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 Forceand 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 length2. Volume is length3.

Base QuantitiesQuantity Metric

(SI) unitMetric symbol

English unit

English symbol

length meter m foot ft

mass kilogram kg slug

time second s second s

Temperature Kelvin K Fahrenheit oF

Electric current

Ampere A

Amount of substance

mole mol

Light intensity

candela cd

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 1000. 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 symbol meaning example

Tera 1012 T trillion terawatt

Giga 109 G billion gigabyte

Mega 106 M million megaton

Kilo 103 K thousand kilogram

centi 10-2 c hundreth centimeter

milli 10-3 m thousandth milliliter

micro 10-6 millionth microsecond

nano 10-9 n billionth nanometer

pico 10-12 p trillionth 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 / s2

• 1N = 0.22 lb• 1kg weighs 9.8 N or 2.2 lb• 1 slug weighs 32.2 lb• 1 slug = 14.59 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/s2.

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 c2 = a2 + b2

• Thus c = (a2 + b2)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 1st 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 1st 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.