Everyday ForcesEveryday ForcesChapter 4 Section 4Chapter 4 Section 4

What is Weight?What is Weight?

Weight Weight – The magnitude of the force of – The magnitude of the force of gravity acting on an object.gravity acting on an object. Weight is directly proportional to forceWeight is directly proportional to force

Weight Weight ~ Force~ Force Since weight is a force, it can be related to Since weight is a force, it can be related to

Newton’s 2Newton’s 2ndnd Law. Law.F = maF = ma

Fg = mg (Where “g” is equal to 9.8m/s²)Fg = mg (Where “g” is equal to 9.8m/s²)

W = mgW = mg

Weight Depends on GravityWeight Depends on Gravity

Since weight is dependant on gravity, Since weight is dependant on gravity, weight depends on location. Such as weight depends on location. Such as planets.planets. Earth (g = 9.8m/sEarth (g = 9.8m/s²)²) Moon (g = 1.6m/sMoon (g = 1.6m/s²)²) Jupiter (g = 23.1m/sJupiter (g = 23.1m/s²)²)

An astronaut on Earth that weights 800N An astronaut on Earth that weights 800N (180 lb) would weight 130 N (30 lb) on the (180 lb) would weight 130 N (30 lb) on the moon.moon.

Weight Depends on ElevationWeight Depends on Elevation

Since weight depends on how far away Since weight depends on how far away the object is away from the center of the the object is away from the center of the planet, the altitude will effect the value of planet, the altitude will effect the value of g.g. At sea level the value of g is different then it At sea level the value of g is different then it

would be at the top of Mount Everest would be at the top of Mount Everest (elevation - 6200m)(elevation - 6200m)

About a 0.2% difference About a 0.2% difference Person weighing 180 lbs at sea level would weight Person weighing 180 lbs at sea level would weight 179.6 lbs at the top of Mount Everest.179.6 lbs at the top of Mount Everest.

Normal ForceNormal Force

Normal ForceNormal Force – A contact force exerted by – A contact force exerted by one object on another in a direction one object on another in a direction perpendicular to the surface of contact.perpendicular to the surface of contact. If a book is sitting on a desk and gravity is If a book is sitting on a desk and gravity is

pulling down on the book with 10N, the pulling down on the book with 10N, the normal force is going to be 10N pushing up on normal force is going to be 10N pushing up on the book.the book.

Normal Force – FnNormal Force – Fn

Also Known as the “Support Force”Also Known as the “Support Force”

Normal Force on an InclineNormal Force on an InclineThe normal Force is always perpendicular The normal Force is always perpendicular to the surface the object is resting on, not to the surface the object is resting on, not necessarily opposite the force of gravity.necessarily opposite the force of gravity.As the incline increase, the normal force As the incline increase, the normal force will decrease.will decrease.

Normal Force on InclineNormal Force on InclineFn = mg cosFn = mg cosθθ

**Where the normal force is the only upward force acting **Where the normal force is the only upward force acting on the object in the vertical direction.on the object in the vertical direction.

Force of FrictionForce of Friction

Friction occurs in all movement, just at Friction occurs in all movement, just at different levels.different levels.

From Newton’s 2From Newton’s 2ndnd Law it is stated that any Law it is stated that any applied force causes an acceleration, but if applied force causes an acceleration, but if a small force is applied to a large mass a small force is applied to a large mass object (when compared to the force) it object (when compared to the force) it usually doesn’t move. Why?usually doesn’t move. Why?

Friction Opposes the Applied ForceFriction Opposes the Applied Force

Friction forces always act in the direction Friction forces always act in the direction opposite to the motion or the applied force.opposite to the motion or the applied force.

If a car is driving down the road due north, If a car is driving down the road due north, the air resistance acting on the car is due the air resistance acting on the car is due south.south.

Static FrictionStatic Friction

Static FrictionStatic Friction – The force exerted on a motion- – The force exerted on a motion-less body by its environment to resist an less body by its environment to resist an external force.external force.

The static friction force is equal to the applied The static friction force is equal to the applied force and opposite in directionforce and opposite in direction

Fs = FFs = F

As the applied force increase, the static friction As the applied force increase, the static friction force increases. As the applied force decrease force increases. As the applied force decrease the static friction force decreases.the static friction force decreases.

Maximum Static Friction Maximum Static Friction

When the applied force is as great as it When the applied force is as great as it can be without causing the an object to can be without causing the an object to move, the force of static friction reaches its move, the force of static friction reaches its maximum value (Fsmaximum value (Fsmaxmax).).

Once the object begins to move, the Once the object begins to move, the friction force becomes less then Fsfriction force becomes less then Fsmaxmax

Kinetic FrictionKinetic Friction

Kinetic FrictionKinetic Friction – The force exerted on a – The force exerted on a moving object opposite to the direction of moving object opposite to the direction of motion.motion.

The force of kinetic friction (FThe force of kinetic friction (Fkk) is less then ) is less then the force of the maximum static friction the force of the maximum static friction (Fs(Fsmaxmax))

What Causes Kinetic Friction?What Causes Kinetic Friction?

Frictional force arises from the interaction Frictional force arises from the interaction of two surfaces in contact with each other.of two surfaces in contact with each other. The surface of all objects are rough and The surface of all objects are rough and

uneven, which means contact is only made at uneven, which means contact is only made at a few points.a few points.

What causes Static Friction?What causes Static Friction?

When an object is at rest, it is said that the When an object is at rest, it is said that the contact between the two surfaces are in a contact between the two surfaces are in a “cold-weld”.“cold-weld”. A cold-weld, or surface adhesion, is caused A cold-weld, or surface adhesion, is caused

by the intermolecular forces exerted on the by the intermolecular forces exerted on the molecules of the object and the surface at the molecules of the object and the surface at the contact points.contact points.

While an object is moving, these bonds While an object is moving, these bonds can’t be made, so that is why kinetic can’t be made, so that is why kinetic friction is less than static friction.friction is less than static friction.

Graphing FrictionGraphing Friction

Force of Pull

Magnitude of Friction Forces Magnitude of Friction Forces Depends on The Normal ForceDepends on The Normal Force

The magnitude of the friction force is The magnitude of the friction force is determined by the normal force of the two determined by the normal force of the two surfaces in contact.surfaces in contact.

If the normal force increase, the friction If the normal force increase, the friction force will increase as well.force will increase as well.

FFff ~ F~ Fnn

Magnitude of Friction Forces Depends Magnitude of Friction Forces Depends on The Coefficient of Frictionon The Coefficient of Friction

Coefficient of FrictionCoefficient of Friction – The ratio of the – The ratio of the force of friction action between two force of friction action between two objects.objects.The symbol “The symbol “µ” defines the coefficient of µ” defines the coefficient of friction. (Has no units!)friction. (Has no units!) The lowercase Greek letter called, “mu”The lowercase Greek letter called, “mu”

µµss = F = Fssmaxmax/F/Fnn

µµkk = F = Fkk/F/Fnn

The Coefficients are listed on page 144 for The Coefficients are listed on page 144 for different surfaces.different surfaces.

Force of Friction EquationsForce of Friction Equations

The forces of friction can be found using The forces of friction can be found using the equations below:the equations below:

Kinetic Friction ForceKinetic Friction Force

FFkf kf == µµkkFFnn

Static Friction ForceStatic Friction Force

FFsf sf == µµssFFnn

Air ResistanceAir Resistance

Air resistance is a form of frictionAir resistance is a form of friction

Speed and AreaSpeed and AreaYou experience the force due to air resistance when you You experience the force due to air resistance when you stick your hand out of the window of a moving car. stick your hand out of the window of a moving car.

• If the car moves faster, the force on your hand If the car moves faster, the force on your hand increases. increases.

• If instead of just your hand, you hold your physics If instead of just your hand, you hold your physics book out the window with the large side facing book out the window with the large side facing forward, the air resistance force is much larger than forward, the air resistance force is much larger than on your hand at the same speed.on your hand at the same speed.

Air Resistance ProportionAir Resistance Proportion

Air resistance force ~ speed × frontal areaAir resistance force ~ speed × frontal area The expression shows that the air resistance force is The expression shows that the air resistance force is

directly proportional to the speed and frontal area of directly proportional to the speed and frontal area of an object.an object.

Air Resistance and MassAir Resistance and Mass

The mass of an object doesn’t effect the The mass of an object doesn’t effect the air resistance acting on the object, but it air resistance acting on the object, but it allows the object to push through the air allows the object to push through the air easier then an object with less mass.easier then an object with less mass.

The terminal velocity of a larger mass The terminal velocity of a larger mass object will have a high terminal velocity object will have a high terminal velocity then an object with less mass.then an object with less mass.

Terminal VelocityTerminal Velocity

Terminal VelocityTerminal Velocity – – The velocity at which The velocity at which the acceleration of a falling object is zero the acceleration of a falling object is zero because friction balances the weight. because friction balances the weight.

Example Problem #1Example Problem #1

A 25 kg chair initially at rest on a A 25 kg chair initially at rest on a horizontal floor requires a 365 N horizontal horizontal floor requires a 365 N horizontal force to set it in motion. Once the chair is force to set it in motion. Once the chair is in motion, a 327 N horizontal force keeps it in motion, a 327 N horizontal force keeps it moving at a constant velocity.moving at a constant velocity. Find the coefficient of static friction between Find the coefficient of static friction between

the chair and the floor.the chair and the floor. Find the coefficient of kinetic friction between Find the coefficient of kinetic friction between

the chair and the floor.the chair and the floor.

Example Problem #1 AnswerExample Problem #1 Answer

Static friction coefficient 1.49Static friction coefficient 1.49

Kinetic friction coefficient 1.33Kinetic friction coefficient 1.33