EJC Physics H204 Forces 2023 1. Notes (FULL)

A screw is a long inclined plane wrapped around an axis. A force (that is lower in magnitude) is exerted over a long distance along the “ramp” – it takes less effort to rotate the screw but you will need to make many rotations to secure the screw which will then provide a large retention force. Content • Types of force • Centre of gravity • Turning effects of forces • Equilibrium of forces • Upthrust Learning Outcomes Candidates should be able to: (a) show 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 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

Physics tries to understand all the different types of forces in the Universes using the fewest number of basic laws. We currently categorise all forces in terms of 4 fundamental interactions. force effects range gravitational force acts on all masses infinite electromagnetic force acts on electric charges infinite strong nuclear force acts on protons and neutrons holds them together in an atomic nucleus 1510− m weak nuclear force acts on elementary particles results in radioactive decay 1710− m Force is a vector quantity. It has both magnitude and direction. In recognition of Isaac Newton’s work on classical mechanics, specifically Newton’s 2 nd Law of motion (see topic on Dynamics), the SI unit of force is the newton (N). 1 N is the magnitude of a force that acts on a mass of 1 kg resulting in an acceleration of 1 m s-2 in the direction of the force. Forces can act on particles (such as masses and electric charges) without the particle touching other particle(s). Some resources refer to these as “force at a distance”. For A-Levels, we refer to a field of force. If asked to consider the types of force more specifically, we should specify the nature of the force when discussing the field of force. The 4 Fundamental Forces. (from left to right) Gravity, electromagnetism, strong (nuclear) force and weak (nuclear) force. A field of force is a region of space where a particle experiences a force.

field of force specific definition gravitational field (see topic on gravitational field) a region of space in which a ___________________ force acts on a ______________________ electric field (see topic on electric field) a region of space in which an __________________ force acts on a ______________________________ magnetic field (see topic on electricity and magnetism) a region of space in which a __________________ force acts on a ______________________________, ______________________________, or a ______________________________, In our everyday lives, we are familiar with Earth’s gravitational field. We have weight because of the gravitational force that is acting on every part of our body ranging from the head to the toes. It will be simpler to picture the overall effect of gravity acting at a single point – the centre of gravity. The centre of gravity (CG) of an object changes with the shape. For a person standing upright, the CG is somewhere in the middle of the body, approximately behind the belly button. The CG will shift as the posture changes. gravitational mass electric stationary charge magnetic current-carrying conductor moving charge permanent magnet The centre of gravity is the point from where all the weight of a body seems to act The Fosbury flop . The CG of this athlete clearing a high jump bar is shifted out behind the back. Art Meets Science. Animators and game designers work with the concept of CG to convey body language or create realistic animations.

Example 1 Describe how to find the centre of gravity of a thin sheet of irregularly-shaped cardboard. When there is no resultant force on a body, there is no linear acceleration of the body’s centre of gravity. 2 possible scenarios are: • body is stationary • body moves with constant velocity Example 2 3 forces 1 2 3 and FF ,F are parallel to the plane of paper and acts on mass m shown below. If m is in translational equilibrium, state an equation expressing the magnitude of 3F in terms of 1F . Note: We can resolve vector quantities along 2 perpendicular axes and perform vector addition. (i) plumb line suspended from pin irregular shape Solution (i) Suspend a mass on a string from a pin to form a plumb line. (ii) Suspend cardboard freely through a hole near the edge. (iii) Draw a line along the vertical string on the cardboard. (iv) Repeat steps (ii) and (iii) for one or two more different holes. (v) Centre of gravity is at point of intersection of lines. pin Solution no resultant force vertically: no resultant force horizontally: since F1 m θ F2 F3 (not to scale) A body is in translational equilibrium when there is no resultant force.

Example 3 An object X rests on a smooth horizontal surface. Two horizontal forces act on X as shown below. (a) By means of a scale diagram, determine a third horizontal force that allows X to be stationary. (b) Using the resolution of forces, verify that your answer to part (a) is correct. Viscous forces act when there is relative motion between a body and the fluid (either a gas or liquid) surrounding the body. It is known as a dissipative force – some energy is converted and lost as heat to the surroundings when a body experiences viscous force. It acts along (parallel to) the surfaces. 18 N 55 N (to scale) third force X Solution (a) scale is 1 N : 0.2 cm magnitude: 64.7 N direction: as shown in the diagram Note: 1. For vector quantities, answer includes both magnitude and direction. 2. The forces acting on an object in translational equilibrium form a closed polygon – the net effect of the vectors is zero as the vector sum of the forces “close upon themselves”. (b) Let the 3rd force be no resultant force vertically: (1) no resultant force horizontally: (2) (1) ÷ (2) Sub  = 14.6 into (1), F3 = 64.7 N Note: Viscous forces only manifest when there is relative motion. In still water, the drag force acting on a swimmer opposes direction of swim. There is virtually no water resistance along the skin -water interface if a fish moves at the same speed as the flow of water. There is no relative motion