Chapter 1 – Prime Movers Mechanical Systems – Force Fluid Systems – Pressure Electrical Systems – Potential Difference (Voltage) Thermal Systems – Temperature Difference

Chapter 1 – Section 1 Force in Mechanical Systems

Define Force A force is a push or a pull It can be transmitted through direct contact such as a rod, chain, rope, mechanical linkage, etc It can also be transmitted without direct contact. Examples: gravity, magnetism

Measuring Force and other things Base quantities – these form the basis of all other measurements. For example, length is a base quantity, so is time. By dividing length by time, we derive the quantity of speed. Another example of a derived quantity is area. Area is length times length or length 2. Volume is length 3.

Base Quantities QuantityMetric (SI) unit Metric symbol English unit English symbol lengthmetermfootft masskilogramkgslug timeseconds s Temperature KelvinK Fahrenheit oFoF Electric current AmpereA Amount of substance molemol Light intensity candelacd

Metric System Prefixes The metric system uses prefixes in front of a unit to indicate a large or small amount of that unit. Examples – kilo means Thus a kilometer equals 1000 meters. Centi means one hundredth. Thus a centigram is one hundredth of a gram. 100 centigrams equals one gram

Common prefixes you should know prefix exponent symbolmeaningexample Tera10 12 Ttrillionterawatt Giga10 9 Gbilliongigabyte Mega10 6 Mmillionmegaton Kilo10 3 K thousand kilogram centi10 -2 chundreth centimeter milli10 -3 m thousandth milliliter micro10 -6  millionth microsecond nano10 -9 nbillionth nanometer pico ptrillionth picofarad

Back to Force In the SI (metric) system, force is measured in Newtons (N). In English units, it is measured in pounds (lb). Newtons is a derived quantity. It is the amount of force needed to accelerate a one kilogram mass at a rate of one meter per second per second or one meter per second squared.

Measuring force -continued Thus, one newton equals one kilogram - meter per second squared, or 1N = 1 kg * m / s 2 1N = 0.22 lb 1kg weighs 9.8 N or 2.2 lb 1 slug weighs 32.2 lb 1 slug = kg 1 lb = 4.45 N

Measuring force - continued Spring scales are used to measure force Since weight is a force that is proportional to mass, springs scales can also be used to measure mass. However, weight and mass are not the same thing. Weight is the force of gravity acting on a mass. Mass is a measure of an object’s inertia. In the SI system, the acceleration due to gravity is 9.8 m/s 2.

Vectors Quantities that have both a magnitude (a number) and a direction are vector quantities. Ex – force, displacement, velocity, acceleration, momentum. Quantities that have only a magnitude are scalar quantities. Ex – temperature, mass, pressure, time.

Drawing Vectors Vectors are represented by arrows The length of the arrow represents the magnitude The arrowhead indicates the direction

Adding co-linear vectors

Adding non-colinear vectors

Adding non-colinear vectors mathematically By the Pythagorean Theorem c 2 = a 2 + b 2 Thus c = (a 2 + b 2 ) 1/2 This method can be used if the vectors are at right angles to one another If they are not at right angles, they can be added graphically

Adding vectors graphically

Newton’s 1 st Law of Motion An object at rest will remain at rest, or if traveling at a velocity will continue at that velocity in a straight line unless a net force acts on it. In other words, if you don’t push it, it won’t move. It will just sit there and laugh at you. If it’s moving it won’t speed up, slow down, or change direction. And it’s still laughing.

Balanced & Unbalanced Forces If the forces on an object are balanced, there is no net force If the forces are unbalanced, there is a net force

Torque Torque is the product of a force applied to a lever arm.  = FL (force x lever arm) , the Greek letter tau, is used for torque SI units would be N*m English units = ft*lb or in*lb Torque can be applied in a clockwise (cw) or counter clockwise (ccw) direction.

Torque

Torque example problem A 30 lb force is applied to end of an 18 inch wrench as shown What is the torque applied to the nut in ft-lb?

Solution Torque = force times lever arm (  = FL) 18in = 1.5 ft  = FL = 30lb x 1.5ft  = 45 ft-lb

Torque can be transmitted by Chains Pulleys gears

Torque Example Problem Two gears are in contact The larger gear is 10 inches in diameter The smaller gear is 2 inches in diameter A torque of 5 in-lb is applied to the smaller gear What is the torque on the larger gear?

Solution For the smaller gear, we know the torque ( 5 in-lb) and the lever arm ( 1 in ). The lever arm is the radius or ½ the diameter. Thus we can find the force  = FL, thus F =  /L = 5 in-lb / 1 in = 5lb The force on both gears must be the same, therefore for the larger gear:  = FL = 5lb x 5 in = 25 in-lb

Summary A force is a push or a pull. Force is a vector. It has magnitude and direction. Its magnitude is measured in pounds (English) or Newtons (metric). Newton’s 1 st Law – No net force equals no acceleration. A net force is the result of unbalanced forces.

More summary Colinear forces can be added directly. Non colinear forces can be added graphically or using the Pythagorean Theorem. Weight is a force. Mass is a measure of inertia. Torque equals force times lever arm. No net torque equals no angular acceleration.