. 2.3 Translational and rotational equilibrium (g) Apply the principle of moments to new situations or to solve related problems. (h) Show an understanding that, when there is no resultant force and no resultant torque, a system is in equilibrium. (i) Use free -body diagrams and vector triangles to represent forces on bodies that are in rotational and translational equilibrium. 1 The term “body” (or “object”) is used to refer to a collection of matter that can be treated as having no internal structure, or an internal structure that can be ignored in typical contexts.

National Junior College Science Department | Physics 3 2.1 TYPES OF FORCES Self-study resources A SLS lesson on Hooke’s law and the different types of forces. for.edu.sg/types-of-forces 2.1.1 What is a force? In kinematics, we study the motion of objects , including accelerations which are changes in velocities. Physics is also a study of what can cause an object to accelerate. That cause is a force, which is, loosely speaking, a push or pull on the object. The force acts on the object to change its velocity. We define the unit of force in terms of the acceleration a force would give to a 1 kg body . Suppose we put that body on a horizontal, frictionless surface and pull horizontally, as shown in Fig. 2.1, such that the body has an acceleration of 1 m s–2. Then we can define our applied force as having a magnitude of 1 newton (abbreviated N). If we pulled with a force magnitude of 2 N, we would find that the acceleration is 2 m s –2. Thus, the acceleration is proportional to the force. Force is a vector quantity and thus has not only magnitude but also direction. So, if two or more forces act on a body, we find the resultant force (or net force) by adding them as vectors, following the rules of “01 Quantities and Measurements ”. A single force that has the same magnitude and direction as the calculated resultant force would then have the same effect as all the individual forces added together. This is known as the principle of superposition for forces. Forces are most often represented with a vector symbol such as F⃗⃗ or F, and a resultant force is represented with the vector symbol F⃗⃗ resultant, F⃗⃗ net, Fresultant or Fnet. For the rest of the notes, we drop the overhead arrows and just use the symbols to indicate the magnitude of the forces along that axis. Fig. 2.1

National Junior College Science Department | Physics 4 2.1.2 Contact forces This type of force acts when two interacting objects have physical contact with each other. Force Important situations Normal contact force. The force exerted by the surface of one object on the surface of another when they are in physical contact and prevents the objects from passing through each other. The force acts perpendicular (or “normal”) to the surface. • standing on the ground • one object sitting on top of another • object on an inclined surface • leaning against a wall • one object bouncing off another Friction. This is the force which arises when two surfaces rub over one another. Friction arises from the interlocking of the irregularities, as shown below. • pulling an object along the ground • vehicles cornering or skidding • sliding down a slope The harder the surfaces are pushed together, the larger the frictional force. • If an object is sliding along the ground, friction acts in the opposite direction to its motion. • If an object is stationary, but tending to slide – perhaps because it is on a slope – the force of friction acts up the slope to stop it from sliding down. Friction always acts along a surface, never at an angle to it. object pulled along surface object at rest on incline Drag or viscous force. This force is similar to friction. When an object moves through air, there is friction between it and the air. Also, the object has to push aside the air as it moves along. Together, these effects make up drag. Similarly, when an object moves through a liquid, it experiences a drag force. Drag acts to oppose the motion of an object; it acts in the opposite direction to the object’s velocity. It can be reduced by giving the object a streamlined shape. • vehicles moving • aircraft flying • parachuting • objects falling through air or water • ships sailing contact force

National Junior College Science Department | Physics 5 Force Important situations Tension. This is the force in a rope or string wh