RI Chap 2 Forces and Moments Lecture Notes

2 FORCES & MOMENTS H2 Physics 9478 Content Page 2.1 Type of Forces 2 2.2 Moment and torque 6 2.3 Translational and rotational equilibrium 8 2.4 Appendix 13 Learning Outcomes Candidates should be able to: (a) describe the forces on a mass, charge and current-carrying conductor in gravitational, electric and magnetic fields, as appropriate. (b) show a qualitative understanding of forces including normal force, frictional force, buoyant force (upthrust), and viscous force, e.g. air resistance (knowledge of the concepts of coefficients of friction and viscosity is not required). [Buoyant force (upthrust) not in H1 syllabus] (c) recall and apply Hooke’s law ( F = kx, where k is the force constant) to new situations or to solve related problems. (d) define and apply the moment of a force and the torque of a couple. (e) show an understanding that a couple is a pair of forces which tends to produce rotation only. (f) show an understanding that the weight of a body may be taken as acting at a single point known as its centre of gravity. (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 free-body diagrams and vector triangles to represent forces on bodies that are in rotational and translational equilibrium.

RAFFLES INSTITUTION YEAR 56 PHYSICS DEPARTMENT Page| 2 2.1 Type of Forces To date, physicists recognize four fundamental forces in nature: 1. The gravitational force 2. The electromagnetic force 3. The strong nuclear force (not in 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 reaction force and friction, are 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.  Weight and Centre of Gravity 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 gravitational field strength. This force acts vertically downwards towards the centre of the Earth through a single point on or outside the body known as its centre of gravity (C.G.). Fig. 2.1 The dot at the centre of the body is its centre of gravity. W W Definition The centre of gravity of a body is the point at which the weight of the body (or the resultant of the distributed gravitational attraction on the body) appears to act.

RAFFLES INSTITUTION YEAR 56 PHYSICS DEPARTMENT Page| 3  Normal force 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. Fig. 2.2  Buoyant force (Upthrust) [not in H1 syllabus] Upthrust U is the vertical upward force exerted on a body by a fluid when it is fully or partially submerged in the fluid due to the difference in fluid pressure. It can be shown to be equal in magnitude and opposite in direction to the weight W of the fluid displaced by a submerged or floating object. Fig. 2.3 If the upthrust is greater than the weight of the object, the object will accelerate up (float), otherwise it will accelerate downwards (sink). Do not confuse upthrust with thrust. Thrust can be described as a force that is exerted on an object by the expulsion or acceleration of mass in one direction. N N U W fluid

RAFFLES INSTITUTION YEAR 56 PHYSICS DEPARTMENT Page| 4  Frictional force 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. Friction enables a person to walk on a path or to hold an object securely without dropping. Friction also allows wheels to rotate without slipping. On the other hand, friction causes wear and tear in mechanical system and produces excess heat that may cause damage to system. • 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  Viscous force Viscous force arises when an object moves through a fluid, it imparts momentum to the fluid molecules, hence causing itself to slow down. Air resistance is one commonly experienced viscous force as objects move through air. Viscous force depends on: • the shape of the body, • the speed of the body, and • the viscosity of the fluid. Does a viscous liquid necessarily have a large density?  Tension and Compression 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. When the object (e.g. a rigid rod) is pushed on both ends, we say that the object is in compression. We often deal with springs, strings or ropes that are in tension, i.e., experiencing a pulling force. F F bar in tension F F bar in compression

RAFFLES INSTITUTION YEAR 56 PHYSICS DEPARTMENT Page| 5  Summary of Forces Force Direction Weight Acts vertically downwards towards the centre of Earth through an object’s centre of gravity (c.g.). Normal contact force Always perpendicular to the surfaces in contact. Frictional force Always opposite to the tendency or direction of motion, and parallel to the two surfaces in contact. Tension When forces are directed away from the object affected along the object. Compression When forces are directed towards the object affected along the object. Upthrust Vertical upward force exerted by a fluid on a body submerged fully or partially in the fluid. Viscous force Always opposite to the direction of relative motion of the object moving in a fluid.

RAFFLES INSTITUTION YEAR 56 PHYSICS DEPARTMENT Page| 6  Hooke’s Law 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. Fig. 2.4 F = kx where k is the force (or spring) constant 2.2 Moment and torque  Moment The turning effect of a force is called the moment of the force. Consider a force F acting on a rigid body in the plane of the paper so as to cause it to turn about an axis perpendicular to the paper, with pivot at O on the same plane as shown in Fig. 2.5. Moment τ of the force = L × F Units of moment: N m Definition Hooke’s Law states that the extension of a body is proportional to the applied load if the limit of proportionality is not exceeded. F x limit of proportionality Force, F Extension, x 0 gradient = k O F2 line of action of F2 line of action of F1 F1 Fig. 2.5 Fig. 2.6 L1 L2 O L F line of action of F

RAFFLES INSTITUTION YEAR 56 PHYSICS DEPARTMENT Page| 7 In Fig. 2.6, a rigid body is acted on by forces F1 and F2 lying in the plane of the paper. F1 would produce a counter -clockwise rotation , whilst F2 a clockwise rotation about O. If we take clockwise moment as positive, anticlockwise moment would be negative. The net moment of the two forces about O is