Chapter 4Chapter 4

Forces and the Laws of Forces and the Laws of MotionMotion

Changes in MotionChanges in Motion

When we think of Force, we typically When we think of Force, we typically imagine a push or pull exerted on an imagine a push or pull exerted on an object.object.

Force can be defined as causing a Force can be defined as causing a change in the motion of an object.change in the motion of an object.

Force…Force…

Can make an object accelerateCan make an object accelerate Can make an object decelerateCan make an object decelerate Can make an object change directionCan make an object change direction

NewtonNewton

Force is measured in newtons.Force is measured in newtons. A newton (N) is defined as the amount A newton (N) is defined as the amount

of force that will accelerate a 1kg of force that will accelerate a 1kg object by 1m/sobject by 1m/s22

N = kg•m/sN = kg•m/s22

An objects weight, in lbs. Is the An objects weight, in lbs. Is the measure of the force of gravity on that measure of the force of gravity on that object.object.

1lb = 4.4N 1N = .23lbs1lb = 4.4N 1N = .23lbs

Types of ForcesTypes of Forces

Contact Forces result from physical Contact Forces result from physical contact between two objectscontact between two objects Throwing a ballThrowing a ball Braking in your carBraking in your car

Field forces do not require contactField forces do not require contact GravityGravity MagnetismMagnetism All fundamental forces. All fundamental forces.

Force (cont)Force (cont)

Force is a vector. Its effect depends Force is a vector. Its effect depends on both its magnitude and directionon both its magnitude and direction

We can use force diagrams, which We can use force diagrams, which represent force vectors with arrows, represent force vectors with arrows, to help us understand all the forces to help us understand all the forces acting on an object.acting on an object.

We will assume all forces act on the We will assume all forces act on the center of an object.center of an object.

Force DiagramsForce Diagrams

A force diagram isolates one object and A force diagram isolates one object and illustrates all the forces acting on that object.illustrates all the forces acting on that object.

Force diagrams should always include the Force diagrams should always include the force of gravityforce of gravity

If the object is on the ground the Normal If the object is on the ground the Normal force will negate the force of gravity. To keep force will negate the force of gravity. To keep the object from accelerating through the the object from accelerating through the ground. (or lifting off of it)ground. (or lifting off of it)

The force of friction will always oppose The force of friction will always oppose motion.motion.

Normal ForceNormal Force The normal force the force exerted on on The normal force the force exerted on on

object by the floor. object by the floor. It keeps the forces in the y direction equal It keeps the forces in the y direction equal

to zero.to zero. If there is no vertical forces other than If there is no vertical forces other than

gravity, then the normal force will equal gravity, then the normal force will equal gravity but in the opposite direction.gravity but in the opposite direction.

If there are vertical forces, then the If there are vertical forces, then the normal force will simply be enough to normal force will simply be enough to cancel the other vertical forces.cancel the other vertical forces.

FrictionFriction

The force of friction depends on the The force of friction depends on the surfaces in contact.surfaces in contact.

There are two types of FrictionThere are two types of Friction Static Friction - opposes initial Static Friction - opposes initial

motion of an object (Fmotion of an object (Fs,maxs,max)) Kinetic Friction - opposing force on a Kinetic Friction - opposing force on a

moving object (Fmoving object (Fkk)) Kinetic Friction is always less than Kinetic Friction is always less than

static friction static friction

Coefficient of Friction Coefficient of Friction

Forces of both static friction and kinetic Forces of both static friction and kinetic friction are dependant on the normal force friction are dependant on the normal force acting on an object multiplied by the acting on an object multiplied by the coefficient of friction for the contact pairs in coefficient of friction for the contact pairs in question.question.

FFs,max s,max = = ss(F(Fnn))

FFk k = = kk(F(Fnn))

Table 4-2 lists both Table 4-2 lists both s s and and kk for several for several surface pairssurface pairs

Coefficient of Friction is a unit-less value Coefficient of Friction is a unit-less value

ExampleExample

How much force would be needed to How much force would be needed to start moving a 2kg aluminum weight start moving a 2kg aluminum weight on a steel surface? (Fon a steel surface? (Fs,maxs,max))

FFnn= F= Fg g = m= mwwaagg = 2kg (9.8m/s = 2kg (9.8m/s22) = ) = 19.6 N19.6 N

FFs,maxs,max= = ss(F(Fnn) = (0.61)(19.6N) = 12 N) = (0.61)(19.6N) = 12 N

ExampleExample

An object has a weight of 14,700 N. An object has a weight of 14,700 N. It is being pulled backward at an angle of 10º It is being pulled backward at an angle of 10º

from the horizontal, with a force of 5,800 N.from the horizontal, with a force of 5,800 N. The object is experiencing 775N of friction.The object is experiencing 775N of friction. Draw that diagramDraw that diagram

-14,700 N = Fg

5,800 N = Fp

10º

13,390 N = Fn

755 N = Ff

Resolving Force Resolving Force DiagramsDiagrams

Each force can be resolved into its x Each force can be resolved into its x and y components using the sine and and y components using the sine and cosine functions. cosine functions.

The Resultant force can be found The Resultant force can be found using the Pythagorean Theorem.using the Pythagorean Theorem.

FFRR= = √(sum x forces)√(sum x forces)2 2 + (sum y + (sum y forces)forces)22

ExampleExample

Solve the example force diagram for Solve the example force diagram for Net Force (FNet Force (Fnetnet))

Resolve x and y components of any Resolve x and y components of any “slanted” forces. (F“slanted” forces. (Fpp)) FFxx= F cos= F cos FFyy = F sin = F sin FFxx= (5800N)cos10= (5800N)cos10 FFyy = (5800N)sin10 = (5800N)sin10

FFxx= -5710 N= -5710 N FFyy = 1010 N = 1010 N

Sum x and y ForcesSum x and y Forces

X ForcesX Forces FFf f = 755 N= 755 N

FFp,x p,x = -5710 N= -5710 N

FFX X = -4955 N= -4955 N

Y ForcesY Forces FFgg= -14,700 N= -14,700 N

FFnn=13,690 N=13,690 N

FFp,y p,y = 1010 N= 1010 N

FFY Y = 0 N= 0 N

Example 2Example 2

A tug boat has a propeller on each of its A tug boat has a propeller on each of its sides.sides.

Each motor is capable of producing Each motor is capable of producing 25,000N. (assume the boat is aligned with 25,000N. (assume the boat is aligned with the compass)the compass)

If both the north and south motors are If both the north and south motors are pointed south, the east motor is pointed pointed south, the east motor is pointed 25º south of east, and the west motor is 25º south of east, and the west motor is pointed 40º south of west, what is the pointed 40º south of west, what is the result force?result force?

Newton’s 1st LawNewton’s 1st Law

An object will continue to maintain its An object will continue to maintain its state of rest or of uniform motion unless it state of rest or of uniform motion unless it experiences a net external force. (Inertia)experiences a net external force. (Inertia)

Examples:Examples: An car moving at a constant velocity An car moving at a constant velocity

experiences several forces but no net forceexperiences several forces but no net force If you increase the force forward, the car will If you increase the force forward, the car will

accelerate in that directionaccelerate in that direction If you add a new force, brakes, in the opposite If you add a new force, brakes, in the opposite

direction the car will decelerate direction the car will decelerate

Newton’s 2nd LawNewton’s 2nd Law

The acceleration of an object is The acceleration of an object is directly proportional to the net directly proportional to the net external force and inversely external force and inversely proportional to the mass of the proportional to the mass of the object.object.

Force = mass x acceleration (F = Force = mass x acceleration (F = ma)ma)

ExampleExample

If a 2000kg car experiences an If a 2000kg car experiences an acceleration of 10 m/sacceleration of 10 m/s22, what is the , what is the net external force acting on that net external force acting on that object?object?

FFnetnet = ma = ma

FFnetnet = (2000kg)(10 m/s = (2000kg)(10 m/s22) = 20,000 N) = 20,000 N

Example 2Example 2

If a 45N force is exerted on an If a 45N force is exerted on an object with a mass of 0.75kg, what is object with a mass of 0.75kg, what is its acceleration?its acceleration?

F = maF = ma a = F/m a = F/m a = (45N)/(0.75kg) = 60m/sa = (45N)/(0.75kg) = 60m/s22

Newton’s 3rd LawNewton’s 3rd Law

If two bodies interact, the magnitude of If two bodies interact, the magnitude of the force exerted on object 1 onto the force exerted on object 1 onto object 2 is equal to the magnitude of object 2 is equal to the magnitude of the force exerted by object 2 onto the force exerted by object 2 onto object 1, and these two forces will be in object 1, and these two forces will be in opposite directionopposite direction

Every action has an equal and opposite Every action has an equal and opposite reaction.reaction.

FF11 = F = F22

mm11aa1 1 = m= m22aa22

ExampleExample

If a 3.10 kg rifle were hung from a If a 3.10 kg rifle were hung from a ceiling and fires an 11.0g bullet which ceiling and fires an 11.0g bullet which accelerates at 1340m/saccelerates at 1340m/s22, what force is , what force is experienced by the bullet and what experienced by the bullet and what acceleration is experienced by the gun? acceleration is experienced by the gun?

FFbb = (0.011kg)(1340m/s = (0.011kg)(1340m/s22) = 14.7 N) = 14.7 N

FFb b = F= Fgg = m = mggaag g

aagg = F = Fbb/m/mg g = (14.7N)/(3.10kg) = = (14.7N)/(3.10kg) = 4.74m/s4.74m/s22