drag forces lecturer: professor stephen t. thornton

Drag Forces

Lecturer: Professor Stephen T. Thornton

R

vv

A) A) FFcc = = NN + + mgmg

B) B) FFcc = = mgmg – – NN

C) C) FFcc = = TT + + NN – – mgmg

D) D) FFcc = = NN

E) E) FFcc = = mgmg

A skier goes over a small round hill A skier goes over a small round hill

with radius with radius RR. Because she is in . Because she is in

circular motion, there has to be a circular motion, there has to be a

centripetal force.centripetal force. At the top of the At the top of the

hill, what is hill, what is FFcc of the skier equal to? of the skier equal to?

Reading QuizReading Quiz

R

vvFFcc points toward the center of points toward the center of

the circle (the circle (i.ei.e., downward in ., downward in

this case).this case). The weight vectorweight vector points downdown and the normal normal

forceforce (exerted by the hill) points upup. The magnitude of the net force, therefore, is

FFcc = = mgmg – – N.N.

mgg NN

A skier goes over a small round hill A skier goes over a small round hill

with radius with radius RR. Because she is in . Because she is in

circular motion, there has to be a circular motion, there has to be a


hill, what is hill, what is FFcc of the skier equal to? of the skier equal to?

Reading QuizReading Quiz

Follow-up:Follow-up: What happens when What happens when the skier goes into a small dip?the skier goes into a small dip?

A) A) FFcc = = NN + + mgmg

B) B) FFcc = = mgmg – – NN

C) C) FFcc = = TT + + NN – – mgmg

D) D) FFcc = = NN

E) E) FFcc = = mgmg

Last Time

Circular motion

Motion on banked curves

Lots of Conceptual Quizzes

Today

Non-uniform circular motion

Drag

Terminal velocity

Fundamental forces

Banked Curve. A curve of radius 68 m is banked for a design speed of 85 km/h. If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely make the curve? [Hint: Consider the direction of the friction force when the car goes too slow or too fast.]

Conceptual QuizA) toward the top of the poleoward the top of the poleB) toward the groundtoward the groundC) along the horizontal component along the horizontal component

of the tension forceof the tension forceD) along the vertical component along the vertical component

of the tension forceof the tension forceE) tangential to the circletangential to the circle

In the game of In the game of tetherball, the struck tetherball, the struck ball whirls around a ball whirls around a pole. In what pole. In what direction does the direction does the net net forceforce on the ball on the ball point?point?

W

T

The vertical component of vertical component of the tensionthe tension balances the weightweight. The horizontal horizontal component of tensioncomponent of tension provides the centripetal forcecentripetal force that points toward the center of the circle.

W T

W

T

Conceptual QuizA) toward the top of the poleoward the top of the poleB) toward the groundtoward the groundC) along the horizontal component along the horizontal component

of the tension forceof the tension forceD) along the vertical component along the vertical component

of the tension forceof the tension forceE) tangential to the circletangential to the circle

In the game of In the game of tetherball, the struck tetherball, the struck ball whirls around a ball whirls around a pole. In what pole. In what direction does the direction does the net forcenet force on the ball on the ball point?point?

AA) car’s engine is not strong ) car’s engine is not strong enough to keep the car from enough to keep the car from being pushed outbeing pushed out

BB) friction between tires and road ) friction between tires and road is not strong enough to keep is not strong enough to keep car in a circlecar in a circle

CC) car is too heavy to make the ) car is too heavy to make the turnturn

DD) a deer caused you to skid) a deer caused you to skidEE) none of the above) none of the above

You drive your car too You drive your car too fast around a curve and fast around a curve and the car starts to skid. the car starts to skid. What is the correct What is the correct description of this description of this situation?situation?

Conceptual Quiz

The friction force between tires and road provides the centripetal force that keeps the car moving in a circle. If this force is too small, the car continues in a straight line!

AA) car’s engine is not strong enough ) car’s engine is not strong enough to keep the car from being to keep the car from being pushed outpushed out

BB) friction between tires and road is ) friction between tires and road is not strong enough to keep car in not strong enough to keep car in a circlea circle

CC) car is too heavy to make the turn) car is too heavy to make the turnDD) a deer caused you to skid) a deer caused you to skidEE) none of the above) none of the above

You drive your car You drive your car too fast around a too fast around a curve and the car curve and the car starts to skid. What starts to skid. What is the correct is the correct description of this description of this situation?situation?

Conceptual Quiz

Follow-up:Follow-up: What could be done to What could be done to the road or car to prevent skidding?the road or car to prevent skidding?

Conceptual QuizA Ping-Pong ball is shot into a circular tube that is lying flat (horizontal) on a tabletop. When the Ping-Pong ball leaves the track, which path will it follow?

Conceptual Quiz

Once the ball leaves the tube, there is no longer a force to keep it going in a circle. Therefore, it simply continues in a straight line, as Newton’s First Law requires!

A Ping-Pong ball is shot into a circular tube that is lying flat (horizontal) on a tabletop. When the Ping-Pong ball leaves the track, which path will it follow?

Follow-up:Follow-up: What physical force provides the centripetal force? What physical force provides the centripetal force?

R

vtop

A) A) FFcc = = TT – – mgmg

B) B) FFcc = = TT + + NN – – mgmg

C) C) FFcc = = TT + + mgmg

D) D) FFcc = = T T

E) E) FFcc = = mgmg

You swing a ball at the end of string You swing a ball at the end of string

in a vertical circle. Because the ball in a vertical circle. Because the ball

is in circular motion there has to be a is in circular motion there has to be a


ball’s path, what is ball’s path, what is FFcc equal to? equal to?

Conceptual QuizConceptual Quiz

R

vTTmgg

FFcc points toward the center of the circle points toward the center of the circle

((i.ei.e., downward in this case).., downward in this case). The

weight vectorweight vector points downdown and the

tensiontension (exerted by the string) also

points downdown. The magnitude of the

net force, therefore, is FFcc = = TT+ + mg.mg.


A) A) FFcc = = TT – – mgmg

B) B) FFcc = = TT + + NN – – mgmg

C) C) FFcc = = TT + + mgmg

D) D) FFcc = = T T

E) E) FFcc = = mgmg

You swing a ball at the end of string You swing a ball at the end of string

in a vertical circle. Because the ball in a vertical circle. Because the ball

is in circular motion there has to be a is in circular motion there has to be a


ball’s path, what is ball’s path, what is FFcc equal to? equal to?

Conceptual QuizA rider in a “barrel of A rider in a “barrel of fun” finds herself stuck fun” finds herself stuck with her back to the wall. with her back to the wall. Which diagram correctly Which diagram correctly shows the forces acting shows the forces acting on her?on her? A B C D E

The normal forcenormal force of the wall on the

rider provides the centripetal forcecentripetal force

needed to keep her going around

in a circle. The downward force of downward force of

gravity is balanced by the upward gravity is balanced by the upward

frictional forcefrictional force on her, so she does

not slip vertically.


A rider in a “barrel of fun” A rider in a “barrel of fun”

finds herself stuck with finds herself stuck with

her back to the wall. her back to the wall.

Which diagram correctly Which diagram correctly

shows the forces acting shows the forces acting

on her?on her?A B C D E

See See http://physics.bu.edu/~duffy/semester1/semester1.htmlhttp://physics.bu.edu/~duffy/semester1/semester1.html

http://physics.bu.edu/~duffy/semester1/semester1.html

Nonuniform Circular Motion

If an object is moving in a circular path but at varying speeds, it must have a tangential component to its acceleration as well as the radial one.

Nonuniform Circular Motion

This concept can be used for an object moving along any curved path, as any small segment of the path will be approximately circular.

Drag Forces

Here,

FD is the drag force;

ρ the density of the medium;

A the cross-sectional area of the object;

CD the drag coefficient.

21

2D DF AC vr=

Velocity-Dependent Forces:

Drag and Terminal VelocityWhen an object moves through a fluid at low speed, it experiences a drag force that depends on the velocity of the object.

For small velocities, the force is approximately proportional to the velocity; for higher speeds, the force is approximately proportional to the square of the velocity.

DF bv

2

DF v

If the drag force on a falling object is proportional to its velocity, the object gradually slows until the drag force and the gravitational force are equal. Then it falls with constant velocity, called the terminal velocity (~120 mph for humans).

T

when equal, no net force

terminal velocity

mg bv

mgv

b

Simplified Top View of aCentrifuge in Operation

Separate red and white blood cells from serum.

anemia 45%

More dense

Less dense

Centrifuges

Centrifuges have many uses.

• Separating red and white blood cells from serum.

• Separating 235U from 238U to produce fissionable material.

• Separating large molecules from smaller molecules for research and pharmaceutical purposes.

Fundamental Forces

• Universal gravitation: gravitational force between any two masses

• Electroweak force: includes electric, magnetic, and weak nuclear forces (responsible for radioactive decay)

• Strong (nuclear) force: binds protons and neutrons together in nucleus


A) moves to the left

B) moves to the right

C) moves up

D) moves down

E) the box does not move

A box of weight 100 N is at

rest on a floor where s = 0.4.

A rope is attached to the box

and pulled horizontally with

tension T = 30 N. Which way

does the box move?

Tm

Static friction

(s= 0.5)

The static friction force has a

maximummaximum of ssNN = = 40 N40 N. The

tension in the rope is only 30 N30 N.

So the pulling force is not big

enough to overcome friction.


A) moves to the left

B) moves to the right

C) moves up

D) moves down

E) the box does not move

A box of weight 100 N is at

rest on a floor where s = 0.4.

A rope is attached to the box

and pulled horizontally with

tension T = 30 N. Which way

does the box move?

Tm

Static friction

(s= 0.4)

Follow-up:Follow-up: What happens if the tension is What happens if the tension is 35 N35 N? What about ? What about 45 N45 N??

drag forces lecturer: professor stephen t. thornton

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