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Problem exercises

A 5 . 00 × 10 5 -kg size 12{5 "." "00" times "10" rSup { size 8{5} } "- kg"} {} rocket is accelerating straight up. Its engines produce 1 . 250 × 10 7 N size 12{1 "." "250" times "10" rSup { size 8{7} } " N"} {} of thrust, and air resistance is 4 . 50 × 10 6 N size 12{4 "." "50" times "10" rSup { size 8{6} } " N"} {} . What is the rocket’s acceleration? Explicitly show how you follow the steps in the Problem-Solving Strategy for Newton’s laws of motion.

An object of mass m is shown. Three forces acting on it are tension T, shown by an arrow acting vertically upward, and friction f and gravity m g, shown by two arrows acting vertically downward.

Using the free-body diagram:

F net = T f m g = ma size 12{F rSub { size 8{"net"} } =T - f= ital "ma"} {} ,

so that

a = T f mg m = 1 . 250 × 10 7 N 4.50 × 10 6 N ( 5.00 × 10 5 kg ) ( 9. 80 m/s 2 ) 5.00 × 10 5 kg = 6.20 m/s 2 size 12{a= { {T` - `f` - ` ital "mg"} over {m} } = { {1 "." "250" times "10" rSup { size 8{7} } " N" - 4 "." "50" times "10" rSup { size 8{"6 "} } N - \( 5 "." "00" times "10" rSup { size 8{5} } " kg" \) \( 9 "." "80 m/s" rSup { size 8{2} } \) } over {5 "." "00" times "10" rSup { size 8{5} } " kg"} } ="6" "." 20" m/s" rSup { size 8{2} } } {} .

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The wheels of a midsize car exert a force of 2100 N backward on the road to accelerate the car in the forward direction. If the force of friction including air resistance is 250 N and the acceleration of the car is 1 . 80 m/s 2 size 12{1 "." "80 m/s" rSup { size 8{2} } } {} , what is the mass of the car plus its occupants? Explicitly show how you follow the steps in the Problem-Solving Strategy for Newton’s laws of motion. For this situation, draw a free-body diagram and write the net force equation.

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Calculate the force a 70.0-kg high jumper must exert on the ground to produce an upward acceleration 4.00 times the acceleration due to gravity. Explicitly show how you follow the steps in the Problem-Solving Strategy for Newton’s laws of motion.

  1. Use Newton’s laws of motion.
    Two forces are acting on an object of mass m: F, shown by an arrow pointing upward, and its weight w, shown by an arrow pointing downward. Acceleration a is represented by a vector arrow pointing upward. The figure depicts the forces acting on a high jumper.
  2. Given : a = 4.00 g = ( 4.00 ) ( 9. 80 m/s 2 ) = 39.2 m/s 2 ; size 12{a=4 "." "00" g= \( 4 "." "00" \) \( 9 "." "80 m/s" rSup { size 8{2} } \) ="39" "." 2" m/s" rSup { size 8{2} } " ; "} {} m = 70 . 0 kg size 12{m="70" "." "0 kg"} {} ,

    Find: F size 12{F} .

  3. {} {} F =+ F w = ma , size 12{ Sum {F"=+"F - w= ital "ma"" ,"} } {} so that F = ma + w = ma + mg = m ( a + g ) size 12{F= ital "ma"+w= ital "ma"+ ital "mg"=m \( a+g \) } {} .

    F = ( 70.0 kg ) [ ( 39 . 2 m/s 2 ) + ( 9 . 80 m/s 2 ) ] size 12{F= \( "70" "." 0" kg" \) \[ \( "39" "." "2 m/s" rSup { size 8{2} } \) + \( 9 "." "80 m/s" rSup { size 8{2} } \) \] } {} = 3. 43 × 10 3 N size 12{ {}= {underline {`3 "." "43" times "10" rSup { size 8{3} } " N"}} } {} . The force exerted by the high-jumper is actually down on the ground, but F size 12{F} is up from the ground and makes him jump.

  4. This result is reasonable, since it is quite possible for a person to exert a force of the magnitude of 10 3 N size 12{"10" rSup { size 8{3} } " N"} {} .
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When landing after a spectacular somersault, a 40.0-kg gymnast decelerates by pushing straight down on the mat. Calculate the force she must exert if her deceleration is 7.00 times the acceleration due to gravity. Explicitly show how you follow the steps in the Problem-Solving Strategy for Newton’s laws of motion.

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A freight train consists of two 8.00 × 10 4 -kg engines and 45 cars with average masses of 5.50 × 10 4 kg . (a) What force must each engine exert backward on the track to accelerate the train at a rate of 5.00 × 10 –2 m/s 2 size 12{5 "." "00" times "10" rSup { size 8{"–2"} } " m/s" rSup { size 8{2} } } {} if the force of friction is 7 . 50 × 10 5 N size 12{7 "." "50" times "10" rSup { size 8{5} } " N"} {} , assuming the engines exert identical forces? This is not a large frictional force for such a massive system. Rolling friction for trains is small, and consequently trains are very energy-efficient transportation systems. (b) What is the force in the coupling between the 37th and 38th cars (this is the force each exerts on the other), assuming all cars have the same mass and that friction is evenly distributed among all of the cars and engines?

(a) 4 . 41 × 10 5 N size 12{4 "." "41" times "10" rSup { size 8{5 } } " N"} {}

(b) 1 . 50 × 10 5 N size 12{1 "." "47" times "10" rSup { size 8{5 } } " N"} {}

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Commercial airplanes are sometimes pushed out of the passenger loading area by a tractor. (a) An 1800-kg tractor exerts a force of 1 . 75 × 10 4 N size 12{1 "." "75" times "10" rSup { size 8{4 } } " N"} {} backward on the pavement, and the system experiences forces resisting motion that total 2400 N. If the acceleration is 0 . 150 m/s 2 size 12{0 "." "150 m/s" rSup { size 8{2} } } {} , what is the mass of the airplane? (b) Calculate the force exerted by the tractor on the airplane, assuming 2200 N of the friction is experienced by the airplane. (c) Draw two sketches showing the systems of interest used to solve each part, including the free-body diagrams for each.

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Questions & Answers

what is ohm's law
Pamilerin Reply
states that electric current in a given metallic conductor is directly proportional to the potential difference applied between its end, provided that the temperature of the conductor and other physical factors such as length and cross-sectional area remains constant. mathematically V=IR
ANIEFIOK
A body travelling at a velocity of 30ms^-1 in a straight line is brought to rest by application of brakes. if it covers a distance of 100m during this period, find the retardation.
Pamilerin Reply
what is distribution of trade
Grace Reply
what's acceleration
Joshua Reply
The change in position of an object with respect to time
Mfizi
Acceleration is velocity all over time
Pamilerin
hi
Stephen
It's not It's the change of velocity relative to time
Laura
Velocity is the change of position relative to time
Laura
acceleration it is the rate of change in velocity with time
Stephen
acceleration is change in velocity per rate of time
Noara
what is ohm's law
Stephen
Ohm's law is related to resistance by which volatge is the multiplication of current and resistance ( U=RI)
Laura
how i don understand
Willam Reply
how do I access the Multiple Choice Questions? the button never works and the essay one doesn't either
Savannah Reply
How do you determine the magnitude of force
Peace Reply
mass × acceleration OR Work done ÷ distance
Seema
Which eye defect is corrected by a lens having different curvatures in two perpendicular directions?
Valentina Reply
acute astigmatism?
the difference between virtual work and virtual displacement
Noman Reply
How do you calculate uncertainties
Ancilla Reply
What is Elasticity
Salim Reply
using a micro-screw gauge,the thickness of a piece of a A4 white paper is measured to be 0.5+or-0.05 mm. If the length of the A4 paper is 26+or-0.2 cm, determine the volume of the A4 paper in: a). Cubic centimeters b). Cubic meters
Ancilla Reply
what is module
Alex Reply
why it is possible for an object(man) to stay on air without falling down?
akande Reply
its impossible, what do you mean exactly?
Ryan
Exactly
Emmanuella
it's impossible
Your
Why is it not possible to stand in air?
bikko
the air molecules are very light enough to oppose the gravitational pull of the earth on the man..... hence, freefall occurs
Arzail
because of gravitational forces
Pamilerin
this mostly occur in space
Stephen
what is physics
Joshua Reply
no life without physics ....that should tell you something
Exactly
Emmanuella
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E=MC^2
study of matter and energy and an inter-relation between them.
Minahil
that's how the mass and energy are related in stationery frame
Arzail
Ketucky tepung 10m
firdaus
Treeskin, 6m Cloud gam water 2m Cloud gam white 2m And buur
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Like dont have but have
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DNA card
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War right? My impesilyty again. Don't have INSURAN for me
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I give
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All physics... Hahahaha
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Tree skin and two cloud have tokside maybe
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thanks
firdaus
Kinetic energy is the energy due to montion of waves,electrons,atoms, molecule,substances an object s.
Emmanuella
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SOME N
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firdaus
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Hilal
plz anyone can tell what is meteor and why meteor fall in night? can meteor fall in the day
Hilal
meteor are the glowy (i.e. heated when the enter into our atmosphere) parts of meteoroids. now, meteoroids are the debris resulting from the collision of asteroids or comets. yes, it occurs in daytime too, but due to the daylight, we cant observe it as clearly as in night
Arzail
thank's
Hilal
hello guys
Waka
wich method we use to find the potential on a grounded sphere
Noman
hello
Pamilerin
Physics is the science that studies everything around us from the smallest things like quarks to the biggest things like galaxies. It's simply everything.
Laura
Good day everyone
Divine
It talks mainly about matter with related topics such as forces energy gravity and time. It's amazing
Laura
Hi
Alpha
Physics generally is the study of everything around us.
Steven
physics is the branch of sceince
shafiu
physics is the branch of sceince that deal with motion
shafiu
physics is the branch of sceince that deal with motion &energy
shafiu

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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