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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

how many subject is in physics
Adeshina Reply
the write question should be " How many Topics are in O- Level Physics, or other branches of physics.
effiom
how many topic are in physics
Praise
yh I need someone to explain something im tryna solve . I'll send the question if u down for it
Tamdy Reply
a ripple tank experiment a vibrating plane is used to generate wrinkles in the water .if the distance between two successive point is 3.5cm and the wave travel a distance of 31.5cm find the frequency of the vibration
Tamdy
the range of objects and phenomena studied in physics is
Bethel Reply
what is Linear motion
Hamza Reply
straight line motion is called linear motion
then what
Amera
linear motion is a motion in a line, be it in a straight line or in a non straight line. It is the rate of change of distance.
Saeedul
Hi
aliyu
your are wrong Saeedul
Richard
Linear motion is a one-dimensional motion along a straight line, and can therefore be described mathematically using only one spatial dimension
Jason
is a one-dimensional motion along a straight line, and can therefore be described mathematically using only one spatial dimensions. 
Praise
what is a classical electrodynamics?
Marga
what is dynamics
Marga
dynamic is the force that stimulates change or progress within the system or process
Oze
what is the formula to calculate wavelength of the incident light
David Reply
if a spring is is stiffness of 950nm-1 what work will be done in extending the spring by 60mmp
Hassan Reply
State the forms of energy
Samzy Reply
machanical
Ridwan
Word : Mechanical wave Definition : The waves, which need a material medium for their propagation, e.g., Sound waves. \n\nOther Definition: The waves, which need a material medium for their propagation, are called mechanical waves. Mechanical waves are also called elastic waves. Sound waves, water waves are examples of mechanical waves.t Definition: wave consisting of periodic motion of matter; e.g. sound wave or water wave as opposed to electromagnetic wave.h
Clement Reply
correct
Akinpelu
what is mechanical wave
Akinpelu Reply
a wave which require material medium for its propagation
syed
The S.I unit for power is what?
Samuel Reply
watt
Okoli
Am I correct
Okoli
it can be in kilowatt, megawatt and so
Femi
yes
Femi
correct
Jaheim
kW
Akinpelu
OK that's right
Samuel
SI.unit of power is.watt=j/c.but kw.and Mw are bigger.umots
syed
What is physics
aish Reply
study of matter and its nature
Akinpelu
The word physics comes from a Greek word Physicos which means Nature.The Knowledge of Nature. It is branch of science which deals with the matter and energy and interaction between them.
Uniform
why in circular motion, a tangential acceleration can change the magnitude of the velocity but not its direction
Syafiqah Reply
reasonable
Femi
because it is balanced by the inward acceleration otherwise known as centripetal acceleration
MUSTAPHA
What is a wave
Mutuma Reply
Tramsmission of energy through a media
Mateo
is the disturbance that carry materials as propagation from one medium to another
Akinpelu
mistakes thanks
Akinpelu
find the triple product of (A*B).C given that A =i + 4j, B=2i - 3j and C = i + k
Favour Reply
Difference between north seeking pole and south seeking pole
Stanley Reply

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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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