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Significance

In the both of the previous examples, we found “limiting” values. The terminal velocity is the same as the limiting velocity, which is the velocity of the falling object after a (relatively) long time has passed. Similarly, the limiting distance of the boat is the distance the boat will travel after a long amount of time has passed. Due to the properties of exponential decay, the time involved to reach either of these values is actually not too long (certainly not an infinite amount of time!) but they are quickly found by taking the limit to infinity.

Check Your Understanding Suppose the resistive force of the air on a skydiver can be approximated by f = b v 2 . If the terminal velocity of a 100-kg skydiver is 60 m/s, what is the value of b?

0.27 kg/m

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Summary

  • Drag forces acting on an object moving in a fluid oppose the motion. For larger objects (such as a baseball) moving at a velocity in air, the drag force is determined using the drag coefficient (typical values are given in [link] ), the area of the object facing the fluid, and the fluid density.
  • For small objects (such as a bacterium) moving in a denser medium (such as water), the drag force is given by Stokes’ law.

Key equations

Magnitude of static friction f s μ s N
Magnitude of kinetic friction f k = μ k N
Centripetal force F c = m v 2 r or F c = m r ω 2
Ideal angle of a banked curve tan θ = v 2 r g
Drag force F D = 1 2 C ρ A v 2
Stokes’ law F s = 6 π r η v

Conceptual questions

Athletes such as swimmers and bicyclists wear body suits in competition. Formulate a list of pros and cons of such suits.

The pros of wearing body suits include: (1) the body suit reduces the drag force on the swimmer and the athlete can move more easily; (2) the tightness of the suit reduces the surface area of the athlete, and even though this is a small amount, it can make a difference in performance time. The cons of wearing body suits are: (1) The tightness of the suits can induce cramping and breathing problems. (2) Heat will be retained and thus the athlete could overheat during a long period of use.

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Two expressions were used for the drag force experienced by a moving object in a liquid. One depended upon the speed, while the other was proportional to the square of the speed. In which types of motion would each of these expressions be more applicable than the other one?

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As cars travel, oil and gasoline leaks onto the road surface. If a light rain falls, what does this do to the control of the car? Does a heavy rain make any difference?

The oil is less dense than the water and so rises to the top when a light rain falls and collects on the road. This creates a dangerous situation in which friction is greatly lowered, and so a car can lose control. In a heavy rain, the oil is dispersed and does not affect the motion of cars as much.

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Why can a squirrel jump from a tree branch to the ground and run away undamaged, while a human could break a bone in such a fall?

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Problems

The terminal velocity of a person falling in air depends upon the weight and the area of the person facing the fluid. Find the terminal velocity (in meters per second and kilometers per hour) of an 80.0-kg skydiver falling in a pike (headfirst) position with a surface area of 0.140 m 2 .

115 m/s or 414 km/h

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Questions & Answers

what is velocity
Austine Reply
speed per unit time is called velocity. it is a vector quantity
Mukulika
velocity is distances overall time taking,it is a vector quantity, the units is metre per second.
Samuel
frequency is rate at which something happens or is repeated. it is a vector quantity
mawuo
what is the difference between resultant force and net force
Ogali Reply
net force is when you add forces numerically I.e. the total sum of all positive and negative or balanced and unbalanced forces. resultant force is a single vector which is the combination or addition of all x and y axes vector component forces in a system.
emmanuel
thanks
Ogali
Damping is provided by tuning the turbulence levels in the moving water using baffles.How it happens? Give me a labelled diagram of it.
Shaina Reply
A 10kg ball travelling at 4meter per second collides elastically in a head-on collision with a 2kg ball.What are (a)the velocities and (b)the total momentum of the balls after collision?
Law Reply
a)v1 8/3s&v2 20/3s. b)in elastic collision total momentum is conserved.
Bala
The displacement of the air molecules in sound wave is modeled with the wave function s(x,t)=5.00nmcos(91.54m−1x−3.14×104s−1t)s(x,t)=5.00nmcos(91.54m−1x−3.14×104s−1t) . (a) What is the wave speed of the sound wave? (b) What is the maximum speed of the air molecules as they oscillate in simple harmon
Shaina Reply
practical 1st year physics
Nsc Reply
huh
Luminous
Whats the formular for newton law of motion
Ahmad Reply
f=ma
Fahad
F=m×a Where F=force M=mass of a body of an object a=acceleration due to gravity
Abubakar
what is speed
Hassan Reply
distance travelled per unit of time is speed.
Fahad
distance travelled in a particular direction it is.
Andrew
Speed is define as the distance move per unit time. Mathematically is given as Speed = distance/time Speed = s/t
Abubakar
speed is a vector quantity. It is defined distance per unit time.It's unit in c.g.s cm/s and in S.I. m/s.It’s dimension is LT^-1
Mukulika
formula for velocity
Amraketa Reply
v=ms^-1 velocity=distance time
Cleophas
(p-a/v)(v-b)=nrt what is the dimension of a
Amraketa
velocity= displacement time
Gold
Velocity = speed/time
Abubakar
what are evasive medical diagnosis?
Shaina Reply
If the block is displaced to a position y , the net force becomes Fnet=k(y−y0)−mg=0Fnet=k(y−y0)−mg=0 . But we found that at the equilibrium position, mg=kΔy=ky0−ky1mg=kΔy=ky0−ky1 . Substituting for the weight in the equation yields. Show me an equation of graph.
Shaina
where are you come from
Lida
samastipur Bihar
carrier
simple harmonic motion defination
Maharam Reply
how to easily memorize motion equation
Maharam
how speed destrog is uranium
Sayed Reply
where can we find practice problems?
bonokuhle Reply
I'm not well
YAZID
ask
Sayed
can u tell me the expression for radial acceleeation
Shikha Reply
No
YAZID
Is equal to the square of the velocity divided by the radius of circular path of the object
Mukhtaar
how to find maximum acceleration and velocity of simple harmonic motion?
chander
how to find maximum acceleration and velocity of simple harmonic motion and where it occurres?
chander
you can use either motion equations or kinetic equation and potential equation .
lasitha
how destraction 1kg uranium
Sayed
A Radial Acceleration is defined as the upward movement of an object.
Andrew
A body of 2.0kg mass makes an elastic collision with another at rest and continues to more in the original direction but with 1/4 of its ori is the mass of the struck body?
bright Reply
pls help me solve this problem
bright
Practice Key Terms 2

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Source:  OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5
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