Newton’s Second Law Newton’s Second Law of Motion – Force and of Motion – Force and

AccelerationAcceleration

Chapter 6Chapter 6

ObjectivesObjectives• State the relationship between acceleration State the relationship between acceleration

and net force.and net force.• State the relationship between acceleration State the relationship between acceleration

and mass.and mass.• State and explain Newton’s 2State and explain Newton’s 2ndnd law of motion. law of motion.• List the factors that affect the force of friction List the factors that affect the force of friction

between surfaces.between surfaces.• Distinguish between force and pressure.Distinguish between force and pressure.• Explain why the acceleration of an object in Explain why the acceleration of an object in

free fall does not depend upon the mass of the free fall does not depend upon the mass of the object.object.

• List the factors that affect the air resistance List the factors that affect the air resistance force on an object.force on an object.

6.1 Force Causes 6.1 Force Causes AccelerationAcceleration• At rest, a hockey puck is in At rest, a hockey puck is in

equilibrium – gravity and the equilibrium – gravity and the support force are balanced.support force are balanced.

• If a player exerts an unbalanced If a player exerts an unbalanced force on the puck (pushes it), it force on the puck (pushes it), it accelerates.accelerates.

• When the puck is no longer When the puck is no longer being pushed, there is no being pushed, there is no longer an unbalanced force longer an unbalanced force acting on it. The puck does not acting on it. The puck does not accelerate but moves at accelerate but moves at constant velocity.constant velocity.

*Unbalanced forces acting on an object cause the object to accelerate.

6.1 Force Causes 6.1 Force Causes AccelerationAcceleration

• Since one force is usually not the only force Since one force is usually not the only force acting on an object, we must amend our acting on an object, we must amend our statement: statement: Acceleration depends on Acceleration depends on net force.net force.

• In fact, an object’s acceleration is In fact, an object’s acceleration is directly directly proportionalproportional to the net force acting on it. to the net force acting on it.o If you double the force, the acceleration doubles.If you double the force, the acceleration doubles.o If you increase the force by a factor of ten, the If you increase the force by a factor of ten, the

acceleration increases by a factor of ten.acceleration increases by a factor of ten.

• We can write: We can write: acceleration ~ net forceacceleration ~ net force (The symbol ~ stands for “is directly proportional to”).(The symbol ~ stands for “is directly proportional to”).

6.2 Mass Resists 6.2 Mass Resists AccelerationAcceleration

100 N

100 N

•Review the diagrams to the left.•The car of greater mass will accelerate less than the car of smaller mass with the same applied force.•Therefore, acceleration depends on the size of the mass being pushed.•In fact, acceleration is inversely proportional to the mass.

•If mass is doubled (see diagram), then the acceleration is halved.•Acceleration ~ 1 mass•This means the 2 values change in opposite directions. If mass increases, acceleration must decrease.

0.1

6.3 Newton’s Second Law6.3 Newton’s Second Law

• Newton realized acceleration depends Newton realized acceleration depends not only on the force of a push but also not only on the force of a push but also on an object’s mass.on an object’s mass.

*The acceleration produced by a net The acceleration produced by a net force on an object is directly force on an object is directly proportional to the magnitude of the proportional to the magnitude of the net force, is in the same direction as net force, is in the same direction as the net force, and is inversely the net force, and is inversely proportional to the mass of the proportional to the mass of the object.object.

6.3 Newton’s Second Law6.3 Newton’s Second Law• This means: acceleration ~ This means: acceleration ~ net forcenet force massmass

• When force is in newtons (N), mass is in When force is in newtons (N), mass is in kilograms (kg) and acceleration is in meters per kilograms (kg) and acceleration is in meters per second squared (m/ssecond squared (m/s22), we get the equation:), we get the equation:

acceleration = acceleration = net forcenet force massmass

a = F/m or F = ama = F/m or F = am

What is the acceleration due to gravity of these 2 objects?Recall: Force due to gravity = weight and W = mg

PracticePractice• A car has a mass of 1250 kg. What is the A car has a mass of 1250 kg. What is the

acceleration produced by a force of 2250 N?acceleration produced by a force of 2250 N?• What is the acceleration if the force is What is the acceleration if the force is

doubled?doubled?• What is the acceleration if the mass is What is the acceleration if the mass is

doubled?doubled?• How much force is needed to accelerate a How much force is needed to accelerate a

35,000 kg plane by 1.2 m/s35,000 kg plane by 1.2 m/s22??• If a car can accelerate at 5 m/sIf a car can accelerate at 5 m/s22, what , what

acceleration can it attain if it tows another acceleration can it attain if it tows another car that has a mass equal to its own?car that has a mass equal to its own?

PracticePractice

• Suppose a plane is flying at a Suppose a plane is flying at a constant 900 km/hr and the thrust constant 900 km/hr and the thrust (force) of the engines is a constant (force) of the engines is a constant 80,000 N. What is the acceleration 80,000 N. What is the acceleration of the plane?of the plane?

• What is the force of air resistance What is the force of air resistance that acts on the plane’s outside that acts on the plane’s outside surface?surface?

6.4 Friction6.4 Friction • Recall (from Ch. 2 & 3) Recall (from Ch. 2 & 3) that friction acts on that friction acts on materials that are in materials that are in contact with one contact with one another.another.

• It always acts in a It always acts in a direction opposite to the direction opposite to the relative motion.relative motion.

• Friction is due to Friction is due to irregularities in the 2 irregularities in the 2 surfaces. It requires surfaces. It requires force for a surface to force for a surface to overcome the “bumps” overcome the “bumps” in another surface.in another surface.

FRICTION

PUSH

6.4 Friction6.4 Friction• More specifically, the force of More specifically, the force of

friction depends on the KINDS of friction depends on the KINDS of material that are in contact and material that are in contact and HOW MUCH the surfaces are HOW MUCH the surfaces are pressed together.pressed together.٠ For example, rubber against concrete For example, rubber against concrete

produces more friction that steel produces more friction that steel against steel.against steel.

• Friction occurs between solids, Friction occurs between solids, liquids, gases, or any combination of liquids, gases, or any combination of the states of matter.the states of matter.

Types of Friction ForceTypes of Friction Force• Static frictionStatic friction: the resistance force that must : the resistance force that must

be overcome to start an object in motion.be overcome to start an object in motion.• Kinetic or sliding frictionKinetic or sliding friction: the resistance : the resistance

force between two surfaces already in motion.force between two surfaces already in motion.• Rolling frictionRolling friction: the resistance force : the resistance force

between a surface and a rolling object.between a surface and a rolling object.• Fluid frictionFluid friction: the resistance force of a gas or : the resistance force of a gas or

a liquid as an object passes through. a liquid as an object passes through. Air Air resistanceresistance is a special type of fluid friction. is a special type of fluid friction.

Friction ForceFriction Force

• Force of Force of sliding sliding friction = friction = (coefficient of (coefficient of friction) friction) (normal (normal force)force)

• FFff = µ x F = µ x Fnn

6.4 Friction6.4 Friction

• A diagram (like the ones A diagram (like the ones shown here) in which all shown here) in which all the forces acting on an the forces acting on an object are shown is called object are shown is called a a free-body diagramfree-body diagram..

• Here, the forces are Here, the forces are balanced – the net force is balanced – the net force is zero in each case. zero in each case. Therefore, the objects are Therefore, the objects are not accelerating but are not accelerating but are moving with a constant moving with a constant velocity.velocity.

6.5 Applying Force - 6.5 Applying Force - PressurePressure

• If you stand on your If you stand on your bathroom scale, the bathroom scale, the force measured is force measured is called your weight. called your weight. (F(Fgravgrav = W = mg) = W = mg)

• Will the reading change Will the reading change if you stand on one if you stand on one foot?foot?

• Will the reading change Will the reading change if you stand on one toe?if you stand on one toe?

• What does change?What does change?

6.5 Applying Force - 6.5 Applying Force - PressurePressure

• Although the force (your weight) is the same Although the force (your weight) is the same in all 3 cases, the area of contact is different in all 3 cases, the area of contact is different in each case. That is, in each case. That is, the area supporting the the area supporting the weightweight in each case is different. in each case is different.

• Since Since pressurepressure is defined as force per unit is defined as force per unit area, area,

Pressure = Pressure = forceforce or P = or P = FF area of application Aarea of application A

it is the it is the pressurepressure exerted on the surface that exerted on the surface that changes in each of our cases changes in each of our cases

• For a constant force, an INCREASE in area of For a constant force, an INCREASE in area of contact will cause a DECREASE in the contact will cause a DECREASE in the pressure.pressure.

PracticePractice

* Note: Pressure is measured in newtons (N) Note: Pressure is measured in newtons (N) per square meter (mper square meter (m22) or ) or pascals (Pa).pascals (Pa).

•What are 2 ways to increase the pressure What are 2 ways to increase the pressure on something?on something?

•What is the pressure exerted by a 400 N What is the pressure exerted by a 400 N force if its contact area is force if its contact area is •4 m4 m22??

•0.4 m0.4 m22??

•0.04 m0.04 m22??

6.6 Free Fall Explained6.6 Free Fall Explained

• Recall (Ch. 4) that in Recall (Ch. 4) that in free fall, gravity is the free fall, gravity is the only thing that affects a only thing that affects a falling object.falling object.

• Galileo showed that Galileo showed that falling objects, falling objects, regardless of their mass, regardless of their mass, accelerate equally.accelerate equally.

• Galileo could not explain Galileo could not explain why this was true.why this was true.

6.6 Free Fall Explained6.6 Free Fall Explained

• Recall (Ch. 3) that mass and weight are Recall (Ch. 3) that mass and weight are proportional to each other.proportional to each other.– A 10 kg. mass weighsabout 10x as much as A 10 kg. mass weighsabout 10x as much as

a 1 kg. mass.a 1 kg. mass.

• In fact, since weight is the In fact, since weight is the forceforce of of gravity on an object, we can use the gravity on an object, we can use the equation F = ma to express weight this equation F = ma to express weight this way: weight (W) = mass (m) times way: weight (W) = mass (m) times acceleration due to gravity (g) or acceleration due to gravity (g) or W = W = mgmg..

6.6 Free Fall Explained6.6 Free Fall Explained• Therefore, the Therefore, the ratioratio of weight of weight (force) to mass is (force) to mass is the same for any the same for any objects.objects.

• All free falling All free falling objects undergo objects undergo the the same same acceleration acceleration at at the same place on the same place on Earth. Earth.

• This is represented This is represented by g and equals by g and equals approximately 10 approximately 10 m/sm/s22..

Cartoon from text p. Cartoon from text p. 9494

All freely All freely falling objects falling objects fall with the fall with the same same acceleration acceleration because the because the net force on an net force on an object is only object is only its weight, and its weight, and the ratio of the ratio of weight to mass weight to mass is the same for is the same for all objects.all objects.

6.7 Falling and Air 6.7 Falling and Air ResistanceResistance

In a vacuum (no air resistance) In presence of air

6.7 Falling and Air 6.7 Falling and Air ResistanceResistance

• Focus on the feather in the 2Focus on the feather in the 2ndnd animation. animation.• When falling in air, it is obvious that air When falling in air, it is obvious that air

resistance (a frictional force) does have an affect resistance (a frictional force) does have an affect on the NET force of the falling objects – it on the NET force of the falling objects – it decreases it.decreases it.

• The net force is equal to the force or weight of The net force is equal to the force or weight of the object MINUS its air resistance.the object MINUS its air resistance.

• Net Force = FNet Force = Fgravgrav - F - Fairair

• Therefore, since the FTherefore, since the Fnetnet is less, acceleration of a is less, acceleration of a falling object is less and its resulting velocity is falling object is less and its resulting velocity is less.less.

Speed and Speed and AreaArea

• The two most commonThe two most common factors which have a factors which have a direct effect upon the direct effect upon the amount of air resistance present are:amount of air resistance present are: 1. The speed of the object: the greater the 1. The speed of the object: the greater the

speed, speed, the greater the force of air resistance.the greater the force of air resistance. 2. The frontal area of the object: the greater the 2. The frontal area of the object: the greater the frontal area, the greater the air resistance.frontal area, the greater the air resistance.

*Air resistance force ~ speed x frontal areaAir resistance force ~ speed x frontal area

Terminal VelocityTerminal Velocity• As a skydiver falls, his velocity continually increases As a skydiver falls, his velocity continually increases

– he is accelerating due to gravity.– he is accelerating due to gravity.• Since air resistance is proportional to speed, as his Since air resistance is proportional to speed, as his

speed increases speed increases so does the air resistanceso does the air resistance he he encounters.encounters.

• When the magnitude of the air resistance When the magnitude of the air resistance equals the weight of the skydiverequals the weight of the skydiver (his force due (his force due to gravity), there is no longer any NET force on the to gravity), there is no longer any NET force on the sky diversky diver

Terminal VelocityTerminal Velocity• With no net force on a With no net force on a

falling object, there is falling object, there is no acceleration and the no acceleration and the velocity remains velocity remains constant.constant.

• The speed of an object The speed of an object when its acceleration is when its acceleration is zero (zero (becausebecause F Fairair balances Fbalances Fgravgrav) is called ) is called the the terminal speed.terminal speed.

• Since we know the Since we know the direction (downward), direction (downward), we can call it the we can call it the terminal velocityterminal velocity..

Fair

Fgrav

• Objects which have a large area relative to their Objects which have a large area relative to their weight will reach their terminal velocity very quicklyweight will reach their terminal velocity very quickly ..° The feather pictured above has a large area compared to its The feather pictured above has a large area compared to its

weight. It encounters a lot of air resistance very quickly.weight. It encounters a lot of air resistance very quickly.° The elephant has a relatively small area compared to its weight. It The elephant has a relatively small area compared to its weight. It

will accelerate for a longer period of time before the force of air will accelerate for a longer period of time before the force of air resistance equals the force due to gravity and the terminal velocity resistance equals the force due to gravity and the terminal velocity is reached.is reached.

Terminal VelocityTerminal Velocity• Since living things can Since living things can

change their body change their body orientation, changing their orientation, changing their “area” relative to their “area” relative to their weight, they can somewhat weight, they can somewhat control their terminal speed.control their terminal speed.

Terminal VelocityTerminal Velocity

•Parachutes can Parachutes can also greatly also greatly increase air increase air resistance.resistance.•Terminal velocity Terminal velocity can be cut from can be cut from 150-200 km/hr. to 150-200 km/hr. to 15-25 km/hr.15-25 km/hr.•Slow terminal Slow terminal speeds insure a speeds insure a safe landing.safe landing.

A final note about Galileo A final note about Galileo . . . .

• When Galileo dropped objects from the Leaning When Galileo dropped objects from the Leaning Tower of Pisa, the heavier object DID hit the Tower of Pisa, the heavier object DID hit the ground first. The time difference was so small, ground first. The time difference was so small, however, it could not be detected.however, it could not be detected.

• At low speeds (short distances of fall), air At low speeds (short distances of fall), air resistance is negligible.resistance is negligible.

• At high speeds (long falls where air resistance At high speeds (long falls where air resistance can “build up”), the effect of air resistance is can “build up”), the effect of air resistance is more pronounced.more pronounced.

• The effect of air resistance is also more The effect of air resistance is also more pronounced on lighter objects. Lighter objects pronounced on lighter objects. Lighter objects behave more like a parachute than heavier behave more like a parachute than heavier objects.objects.

PracticePractice• What is the net force of What is the net force of

the falling object?the falling object?• What is the acceleration What is the acceleration

of the falling object?of the falling object?• What will be the What will be the

acceleration of the object acceleration of the object when it reaches its when it reaches its terminal velocity?terminal velocity?

• Which mass will reach the Which mass will reach the ground first – a 10 kg. ground first – a 10 kg. mass or a 100 kg. mass? mass or a 100 kg. mass? Why?Why?

Fair = 10 N

10 kg.

Fgrav = 100 N

Check your Check your UnderstandingUnderstanding

• A sky diver jumps from a hot air balloon. A sky diver jumps from a hot air balloon. • As she falls faster & faster, does air As she falls faster & faster, does air

resistance increase, decrease, or remain resistance increase, decrease, or remain the same?the same?

• Does the net force on her increase, Does the net force on her increase, decrease, or remain the same?decrease, or remain the same?

• As she falls faster & faster, does her As she falls faster & faster, does her acceleration increase, decrease, or remain acceleration increase, decrease, or remain the same?the same?

• How can she change the air resistance How can she change the air resistance force she experiences?force she experiences?

PracticePractice• Draw a series of free body diagrams to Draw a series of free body diagrams to

represent an 85 kg skydiver undergoing represent an 85 kg skydiver undergoing free fall. Show a diagram for the instances free fall. Show a diagram for the instances when the Fwhen the Fair air is 0 N, 350 N, 700 N and 833 is 0 N, 350 N, 700 N and 833 N.N.

In each instance, determine the FIn each instance, determine the Fgravgrav, F, Fnetnet, , and the acceleration. and the acceleration.