H204 Forces - 1. Notes (1718) [For Upload]

9749 H2 Physics Lecture Notes Topic 4: Forces Page 1 of 20 Topic 4 Forces Content  Types of force  Centre of gravity  Turning effects of forces  Equilibrium of forces  Upthrust 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 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 take n 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. (j)* derive, from definitions of pressure and density, the equation p = gh. (k)* solve problems using the equation p = gh. (l)* show an understanding of the origin of the upthrust acting on a body in a fluid. (m)* state that upthrust is equal to the weight of the fluid displaced by a submerged or floating object. (n)* calculate the upthrust in terms of the weight of the displaced fluid. (o)* recall and apply the principle that, for an object floating in equilibrium, the upthrust is equal to the weight of the object to new situations or to solve related problems. * Not required for 8867 H1 Physics

9749 H2 Physics Lecture Notes Topic 4: Forces Page 2 of 20 4.0 Introduction One of the main goals of Physics has been to understand the immense variety of forces in the universe in terms of the fewest number of fundamental laws. Today, all forces are understood in terms of just four fundamental interactions as follows: Force Effects Range/m Gravitational Force Weakest. Acts on all masses infinite Electromagnetic Force Acts on electric charges infinite Strong Nuclear Force Holds protons and neutrons together in a nucleus 10-15 Weak Nuclear Force Causes radioactive decay processes. 10-17 A force is a push or pull exerted by one body on another. It is an interaction between two bodies or between a body and its environment . Force is a vector quantity and hence it is quantified by having both a magnitude and a direction. The unit of force is newton (N). 1 N is defined as the magnitude of a force that accelerates a mass of 1 kg at a rate of 1 m s-2 in the direction of the force.

9749 H2 Physics Lecture Notes Topic 4: Forces Page 3 of 20 4.1 Types of Forces 4.1.1 Force on a Mass in a Gravitational Field When a body of mass m is placed in a gravitational field of gravitational field strength gሬ⃑, it will experience a gravitational force Fሬሬ⃑G with a magnitude given by Fሬሬ⃑G = mgሬ⃑ and Fሬሬ⃑G acts in the direction of the gravitational field strength gሬ⃑ at that point If gሬ⃑ is set up by a massive body, Fሬሬ⃑G is also called the weight of a body of mass m. The weight can be taken to act at a single point known as the centre of gravity of the body. Conceptual Question Does the centre of mass and the centre of gravity of a body always coincide? No. The two points will only coincide when the body is place in a region of uniform gravitational field. 4.1.2 Force on a Charge in an Electric Field When a charge q is placed in an electric field of electric field strength Eሬሬ⃑, it will experience an electric force Fሬሬ⃑E where Fሬሬ⃑E = qEሬሬ⃑ If q is positive, Fሬሬ⃑E is in the direction of Eሬሬ⃑. If q is negative, Fሬሬ⃑E is in the opposite direction to Eሬሬ⃑. g FG g FG m m E FE E FE +q +q FE -q FE -q

9749 H2 Physics Lecture Notes Topic 4: Forces Page 4 of 20 4.1.3 Force on a Moving Charge in a Magnetic Force When a charge q is moving with velocity ݒ⃑ at an angle  to the magnetic field Bሬሬ⃑, it will experience a magnetic force Fሬሬ⃑B where Fሬሬ⃑B = qݒ⃑ ×Bሬሬ⃑ Magnitude of ቚFሬሬ⃑Bቚ = q|ݒ⃑|ቚBሬሬ⃑ቚߠ݊݅ܵ The direction of ݒ⃑ follows that of the movement of a positive charges. 4.1.4 Normal Contact Force Normal contact force is the force that the surface of one body exerts (or pushes) on the surface of another body it is in contact with. Normal contact force is always perpendicular (or normal) to the surfaces in contact with each other. The diagram below shows the normal contact forces exerted by the table , block A and block C on block B. Resolving ݒ⃑ perpendicular to ܤሬ⃑ and parallel to ܤሬ⃑ Resolving ܤሬ⃑ perpendicular to ݒ⃑ and parallel to ݒ⃑ NAonB NConB NTableonB B C A NB: 1. Direction of FB is predicted using Fleming’s Left Hand Rule. 2. FB causes q to trace a circular path whose plane is perpendicular to B.

9749 H2 Physics Lecture Notes Topic 4: Forces Page 5 of 20 4.1.5 Tensile and Compressive Forces Tension and compression are one dimensional forces exerted along the axis of a body. These forces cause changes to the linear dimension of the body. A material is in tension when its ends are pulled apart along its axis by equal and opposite external forces. A material in compression when its ends are pushed together along its axis by equal and opposite external forces. Conceptual Question A tensile force is exerted at the lower end of a vertical rod of negligible mass along its axis. Is the tension the same throughout the rod? Yes. If not, it will mean that there will be a resultant force acting various portions of the rod which will in turn cause these portions to experience an acceleration. 4.1.5.1 Hooke’s Law Hooke’s law states that the change in length x of a material is directly proportional to the force F applied on it, provided that the limit of proportionality is not exceeded. F = kx where F is the force applied to the material, Lo is the unstretched length of material L is final length of material x is the extension / compression of the material (L – Lo) or (Lo – L) k is the proportionality (force) constant force L Unstretched spring Stretched spring Lo e

9749 H2 Physics Lecture Notes Topic 4: Forces Page 6 of 20 4.1.6 Friction and Viscous Forces Friction and viscous forces are known as dissipative forces. Some mechanical energy of the object experiencing these forces is dissipated (as heat) to the surroundings. 4.1.6.1 Friction Friction acts along the surface between two objects whenever one moves or tries to move over the other and in the direction so as to oppose relative motion (or impending relative motion) of the surfaces. Close examination of the flattest and most highly polished surface reveals hollows and humps more than one hundred atoms high. When one solid is placed on another, contact occurs only at a few places of small areas. The pressure at the points of contact is extremely high an d causes the humps to flatten out until the increased area of contact enables the upper solid to be supported. At the points of contact, small, cold -welded 'joints' are formed by the strong adhesive forces between molecules which are very close together. These joints have to be broken before one surface can move over the other. The value of frictional force is dependent on the types of surfaces in contact with each other, as well as the magnitude of the normal contact force exerted by one surface on the other. Static friction is the frictional force that acts when there is no relative motion between two su