<< Chapter < Page Chapter >> Page >

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} } } {} .

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.

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"} {} .

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.

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"} {}

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.

Questions & Answers

what are components of cells
ofosola Reply
twugzfisfjxxkvdsifgfuy7 it
Sami
58214993
Sami
what is a salt
John
the difference between male and female reproduction
John
what is computed
IBRAHIM Reply
what is biology
IBRAHIM
what is the full meaning of biology
IBRAHIM
what is biology
Jeneba
what is cell
Kuot
425844168
Sami
what is cytoplasm
Emmanuel Reply
structure of an animal cell
Arrey Reply
what happens when the eustachian tube is blocked
Puseletso Reply
what's atoms
Achol Reply
discuss how the following factors such as predation risk, competition and habitat structure influence animal's foraging behavior in essay form
Burnet Reply
cell?
Kuot
location of cervical vertebra
KENNEDY Reply
What are acid
Sheriff Reply
define biology infour way
Happiness Reply
What are types of cell
Nansoh Reply
how can I get this book
Gatyin Reply
what is lump
Chineye Reply
what is cell
Maluak Reply
what is biology
Maluak
what is vertibrate
Jeneba
what's cornea?
Majak Reply
what are cell
Achol
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Physics 110 at une. OpenStax CNX. Aug 29, 2013 Download for free at http://legacy.cnx.org/content/col11566/1.1
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Physics 110 at une' conversation and receive update notifications?

Ask