Forces in Mechanical Systems 1.1. Objectives Define force and describe how forces are measured. Define force and describe how forces are measured. Describe.

Forces in Mechanical Forces in Mechanical SystemsSystems

1.11.1

ObjectivesObjectives Define force and describe how forces are Define force and describe how forces are

measured.measured. Describe what happens when forces on an Describe what happens when forces on an

object are balanced and when they are object are balanced and when they are unbalanced.unbalanced.

Explain the meaning of Newton’s first law of Explain the meaning of Newton’s first law of motion.motion.

Define scalar, vector, weight, mass and torque.Define scalar, vector, weight, mass and torque. Determine the resultant force on an object Determine the resultant force on an object

when two or more forces act on it.when two or more forces act on it. Solve problems involving force, lever arm, and Solve problems involving force, lever arm, and

torque.torque.

ForceForce

A push or a pullA push or a pull In In Mechanical SystemsMechanical Systems forces forces

change an object’s motion.change an object’s motion. Forces can be transmitted to a Forces can be transmitted to a

variety of mechanical partsvariety of mechanical parts

Bicycle Bicycle

Measuring Forces Measuring Forces

Metric SystemMetric System Based on powers of 10Based on powers of 10

The The SI base unitsSI base units for seven basic for seven basic quantities:quantities:

Quantity Unit Symbol

Length ( l ) meter m

Mass ( m ) kilogram kg

Time ( t ) second s

Electric Current ( I ) ampere A

Temperature ( T ) Kelvin K

Amount of Substance ( n )

mole mol

Luminous intensity candela cd

Derived unitsDerived units – unit made from a – unit made from a combination of base units.combination of base units. SI unit of SI unit of speedspeed is m/s (length / time) is m/s (length / time) AccelerationAcceleration is m/s is m/s22 (speed / time) (speed / time) ForceForce is the Newton (N) which is actually is the Newton (N) which is actually

kg m/skg m/s22

Comparison of English and SI Units Comparison of English and SI Units

Length Time Mass Force

English foot (ft) second (s) slug pound (lb)

SI meter (m) second (s) kilogram (kg) Newton (N)

Weight and Mass Conversions Weight and Mass Conversions

1 pound = 16 ounces 1 kilogram weighs 9.80 N or 2.2 lb

1 pound = 4.45 newtons 1 slug weighs 32.2 lb

1 kilogram = 1000 grams 1 slug = 14.59 kg

Force can be Force can be measured with a measured with a spring scale.spring scale. Spring stretch is Spring stretch is

directly proportional directly proportional to forceto force

Weight is the force Weight is the force due to gravity.due to gravity.

Make sure units match before Make sure units match before calculations are run on values.calculations are run on values.

Force is a Vector Force is a Vector

The effect of force on an object The effect of force on an object depends on two thingsdepends on two things magnitude magnitude direction direction

VectorVector is a quantity that must be is a quantity that must be described by both magnitude and described by both magnitude and direction.direction. Force is a vector quantity.Force is a vector quantity. Displacement, velocity, acceleration, Displacement, velocity, acceleration,

and momentum are also vector and momentum are also vector quantitiesquantities11..

1 We will cover these later.

ScalarsScalars – quantities described by – quantities described by magnitude only.magnitude only. TemperatureTemperature elapsed timeelapsed time PressurePressure massmass

How to Represent Forces How to Represent Forces

Vector drawing – Vector drawing – arrows are arrows are proportional to proportional to magnitude and magnitude and point in the point in the direction of the direction of the vector. (Figs 1.4 vector. (Figs 1.4 and 1.5, p. 9) and 1.5, p. 9)

Balanced and Unbalanced Forces Balanced and Unbalanced Forces

Net forceNet force – the sum of all forces – the sum of all forces acting on an objectacting on an object

FFnetnet = = F = FF = F11 + F + F22 …… ……

Balanced forcesBalanced forces – when the net force – when the net force on an object is equal to zero.on an object is equal to zero. Motion of object stays the same – called Motion of object stays the same – called

equilibriumequilibrium.. Speed and direction stays the same.Speed and direction stays the same.

Unbalanced forcesUnbalanced forces – when the net – when the net force on an object is not equal to force on an object is not equal to zero.zero. Motion of the object changesMotion of the object changes

Falling objects and terminal velocity Falling objects and terminal velocity

Figure 1.7a Figure 1.7a FFgravitygravity > F > Fdragdrag

Figure 1.7b Figure 1.7b FFgravitygravity = F = Fdragdrag

Terminal velocityTerminal velocity – – final velocity final velocity reached when reached when gravity and drag are gravity and drag are balanced. balanced.

Newton’s First Law of Motion Newton’s First Law of Motion

An object at rest remains at rest, An object at rest remains at rest, acted upon by an unbalanced force. acted upon by an unbalanced force. Likewise an object in motion will Likewise an object in motion will keep its velocity, unless an keep its velocity, unless an unbalanced force acts on it.unbalanced force acts on it. Sometimes called the Sometimes called the law of inertialaw of inertia..

Example 1-1Example 1-1 A yo-yo weighing A yo-yo weighing

0.25 lb hangs 0.25 lb hangs motionless at the motionless at the end of a string. end of a string. Draw the forces Draw the forces acting on the yo-acting on the yo-yo. yo.

Adding Forces That Act Along a Adding Forces That Act Along a LineLine

Forces are added to find net force Forces are added to find net force (F(Fnetnet) on an object.) on an object.

Easy if in the same direction.Easy if in the same direction. Sign can be used to indicate directionSign can be used to indicate direction

Forces in the up or to the right Forces in the up or to the right directions are in the directions are in the positivepositive..

Forces in the downward or the left Forces in the downward or the left directions are directions are negativenegative..

Example 1-2 Tug-of-War ProblemExample 1-2 Tug-of-War Problem Five people compete in a tug-of-war. Five people compete in a tug-of-war.

Three people on the left side each Three people on the left side each pull with 230 N of force. Two people pull with 230 N of force. Two people on the right side each pull with 300 N on the right side each pull with 300 N of force. Who will win the tug-of-of force. Who will win the tug-of-war?war?

Adding Forces That Do Not Act Adding Forces That Do Not Act Along a LineAlong a Line

Forces can’t be Forces can’t be added if they do added if they do not act along a not act along a straight line.straight line.

Example in Figure Example in Figure 1.111.11

To solve we use a To solve we use a graphing methodgraphing method Vectors are drawn Vectors are drawn

“head-to-tail.”“head-to-tail.”

Step 1Step 1: Draw first vector: Draw first vector Step 2Step 2: Draw second vector: Draw second vector

““Head-to-tail”Head-to-tail” Step 3Step 3: Draw the resultant : Draw the resultant

forceforce Resultant forceResultant force – single – single

vector representing the vector representing the sum of two or more sum of two or more vectors.vectors.

Step 4Step 4: Determine the : Determine the magnitude and direction of magnitude and direction of the resultant.the resultant. Pythagorean Theorem for Pythagorean Theorem for

right triangles right triangles Step 5Step 5: Make some : Make some

conclusionsconclusions

Weight and Mass Aren’t the Same Weight and Mass Aren’t the Same Thing!Thing!

Unbalanced force acts on object at Unbalanced force acts on object at rest, it will move.rest, it will move.

Two books have twice the mass, and Two books have twice the mass, and require twice the force to get them to require twice the force to get them to move.move.

Since the amount of

inertia depends on the amount of matter, two

books have twice the inertia.

Torque and RotationTorque and Rotation

TorqueTorque – a quantity that causes – a quantity that causes rotation in mechanical systems.rotation in mechanical systems. The effect of a force applied on a body The effect of a force applied on a body

at some distance from the axis of at some distance from the axis of rotation.rotation.

Can be:Can be: Clockwise (cw)Clockwise (cw) Or, counterclockwise (ccw)Or, counterclockwise (ccw)

Line of action – line along the applied force that extends in both directions.

= F L

Torque = applied force x lever arm

What are the English units for What are the English units for torque?torque?

SI units?SI units?

GearGear TeethTeeth ShaftShaft Teeth of one gear mesh with another Teeth of one gear mesh with another

gear.gear. Driving gearDriving gear Driven gearDriven gear

Example 1-3 Calculation of Torque Example 1-3 Calculation of Torque Applied by a Torque WrenchApplied by a Torque Wrench

A torque wrench has a lever arm of A torque wrench has a lever arm of 1.5 ft. A force of 40 lb is applied to 1.5 ft. A force of 40 lb is applied to the end of the wrench to tighten a the end of the wrench to tighten a bolt. Find the torque applied to the bolt. Find the torque applied to the bolt in a.) lb·ft and b.) N·m.bolt in a.) lb·ft and b.) N·m.

Example 1-4 Torques in a Belt-Example 1-4 Torques in a Belt-Driven SystemDriven System

The motor pulley in a belt-driven system has a The motor pulley in a belt-driven system has a radius of 5 cm (0.05 m). The large pulley radius of 5 cm (0.05 m). The large pulley attached to the shaft of a machine has a radius of attached to the shaft of a machine has a radius of 20 cm (0.20 m). The dragging or pulling force of 20 cm (0.20 m). The dragging or pulling force of the belt is 40 N. Assume that the belt doesn’t slip the belt is 40 N. Assume that the belt doesn’t slip as the motor and belt drive the load pulley. What as the motor and belt drive the load pulley. What is the torque applied to each pulley?is the torque applied to each pulley?

Opposing TorquesOpposing Torques

Opposing torques, like forces, can be Opposing torques, like forces, can be in equilibrium. (torques cancel each in equilibrium. (torques cancel each other out)other out) If system at rest, it stays at rest.If system at rest, it stays at rest. If in motion, it continues to rotate.If in motion, it continues to rotate.

If unbalanced, the net torque will If unbalanced, the net torque will cause a change in the rotational cause a change in the rotational speed.speed. It speeds up or slows down.It speeds up or slows down.

Example 1-5 Truck Scales Involve Example 1-5 Truck Scales Involve Opposing TorquesOpposing Torques

A 48 000 lb truck sits on the platform of truck-A 48 000 lb truck sits on the platform of truck-weighing scales. The truck weight acts on a 0.5 ft weighing scales. The truck weight acts on a 0.5 ft lever arm about the pivot point. A 1000 lb lever arm about the pivot point. A 1000 lb balancing weight is hung on the opposite side of balancing weight is hung on the opposite side of the pivot point, 20 ft away. Find: (a.) Torque of the pivot point, 20 ft away. Find: (a.) Torque of truck about pivot point. (b.) Torque of balance truck about pivot point. (b.) Torque of balance weight about the pivot point. (c.) Whether or not weight about the pivot point. (c.) Whether or not the torques are balanced.the torques are balanced.