H2 Forces Lecture Notes

9749 H2 PHYSICS Lecture Notes Nanyang Junior College 1 Chapter 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 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 forc es 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 (j) derive, from the definitions of pressure and density, the equation p  ρgh (k) solve problems using the equation p  ρgh (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.

9749 H2 PHYSICS Lecture Notes Nanyang Junior College 2 Types of Forces In general, forces can be categorized as either non-contact forces or contact forces. Non -contact Forces Gravitational Force Gravitational force is an attractive force exerted by one mass on another, 2 GMmF r Gravitational force is a force on a mass in a gravitational field, in the direction of the field, F = mg The weight (a.k.a. gravitational force exerted by earth on the object ) of an object placed in the gravitational field of the Earth is the gravitational force exerted by the Earth on the object. weight mass gravitational field strength W mg   The centre of gravity of a body is the point at which the entire weight (of body) appears to act. Electric Force Electric force is a force exerted by one charge on another. Like charges repel, unlike charges attract. 2 04 QqF r Electric forc e is a force on a charge in an electric field, in the direction of the field on a positive charge, opposite t he direction of the field on a negative charge , F = qE Magnetic Force                                         Magnetic force is a force on a moving charge in a magnetic field. F = Bqv M m F F - Q q F F E q F g m F   F q v F B r   

9749 H2 PHYSICS Lecture Notes Nanyang Junior College 3 Contact Forces Normal Contact Force (a.k.a. n ormal reaction ) The normal contact force is the force that the one body exerts on another body that are physically in contact. It is always perpendicular (normal) to the surfaces in contact. Frictional Force A frictional force arises when the surfaces in contact are rough to resist motion or tendency of motion. The direction of the frictional force on a body is always in the direction opposite to its motion or impending motion, parallel to the rough surface. Note: 1. Static friction is the frictional force when there is no relative motion between the two surfaces. The magnitude of static friction is self-adjusting such that it is just sufficient to prevent motion, but only up to a maximum value or the limiting static friction. 2. Kinetic friction is the frictional force when the two surfaces slide against each othe r. When the bodies just begin to move against each other, the kinetic friction between the surfaces is smaller than the static friction just before they begin to move. 3. Frictional force depends on the (a) nature of the surface (b) magnitude of the normal contact force. Viscous Force Viscous (drag) force is a resistive force that opposes relative motion. It is present when a body moves through a fluid (i.e. liquid or gas). Air resistance is a common example of viscous force. Note: 1. The direction of viscous force is always opposite to the direction of motion of the body relative to the fluid. 2. Viscous force depends on the (a) speed of the body moving through the fluid (b) the fluid (c) the shape and size of the body. u f v viscous force N W

9749 H2 PHYSICS Lecture Notes Nanyang Junior College 4 Lift Lift is the force that acts on a body such as an airplane wing or a helicopter rotor. Lift acts perpendicular to airplane wings or helicopter rotor. When an airplane is climbing, descendin g or banking in a turn, the lift is tilted with respect to the vertical. Thrust Thrust occurs when a system expels or accelerates mass in one direction. Thrust is the reaction force exerted by the expelled or accelerated mass on that system. When a j et engine of an airplane expels hot gas, the jet engine exerts a force on the hot g as during the expulsion. By Newton’s Third Law of Motion, the hot gas exerts a force that is equal in magnitude but opposite in direction called thrust on the jet engine, propelling the airplane forward. L L expelled hot gas T F

9749 H2 PHYSICS Lecture Notes Nanyang Junior College 5 Hooke’s Law Mathematically, where F is the magnitude of the applied force, x is the extension (or compression) produced, and k is a constant known as the force constant or spring constant. Example 1 A spring obeying Hooke’s Law has an unstretched (natural) length of 50 mm and a spring constant of 400 N m1. Determine the tension in the spring when its overall length is 70 mm.   3400 70 50 10 8.0 N F kx       Elastic Potential Energy When an elastic material is stretched (or compressed) , the energy used to strech the material is stored as the e lastic potential energy . This elastic potential energy (strain energy) is given by the area under the force-extension graph. Linear force-extension graph Non-linear force-extension graph For a body that obeys Hooke’s Law , the force -extension graph will be linear and the elastic potential energy stored in the body, E,         2 Area under of graph 1 2 1 2 1 2 E F x Fx kx x F kx kx Hooke’s Law states that extension (or compression) in a material is directly proport ional to the applied force, provided that the limit of proportionality is not exceeded. F  kx x F extension force x F 0 0 force extension

9749 H2 PHYSICS Lecture Notes Nanyang Junior College 6 Example 2 A sample is placed in a tensile testing machine. It is extended by known amounts and the tension is measured, as shown in the figure below. Determine the work done on the sample when it is given a total extension of 9 mm.    1 3 Area under tension-extension graph 1 5.0 10 602 0.15 J E         2 3 Area under tension-extension graph 1 9.0 5.0 10 60 802 0.28 J E        12 0.15 0.28 0.43 J E E E   Example 3 The graph below shows the variation with extens