RI 2022 Forces

Chapter 4 RAFFLES INSTITUTION 2022 YEAR 5-6 PHYSICS DEPARTMENT FORCES Content • Types of forces • Equilibrium of forces • Turning effects of forces • Centre of gravity Learning Outcomes 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 mass, charge and current-carrying conductor in gravitational, electric and magnetic fields, as appropriate. · (To be covered in later topics.) (c) show 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 c9uple. (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. U) derive, from the definitions of pressure and density, the equation p = pgh. (Not in H1) (k) solve problems using the equation p = pgh. (Not in H1) (I) show an understanding of the origin of the force of upthrust acting on a body in a fluid. (Not in H1) (m) state that an upthrust is equal in magnitude and opposite in direction to the weight of the fluid displaced by a submerged or floating object. (Not in H1) (n) calculate the upthrust in terms of the weight of the displaced fluid. (Not in H1) (o) recall and apply the principle that, for an object floating in equilibrium, the upthrust is equal in magnitude and opposite in direction to the weight of the object to new situations or to solve related problems. (Not in H1) 1

4.1 Y(lo/, there's empty space hllrll fllf' u, to cniwl ... You silly worm, this space is for students to jot down important notes. 4.2 Weight When lab&lli ng fore&S ina Fru Body Diagram, you nud to write out 'weight", 'normal contact force " in full, insteod of just WorN . Normal contact force RAFFLES INSTITUTION 2022 YEAR 5-6 PHYSICS DEPARTMENT Introduction To date, physicists recognize four fundamental forces in nature: 1. The gravitational force 2. The electromagnetic force 3. The strong nuclear force} not in the syllabus 4. The weak (nuclear) force All other forces we know can be derived from these four fundamental forces. Other than the gravitational force, most forces such as pushes, pulls and other contact forces like the normal force and friction, can be considered due to the electromagnetic force acting at the atomic level. In the H2 Physics syllabus, you will learn that a mass experiences a gravitational force in a gravitational field, a charge experiences an electric force in an electric field and a current carrying conductor. experiences a magnetic force in a magnetic field. These forces will be covered in later topics. T es of Forces For a body near the surface of the Earth, its weight W, is defined as the force experienced by a body of mass m in a gravitational field and can be expressed as W=mg where g is the acceleration of free fall. This force acts vertically downwards towards the centre of the Earth through a single point on the body known as its centre of gravity (e.g.). w W: weight of the body The normal contact force N is the force exerted on a body when it is in contact with a surface. The normal contact force is always perpendicular to the contact surface and points away from that surface. N N: normal contact force on the body 2

Friction Furthu vcplanation of static, sliding/kinetic friction can be found in Appendix A. Tension and Compression Examples (Sketch and label the forces acting on each block) You can use symbols (e.g. N, n to label forces provided you have a legend for them.I! RAFFLES INSTITUTION 2022 YEAR 5-6 PHYSICS DEPARTMENT Friction is the force that acts to oppose the relative motion or tendency of relative motion between two surfaces in contact. It acts parallel to the two surfaces In contact. Advantages: Enables a person to walk and hold objects, rotating wheels to move without slipping etc. Disadvantages: Causes objects to wear out and energy wasted in the form of heat. Examples of friction: • Static friction. • Sliding / kinetic friction. • Rolling friction - resistance produced when a rolling body moves over a surface. • Viscous forces or fluid friction - the friction between moving fluids or between fluids and solids. When an object such as a bar (or rod or wire) is pulled at its ends, we say a force F is pulling on the bar, and the magnitude of the force is called the tension in the bar, often denoted by T. A bar in tension: F .. IIIIC============-• F When the object is pushed on both ends, we say that the object is in compression. A bar in compression: F --.c:===========~--F We often deal with springs, strings or ropes that are in tension i.e. experiencing a pulling force. In this syllabus, we always assume that the springs, strings or ropes are massless. We simply regard them as a medium in which forces are transmitted. Whether or not the masses are accelerating, the tension T, on both sides of the rope will always be of the same magnitude as long as the rope remains taut. Tension Tension Weight, mg Weight, Mg (a) Normal contact force Tension friction Weight, Mg I Normal contact force originates from the j bottom surface of block· I and weight from its ( b) centre (along the same! line of action) I L --- Tension Weight, mg 3

Hooke's Law RAFFLES INSTITUTION 2022 YEAR 5-6 PHYSICS DEPARTMENT A spring or wire when stretched is found to obey Hooke's Law, up to a limit called its limit of proportionality. Hooke's Law states that the extension of a body is proportional to the applied load if the limit of proportionality is not exceeded. Consider a spring suspended from the ceiling. It has an extension x when a force F is applied to it. To investigate Hooke's law, a graph of applied force F against the spring extension x, is plotted. Force, F ' limit of proportionality ----x1-· -- -----· gradient= k F 0 "--------- Extension, x Equation for Hooke's Law: F = kx where k is the force constant or spring constant which is a measure of the stiffness of the spring, the value of which can be obtained by calculating the gradient of the force-extension (F-x) graph. Energy stored in a spring From the F-x graph, we can determine the energy stored in the spring when it is stretched. Energy stored in the spring = Work done Win stretching spring = Area under F- x graph 1 = -Fx 2 Since F = kx, d. . 1 k 2 Energy store in a spring = 2 x Force, F F Extension, x X 4

Example 1 Example 2 RAFFLES INSTITUTION 2022 YEAR 5-6 PHYSICS DEPARTMENT A load of 50 N is suspended from a spring with a force constant of 1000 N m-1. Calculate, (a) the extension of the spring and (b) the energy stored in the spring. Solution o.) r:-lc-"ll. .., - .£.. ,._ ..,, -- .J!1--li>.)) - o-o~O~ (l~P b) [ - A load F1 produces an extension of x1 on a spring with force constant k while a larger load F2 produces an extension of X2. Determine the work required to change the extension of the spring from x1 to x2. Force F2 ------------ X 0 Extension Solution Work done to change the extension of the spring = Area of trapezium, X = ½ (F1 + F2) (x2 - X1 ) or L-y-J avg. force increase in length = ½ (F2)(x2) - ½ (F1)(x1) or = ½ k(x2)2 - ½ k(x1)2 This amount of energy is also the additional energy stored in the spring due to the increase in its extension. Common student errors in this example: