DHS 04 Forces (Lecture Notes)

DUNMAN HIGH SCHOOL 9749 H2 PHYSICS Year 5 (2024) TOPIC 4: Forces 1 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 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 force of upthrust acting on a body in a fluid (m) state that upthrust is equal in magnitude and opposite in direction 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 in magnitude and opposite in direction to the weight of the object to new situations or to solve related problems

2 Concept Map 1 Introduction One of the main goals of Physics has been to understand the immense variety of forces in the universe. 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

3 2 Types of Forces Learning Outcomes (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) In the past, we learn that a force is a push or a pull which one body exerts on another. Now, we know that a force is defined as the rate of change of momentum of an object which is free to move. The direction of the force is in the direction of the change in momentum. Conservative and Non Conservative Forces A force is conservative if the work it does on an object moving between two points is ____________________________ the object takes. Gravitational force is an example of a conservative force. A force is non-conservative if the work it does on an object ________________ taken by the object between its initial and final points. Friction is an example of a non-conservative force. Example 1 Forces on a mass in a gravitational, electric and magnetic field (1) Gravitational force: • is due to the interaction between ______ • on an object is called _____ if it is due to the gravitational attraction by the Earth (2) Electric force: • is due to the interaction between ______ + + weight F F F F F

4 (3) Magnetic force: • is due to the interaction between ________________ • acts on moving charges and ______________________________when they are placed in magnetic fields Example 2 Contact forces (1) Forces on the ball T = tension W = weight of ball (2) Forces on the block N = normal contact force W = weight of block F F F F F F F F F F

5 (3) Forces on the block moving to the right F = forward force f = frictional force N = normal contact force W = weight of block (4) Forces on the ball moving through a liquid U = upthrust R = drag force W = weight of ball 3 Frictional and Viscous Forces Friction and viscous forces are known as dissipative forces. Some energy of the object moving through the fluid is dissipated as heat to the surroundings. 3.1 Frictional Force Frictional force is the force exerted by one body on another body when two bodies slide over one another. It is caused by irregularities in the surfaces in mutual contact and depends on the surfaces in contact as well as how much they are pressed against each other. It is the __________________________ along surface of contact. 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 over on another, contact occurs only at a few places of small areas. The pressure at the points of contact is extremely high and 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.

6 3.2 Viscous / Drag Force The frictional force experienced either by an object as it moves through a fluid or by a fluid as it moves over a surface. i.e it is resistance when an object move in a fluid and the force is dependent on the speed of the object. In a viscous flow, fluid can be regarded as a stack of very thin layers, each moving with different speeds due to internal friction between the layers. When an object moves relative to a fluid with velocity v, the layer of fluid P adjacent to the object is pulled along. But the next layer Q slows layer P down. There is a gradual decrease in velocity of the layers with distance away from the object. The overall effect is a net retarding force on the object. This retarding force, F which opposes the motion acts to the right. The magnitude of the viscous force _________ with increase in speed of the object. The exact relationship depends also on the shape, size, texture of surface, viscosity of fluid, etc. Example 3 The mass of a diver is 61 kg. In a free-fall dive from an aircraft, before the parachute opened, the diver reached a terminal speed of 90 m s-1. Ignoring upthrust, calculate (i) the weight of the diver (ii) the force of air resistance on the diver when at the terminal speed

7 (iii) the magnitude and unit of the constant k in the expression air resistance = kv2 (iv) using the expression given in (iii), estimate the air resistance on the diver when he is moving with a speed of 25 m s-1

8 (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 4 Centre of Gravity (C.G.) Every body of mass is attracted toward the centre of the Earth by the force of gravity. The entire weight of a body may be taken as acting at a single point known as its centre of gravity (C.G.). The C.G. of a homogeneous, symmetric body must lie on its axis of symmetry. 5 Free-Body Diagrams A mechan