H1.04. 2022 Forces Notes

CJC H1 PHYSICS LECTURE NOTES JC1 2022 4(1) 4 Forces Main concept(s) 1. Meaning of force 2. Elastic force and Hooke’s law 3. Meaning and examples of contact force and non-contact force 4. Friction and viscous forces 5. Turning effects of a Force, moments and torque of a couple 6. Conditions for Equilibrium 7. Fluid (or hydrostatic) pressure 8. Upthrust, Archimedes’ Principle and Principle of Floatation Learning Outcome(s) Candidates should be able to: (a) recall and apply Hooke’s law (F = kx, where k is the force constant) to new situations or to solve related problems (b) describe the forces on a mass, charge and current-carrying conductor in gravitational, electric and magnetic fields, as appropriate (c) show a qualitative understanding of normal contact forces, frictional forces and viscous forces including air resistance (no treatment of the coefficients of friction and viscosity is required) (d) show an understanding that the weight of a body may be taken as acting at a single point known as its centre of gravity (e) define and apply the moment of a force and the torque of a couple (f) show an understanding that a couple is a pair of forces which tends to produce rotation only (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 a vector triangle to represent forces in equilibrium Introduction The concept of forces is fundamental in Physics and spans across many different topics. This chapter briefly overviews two broad categories of forces, namely contact and non-contact forces. Following that, a more in-depth study of some contact forces including resistive forces, elastic force, fluid pressure and upthrust is presented. You will also learn the turning effects of a force as well as the conditions for a system to be in equilibrium.

CJC H1 PHYSICS LECTURE NOTES JC1 2022 4(2) 1. 4.1 The Meaning of Force • A force is a push or pull. • Exists as a result of interaction between 2 bodies. • Whenever there is an interaction between two bodies, there is a force upon each of the bodies. • Force is a vector quantity that has both magnitude and direction. 1. 4.2 Broad categories of Forces All forces (interactions) between bodies can be placed into two broad categories: • Contact forces are those types of forces that result when the two interacting bodies are physically in contact with each other. • Non-contact forces are forces resulting from action -at-a-distance. These forces between two interacting bodies, which are able to exert a push or pull on each other despite their physical separation. Examples Contact forces Non-contact forces Friction Air Resistance Tension Applied Force Normal Contact Force Spring Force Gravitational Force Electrical Force Magnetic Force The usual abbreviations for the forces are shown in the next table: Type of Force Examples Denoted By Normal Contact Force between objects when they are in contact. This force acts normal (perpendicular) to the surfaces in contact. N Friction Force exerted by a surface as an object moves or try to move across it. Direction of force is such that it opposes the relative motion of the object. f Tension Force transmitted through a cable when forces acting from opposite ends pull it tight. The force is directed along the length of the wire and pulls equally on the objects on the opposite ends. T Air Resistance Force which acts upon objects as they travel through the air. The force of air resistance opposes the motion of an object. fair Spring Force exerted by a compressed or stretched spring. A force acts in the direction, which restores the spring to its equilibrium position. Fspring

CJC H1 PHYSICS LECTURE NOTES JC1 2022 4(3) Gravitational 1. Force of attraction between two masses. 2. The “weight” of an object. [Weight is the force experienced by a mass in a gravitational field.] 3. Acts on the centre of gravity of an object Fg or W Nuclear Cause of beta decay. -- Force of attraction between protons and neutrons in the nucleus. -- 1. 4.3 Overview of Non-contact Forces & Force Fields Two bodies may exert a force on each other even without being in contact. Each of these bodies set up a field of force (or force field) around it. The fields of the two bodies interact, producing a force on each body. Only fields of the same nature can int eract e.g. one gravitational field can interact with another gravitational field but does not interact with an electric field or a magnetic field. Gravitational Forces Gravitational forces exist between any two bodies with mass. These forces only attract. (To be discussed later in detail under the topic of Gravitation) Electric Forces Electric force occurs between electrically charged bodies. Like charges repel and unlike charges attract. (To be discussed later in detail under the topic of Electric Field) Magnetic Forces Magnetic forces exist between any two moving electric charges. Moving electric charges and electrical currents create mag netic fields. Consequently, if you have two moving electric charges or current-carrying conductors, these will create magnetic fields. The magnetic force can be attractive or repulsive. (To be discussed later in detail under the topic of Electromagnetism)

CJC H1 PHYSICS LECTURE NOTES JC1 2022 4(4) 1. 4.4 Elastic (or Restoring) Force & Hooke’s Law 4.4.1 Hooke’s Law Consider a stretched spring. In order to return to its original state, a restoring force F is exerted by the spring. Hooke’s Law is given by the equation: In the form of magnitude only, F = kx In the form of vector, xkF  −= Where : F is the restoring force by elastic body (N) k is the force (or spring) constant (N m-1) [i.e. a measure of stiffness] x is the extension of the body (m) The negative sign (-) indicates that the restoring force always points in a direction opposite to the extension of the elastic body. Hooke’s Law states that force by an elastic body is directly proportional to its extension, provided the limit of proportionality has not been exceeded.

CJC H1 PHYSICS LECTURE NOTES JC1 2022 4(5) For more information on the graph of Force vs Extension, please refer to Appendix A. Quiz The natural l ength of a spring is L o. Sketch the graph of elastic force (F) against TOTAL length of the spring (L). Is F proportional to L? Solution: 4.4.2 Springs in Parallel Extension is same for both springs. So x1 = x2 = x However, the restoring forces are not equal if the spring constants differ. Applied Force is balanced by the Total Restoring Forces, i.e. Applied Force = F1 + F2 [Assume springs have negligible mass.] keff x = k1 x1 + k2 x2 Since x1 = x2 = x, keff = k1 + k2 where keff is the effective spring constant.

CJC H1 PHYSICS LECTURE NOTES JC1 2022 4(6) 4.4.3 Springs in Series Assume springs have negligible mass. Then, restoring force is same for both springs. So F1 = F2 = Applied force F However, the extensions are not equal if the spring constants differ. Total extension, x = x1 + x2 2 2 1 1 eff k F k F k F += Since F1 = F2 = F, 21eff k 1 k 1 k 1 += where keff is the effective spring constant. Example 1 A spring P of force constant 6 N m-1 is connected in series with a spring Q of force constant 3 N m-1as shown in the diagram. One end of the combination is securely anchored and a force of 0.6 N is applied to the other end. a) What is the extension for each spring? Solution: When the 0.6 N force is exerted, an elastic force is generated in the spring , which tends to rest