Forces and the Laws of Motion

Forces and the Laws of Motion

Chapter 4

Forces and the Laws of Motion4.1 Changes in Motion

– Forces• A force is a physical quantity that can affect the state of motion of

an object. Forces are pushes or pulls.• An unbalanced or net force causes acceleration.• Balanced forces (net force = 0) do not cause acceleration.• Forces are measured in newtons (N).

– 1 N = 1 kg.m/s2

• Forces can act through contact or at a distance.– Contact forces occur when objects touch.– Field forces occur when objects do not touch.

» electric fields» magnetic fields» gravitational fields

• Forces are vectors and are drawn with arrows.

Forces and the Laws of Motion• Types of Forces

Weight (Gravitational Force)Applied ForceNormal ForceTension ForceFriction Force (includes Air Resistance)Spring ForceElectrical Force Magnetic Force

Forces and the Laws of Motion• Gravity (Weight)

Fg or FG or W or mg: On Earth the force of gravity is often

referred to as the weight of an object. It is the attractive force of the earth on an object, and is always directed toward the center of the earth. It has a magnitude equal to the mass of the object times the acceleration due to gravity, or mg. The force of gravity is a field force.

Forces and the Laws of Motion• Types of Contact Forces

– Applied Force, Fapp: An applied force is a force exerted on an object by a person, by another object, or by an action which directly pushes or pulls on the object. - pushing a box across the floor

– Spring Force, Fspring, is the force exerted on an object by a compressed or stretched spring.


– Friction Force, Ffrict: The friction force opposes the applied force and is exerted by a surface on an object as it moves across or makes an effort to move across the surface. Air resistance, Fair is a friction force.

– When pushing a box across the floor, the surface of the floor exerts friction on the object.

– Tribology is defined as the science of interacting surfaces in relative motion.


– Tension Force (T, Ftens or FT): This is the force exerted by a rope, cable, or string, when it is attached to an object and pulled taut. It is directed away from the object and along the rope at the point of attachment.


– Normal Force (Fnorm or Fn or FN) : The normal force is a support force that acts on an object at the surface in a direction perpendicular to the surface. (Don’t forget the normal.)

Forces and the Laws of Motion4.1 Free Body Diagrams (FBD) are used to analyze the forces on

a single object.

1. Identify (isolate) the object or system.2. Identify the forces acting on the object and the direction of the forces. 3. Draw a diagram (a dot or box) to represent the isolated object.4. Draw and label vector arrows for all external forces acting on the object.5. Choose a coordinate system.6. Include critical angles and dimensions.

Force Diagrams show all force vectors as arrows. A free body diagram shows all of the external forces acting on a single object (not forces exerted by the object in question on other objects!).

Free body diagrams are used to determine the vector sum of all the forces acting on an object.

Forces and the Laws of Motion4.1 Free Body Diagrams Practice1. A book is at rest on a table top. Diagram the forces acting on the

book.

2. A girl is suspended motionless from the ceiling by two ropes. Diagram the forces acting on the girl.

3. An egg is free-falling from a nest in a tree. Neglect air resistance. Diagram the forces acting on the egg as it is falling.

FN

Fg

FN

mg

Forces and the Laws of Motion4.1 Free Body Diagrams Practice4. A flying squirrel is gliding (no wing flaps) from a tree to the ground at constant velocity. Consider air resistance. Diagram the forces acting on the squirrel.

5. A rightward force is applied to a book in order to move it across a desk with a rightward acceleration. Consider frictional forces. Neglect air resistance. Diagram the forces acting on the book.

Forces and the Laws of Motion4.1 Free Body Diagrams Practice

6. A college student rests a backpack upon his shoulder. The pack is suspended motionless by one strap from one shoulder. Diagram the vertical forces acting on the backpack.


7. A skydiver is descending with a constant velocity. Consider air resistance. Diagram the forces acting upon the skydiver.

8. A force is applied to the right to drag a sled across loosely-packed snow with a rightward acceleration. Diagram the forces acting upon the sled.


9. A football is moving upwards towards its peak after having been booted by the punter. Diagram the forces acting upon the football as it rises upward towards its peak. No air resistance.

10. A car is coasting to the right and slowing down. Diagram the forces acting upon the car.

• Steps for drawing a force diagram:• Identify the object you will draw a diagram for. (If there are multiple objects of interest, you will need to draw

multiple diagrams.) • Identify all the forces acting directly on the object and the object exerting them. With the exception of gravity and

certain other forces rarely used in first semester physics (magnetism, electric force), the two objects will be in direct contact. Do not include forces by an object acting through another object--only include the force due to the intermediate object.

• Draw a dot to represent the object of interest. • Draw a vector to represent each force. Draw it in the direction the force is being exerted, and label it by (a) the

type of force, (b) the object exerting the force, and (c) the object receiving the force (which will be you object of interest). It will have the form F(type)exerting object -> object of interest

• If the object is stationary or is moving at a constant velocity, the vectors should graphically add up to zero. If the object is accelerating, the sum of the vectors should produce a vector in the same direction as the acceleration.

• Writing down the sum of the forces• Identify direction of every force and of acceleration. • Pick a coordinate system to minimize the number of things (forces and acceleration) that must be broken into

components, especially unknown values • Draw the components for any forces or acceleration that does not lie along the X or Y axis, and identify the angle

that is given (or being looked for). • Pick one direction and write down all the forces or components of forces in that direction, using positive and

negative signs to identify those in the positive and negative directions. • Set the sum of the forces in that direction as equal to the mass multiplied by the acceleration in that direction. (If

not moving or moving at a constant velocity in that direction, acceleration will be zero.) • Repeat for the other direction.

Forces and the Laws of Motion4.2 Newton’s First Law – The Law of InertiaIn the absence of a net external force, an object will continue in a state of uniform

motion (including rest) in a straight line. (1687, The Mathematical Principles of Natural Philosophy or Philosophiae Naturalis Principia Mathematica )

An object at rest remains at rest, and an object in motion continues in motion with constant velocity unless acted upon by an unbalanced force or a net external force.

Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it. (Galileo, in the 1630’s, had recognized this about motion.)

Forces and the Laws of Motion4.2 Newton’s First Law – The Law of Inertia

Uniform Motion• not changing

• no acceleration• at rest or

moving at constant velocity

• no change in speed• no change in

direction• all forces balance

• no net force• Fnet = 0

• equilibrium

Nonuniform Motion• changing motion

• acceleration• changing velocity• change in speed

• change in direction • change in speed and

direction• unbalanced force

• net force• Fnet = 0

or

4.2 Newton’s First Law – The Law of Inertia

• An object maintains constant velocity until acted upon by a net force.

• When the net external force on an object is zero, the object does not accelerate.

• Analyze the forces acting on an object using free body diagrams to determine the sum of all the forces acting on the object. This is the net force.


4.2 Determining Net Force

1. Define the problem.2. Select a coordinate system, and apply it to the free-body

diagram. (Make the x-axis parallel to the incline and the y-axis perpendicular to it.)

3. Find the x and y components of all vectors.4. Find the net force in both the x and y directions. (Sum the

forces in the x direction and sum the forces in the y direction.

S Fx and S Fy

5. Find the net force. If there is a net force in both the x and y directions, use vector addition (Pythagorean theorem) to find the total (or single) net force on the object. Use tan-1q to determine the direction of the net force and thus the direction of the acceleration.


Forces and the Laws of Motion4.2 Determining Net Force

Net force is the vector sum of forces acting on an object.

S Fx = Fforward – Ffriction = 0

S Fy =Flift - Fgravity = 0

Fforward

Fgravity

Flift

Ffriction

Fnet = 0 N

• 4.2 Equilibrium

– Fnet = 0– Equilibrium is the state in which the net force on an

object is zero. (Acceleration is zero.)– Objects at rest or at constant velocity are in

equilibrium. – When there is a net force acting on an object, the

equilibrant force is the single force that if applied to an object would balance or cancel the net force and produce equilibrium.


4.2 Newton’s First Law – The law of Inertia– Inertia is the tendency of an object to resist being moved or, if the

object is moving, to resist a change in speed or direction.

– Inertia is the tendency of an object not to accelerate.

– Mass (the amount of matter in an object) is a measure of inertia. – Inertia is directly proportional to mass. The greater mass an object

has then the greater the inertia of that object.



Fnet = 400 N, up

Fnet = 200 N, down

Fnet = 20 N, left


Fnet = 0 N Fnet = 5 N, left

Fnet = 0 N Fnet = 15 N, up


A = 50 NB = 200 N

C = 1100 N D = 20 NE = 300 N

F = 22 N*G = 50 NH = 22 N*

*Any number you choose as long as F = H.

• Vector Review– The resultant vector is the sum of two or more vectors and can

be determined trigonometrically or graphically.– A single vector can be resolved into two or more components

that have the same effect.


q

FFx = F.cosq

Fy = F.sinq

– Concurrent forces act through the same point at the same time and can be combined to find the resultant vector.

4.2 Determining Net Force on Inclines


http://www.physicsclassroom.com/Class/vectors/u3l3e.cfm

FII = Fgrav.sinq

Fperp = Fgrav.cosq

Remember Fgrav = mg

4.2 Determining Net Force on InclinesForces and the Laws of Motion

35oFg

FNFfrict

q

35o

35oq = 35o

55o

Fg.sinq

Fg.cosq

Coordinate System: X-axis is parallel to the slope.Y-axis is perpendicular to the slope.

x

y

4.2 Determining Net Force on InclinesForces and the Laws of Motion

Fg

FNFfrict

q

35o

Fg.sinq

Fg.cosq

S Fx = Fg.sinq - Ffrict

S Fy = FN - Fg.cosq

Remember Fg = mg

x

y

q = 35o

Right is +. Left is -.Up is +. Down is -.

4.2 Determining Net ForceForces and the Laws of Motion


Fnet = 5 N down the ramp

4.2 Determining Net Force - YOU TRY!Forces and the Laws of Motion

Draw a free body diagram for a block on a 25o incline ignoring friction. Show the x and y (parallel and perpendicular) components of gravity.

25o 25o

FN

FG

Fgsin25o

Fgcos25o



100 kg crate

Ffrict = 255 N

Determine Fnet .

255

30o

Fgrav = mg = 100 kg x 9.81 m/s2 = 981 N

FII = Fgrav.sinq = 981 N . sin 30o = 491 N

Fnorm = Fgrav.cosq = 981 N . cos30o = 850 N

981

Fperp = Fgrav.cosq = 981 N . cos30o = 850 N

Fperp

Fnorm – Fperp = 0

Fnet = FII - Ffrict

Fnet = 491 N – 255 N

Fnet = 236 N down the ramp



9810

6937

6937 6.9 4

9810

4905

84968.50


Fg =

10 kg

T1 T2

A 10kg sculpture is hanging stationary by two cables as shown in the diagram. What is the tension in the cables?

Fg = mg Fg = 10 kg x 9.81 m/s2 = 98.1 N

Analyze:The forces are balanced because the object is stationary. Vertical forces cancel or add to zero and so do horizontal forces.T1 and T2 have vertical and horizontal components. T1 and T2 horizontal components cancel each other.What part of the tension force is holding up the structure? The vertical component of the two tension forces. So, T1,y + T2,y = Fg .

VerticalT1,y = T1 x sin 45o and T2,y = T2 x sin 45o

HorizontalT1,x + T2,x = 0 or T1,x = -T2,x T1

.cos45o = T2.cos45o

T1 = T2

98.1 N

Fg = T1,y + T2,y = T1.sin 45o + T2

.sin 45o T1 =T2

98.1 N = T1.sin 45o + T1

.sin 45o

98.1 N = 2(T1.sin 45o)

T1 = 69 N


• Practice – p. 128 1-3– p. 129 1-5

Forces and the Laws of Motion• 4.3 Newton’s Second Law of Motion

– According to Newton’s first law when a net force does act on an object its motion changes, that is, it accelerates.

– The Law of AccelerationThe acceleration of an object is directly proportional to the net

force acting on an object and inversely proportional to the object’s mass.

F = ma a = F/mm = F/a

SF = ma or net force = mass x acceleration


What do we know about acceleration?Acceleration is the rate of change in velocity.Acceleration occurs when an object speeds up, slows down, or

changes direction (at constant speed or changing speed).a = Dv/t = (vf-vi)/tAcceleration is zero if velocity is constant.vf = vi + at

When acceleration is constant:Dx = vit + ½ at2

vf = vi + 2aDx2 2

SF = ma

Forces and the Laws of Motion• 4.3 Newton’s Second Law of Motion

F = ma

Fg = mg = weight

Forces and the Laws of Motion• 4.3 Newton’s Third Law of Motion – The Law

of Recoil– If two objects interact, the magnitude of the force exerted on

object 1 by object 2 is equal to the magnitude of the force simultaneously exerted on object 2 by object 1, and these two forces are opposite in direction.

– For every action force there exists an equal in size and opposite in direction reaction force.

– Forces always exist in pairs.

– Action and reaction forces are two forces that act on two different objects.

– Field forces also exist in pairs. The earth exerts a force of gravity on you and you exert a force of gravity on the earth.

– Practice with handout.

Forces and the Laws of Motion• 4.4 Everyday Forces

– Weight• magnitude of the gravitational force exerted on an object• depends on location • W = Fg = mag = mg = m.9.81 m/s2 on Earth• The greater the distance between Earth and the object the less

weight the object has because the force of gravity decreases with increasing distance.


– The Normal Force• normal means perpendicular• is the support force perpendicular to an object and the

surface it touches

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– Friction• Friction opposes the applied force.• Static friction opposes the initiation of motion

between two surfaces in contact and at rest. Static friction must be overcome before an object will move.

• Fs = Fapp until Fs = Fs,max and a greater Fapp will cause motion.

• 4.4 Everyday Forces

Kinetic friction, Fk, is the retarding force on an object in motion. Fnet = Fapp – Fk

Kinetic friction is less than static friction.


– Friction• Friction results from complex interactions between

contacting surfaces which include electrostatic forces between the molecules and atoms.

• The force of friction, Ff, is proportional to the normal force.

• The force of friction between two surfaces is approximately equal to the normal force multiplied by the coefficient of friction for the two surfaces. Ff = mFn

• Fk = mkFn Fs = msFn

The coefficient of friction is a ratio of forces.mk = Fk/Fn

ms = Fs,max/Fn

The coefficient of friction is a ratio of forces.mk = Fk/Fn

ms = Fs,max/Fn

Forces and the Laws of Motion• 4.4 Air Resistance, FR

• a form of fluid friction• FR increases with

increasing speed.

Net ForceFnet = Fapp – Ff

Fnet = Fapp - mFN

Fnet = Fapp – mFg

Fnet = Fapp - mmg

Net ForceFnet = Fapp – Ff

Fnet = Fapp - mFN

Inclined plane components when gravity is the applied force Fnet = mgsinq - m mgcosqmanet = mgsinq - m mgcosq

Forces and the Laws of Motion• 4.4 Four Fundamental Forces

Unified Field Theory

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Forces and the Laws of Motion