physics 149: lecture 7

PHYSICS 149: Lecture 7• Chapter 2

– 2.8 Tension– 2.9 Fundamental Forces

• Chapter 3– 3.1 Position and Displacement

Lecture 7 Purdue University, Physics 149 1

TensionDefinition:

Magnitude of Contact Force between different segments of the string (or between an end and the object attached there)

Example:

TP

T is the force on the leftportion from the right portion |T| is the tension at point P

NOTE: T can only pull the other objectLecture 7 3Purdue University, Physics 149

Tension


• At any point in the rope (or string, cable or chain), tension is the pulling force exerted on the rope on one side of the point by the rope on the other side.

• At its two ends, tension is the pulling force exerted on the object attached to its ends by the ropes at the ends.

• Note that tension can pull but not push.

“If” the chain’s weight is not negligible,T1 > T2 > T3 > T4 .

For example,T1 = T4 + chain’s weight.

=T1

=T2

=T3

•=T4

Ideal Cord

An ideal cord has NO MASS

Consequence: the tension is the sameat ALL POINTS along the cord.

Lecture 7 5Purdue University, Physics 149

Tension with “Ideal Cord”• “Ideal cord”: a cord that has zero mass and thus zero weight• In an ideal cord, (a) the tension has the same value at all points

along the cord, and (b) the tension is equal to the force that the cord exerts on the objects attached to its ends (as long as there is no external force on the cord).

• Note: In many cases, the weight of a cord is negligibly small compared to the weight of the objects attached to its ends, and thus we may assume that it is an ideal cord.

=T1

=T2

=T3

•=T4 “If” the chain’s weight is negligible (ideal cord),T1 = T2 = T3 = T4 .


Ideal Pulley• Pulley: A pulley serves to change the direction of a tension force, and

may also (in the case of multiple-pulley systems) change its magnitude.

• “Ideal pulley”: a pulley that has no mass and no friction.• The tension of an “ideal cord” that runs through an “ideal pulley” is the

same on both sides of the pulley (and at all points along the cord).

T= =T


Example: Tension


• Given conditions:– “Ideal cord” Tension is same.– Equilibrium Net force = ΣFi = 0


TensionDetermine the tension in the 6 meter rope if it sags 0.12 m in the center when a gymnast with weight 250 N is standing on it.

x-direction: ΣF = m a-TL cosθ + TR cosθ = 0TL = TR

3 m.12 mθy-direction: ΣF = m a

TL sinθ + TR sinθ - W = 02 T sinθ = WT = W/(2 sinθ) = 3115 Ν

y

x

Tension


Θ = tan-1(0.12/3.00) = 2.291°

T1x = –T1 cosΘ T2x = T2 cosΘ Wx = 0T1y = T1 sinΘ T2y = T2 sinΘ Wy = –250 N

x-component: ΣFx = 0ΣFx= T1x + T2x = –T1cosΘ + T2cosΘ = 0

T1 = T2y-component: ΣFy = 0ΣFy= T1y + T2y – W = T1sinΘ + T2sinΘ – W = 2⋅T1sinΘ – W = 0

T1 = T2 = W / (2⋅sinΘ) = 250 N / [2 ⋅ sin(2.291°)] = 3127.0 N

T1 T2

W

y

x

y

xθθ

3.00 m

.12 mtightrope

Example: A Two-Pulley SystemWhat is the tension of the rope?

– FBD for Pulley L

– EquilibriumΣFy= Tc + Tc – W = 0Tc = W /2 = 902 N

– Since tension is the same at all points along the cord C, the person’s pulling force is equal to Tc.

– Therefore, the person pulling the rope only needs to exert a force equal to half the engine’s weight.

W =


Pulley Example

T

200 N

How much is T?

T =100 NExplain why…


ILQ


What can you say about the tensions T1 and T2 at the two ends of the cord?(W is the weight of the cord)

A) T1 > T2B) T2 > T1C) T1=T2D) depends

T1

T2

W

NOTE: this is NOT an ideal cord!

ILQ


If the weight W=0 then the cord is ideal.Is it true that T1=T2 ? A) no, T1>T2B) yes, because of 3rd NLC) no, T1<T2D) yes, because of 1st NL

T1

T2NOTE: this IS an ideal cord!

Fundamental Forces• Gravity

– Acts on particles (and objects) with mass– Always attractive; recall Newton’s law of universal gravitation– Range: unlimited– The weakest of the four fundamental forces

• Electromagnetism– Acts on particles with electric charge– Binds electrons to nuclei to form atoms, and binds atoms in

molecules and solid– Responsible for contact forces like friction and normal force– Either attractive or repulsive– Range: unlimited– Much stronger than gravity, 2nd strongest of the four fundamental

forcesLecture 7 Purdue University, Physics 149 18

Fundamental Forces• The Strong Force

– Binds together the protons and neutrons in atomic nucleus (and also quarks in combinations)

– Very short range: ~10-15 m (about the size of an atomic nucleus)

– The strongest of the four fundamental forces

• The Weak Force– Responsible for some types of radioactive decays,

sunlight– Shortest range: ~10-17 m– 3rd strongest of the four fundamental forces


Fundamental Forces


• Gravity• Strong nuclear force• Weak nuclear force• Electromagnetic force

Zero Net Force vs. Nonzero Net Force• Net Force: the vector sum of all the forces acting

on an object• Zero Net Force (Ch 2)

– When a net force on an object is zero, the velocity (both direction and magnitude) of the object does not change.

• Newton’s First Law of Motion

• Nonzero Net Force (from Ch 3)– When a nonzero net force acts on an object, the

velocity of the object changes.• That is, either the velocity’s direction or magnitude changes, or

both of direction or magnitude change.• Relevant to Newton’s Second Law of Motion



+x-x 0

The variables are time and distancet = 0 start of observations at a point x0t = t end of the observations at a point xf

All quantities except time are vectors but the vector “nature”is contained in whether the quantity is positive or negative

Motion in One Dimension

Objects are in motion and velocity is (change in distance)/time

Velocity can change => acceleration(change in velocity)/time

Position Vector• To describe position, we need

– a reference point (origin), – a distance from the origin, and – a direction from the origin.

• Position Vector (or Position)– A vector quantity that consists of the distance and

direction– An arrow starting at the “origin” and ending with the

arrowhead on the object– Position vector is usually denoted by r.

• The x-, y-, and z- component of r are usually written simply as x, y, and z (instead of rx, ry, and rz).

objectat (x,y)



Position• A vector quantity describing where you are relative

to an “origin”– Point A is located at x=3, y=1 or (3,1)– Point B is located at (-1,-2)

• The vector rA indicating the position of A startsat the origin and terminates with arrowhead A

• Same for rB and B

y

x3

3

-3

-3

A

B

Distance vs. Displacement


• Distance (scalar)– Total length of path traveled– The path of an object does matter

• Displacement (vector)– The change of the position vector (∆r), that is, the final

position vector (rf) minus the initial position vector (ri)= rf + (–ri)

– An arrow starting at the initial position (the tip of the initial position vector) and ending with the arrowhead at the final position (the tip of the final position vector)

– The path of an object does not matter. The displacement depends only on the starting and ending points.

• A vector quantity describing a change in position ∆r = rf - ri– The displacement from A to B is

• We can determine the components– x-direction:

xf - xi = -1 – 3 = -4

– y-direction:yf - yi = -2 – 1 = -3

– ∆r = (-4, -3)– |∆r| = sqrt(42 + 32) = 5

• NOTE: The displacement is not the distance traveled


Displacement (m)

x

y

3

3

-3

-3

A

B

physics 149: lecture 7

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