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Check Your Understanding (a) Draw the free-body diagram for the situation shown. (b) Redraw it showing components; use x -axes parallel to the two ramps.

Two carts are tied with a rope which goes over a pulley on top of a hill. Each cart rests on one  slope of the hill on either side of the pulley. The cart on the left is labeled m1 and the one on the right is labeled m2.

Figure a shows a free body diagram of an object on a line that slopes down to the right. Arrow T from the object points right and up, parallel to the slope. Arrow N1 points left and up, perpendicular to the slope. Arrow w1 points vertically down. Figure b shows a free body diagram of an object on a line that slopes down to the left. Arrow N2 from the object points right and up, perpendicular to the slope. Arrow T points left and up, parallel to the slope. Arrow w2 points vertically down. ;
Figure a shows a free body diagram of an object on a line that slopes down to the right. Arrow T from the object points right and up, parallel to the slope. Arrow N1 points left and up, perpendicular to the slope. Arrow w1 points vertically down. Arrow w1x points left and down, parallel to the slope. Arrow w1y points right and down, perpendicular to the slope. Figure b shows a free body diagram of an object on a line that slopes down to the left. Arrow N2 from the object points right and up, perpendicular to the slope. Arrow T points left and up, parallel to the slope. Arrow w2 points vertically down. Arrow w2y points left and down, perpendicular to the slope. Arrow w2x points right and down, parallel to the slope.

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View this simulation to predict, qualitatively, how an external force will affect the speed and direction of an object’s motion. Explain the effects with the help of a free-body diagram. Use free-body diagrams to draw position, velocity, acceleration, and force graphs, and vice versa. Explain how the graphs relate to one another. Given a scenario or a graph, sketch all four graphs.

Summary

  • To draw a free-body diagram, we draw the object of interest, draw all forces acting on that object, and resolve all force vectors into x - and y -components. We must draw a separate free-body diagram for each object in the problem.
  • A free-body diagram is a useful means of describing and analyzing all the forces that act on a body to determine equilibrium according to Newton’s first law or acceleration according to Newton’s second law.

Key equations

Net external force F net = F = F 1 + F 2 +
Newton’s first law v = constant when F net = 0 N
Newton’s second law, vector form F net = F = m a
Newton’s second law, scalar form F net = m a
Newton’s second law, component form F x = m a x , F y = m a y , and F z = m a z .
Newton’s second law, momentum form F net = d p d t
Definition of weight, vector form w = m g
Definition of weight, scalar form w = m g
Newton’s third law F AB = F BA
Normal force on an object resting on a
horizontal surface, vector form
N = m g
Normal force on an object resting on a
horizontal surface, scalar form
N = m g
Normal force on an object resting on an
inclined plane, scalar form
N = m g cos θ
Tension in a cable supporting an object
of mass m at rest, scalar form
T = w = m g

Conceptual questions

In completing the solution for a problem involving forces, what do we do after constructing the free-body diagram? That is, what do we apply?

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If a book is located on a table, how many forces should be shown in a free-body diagram of the book? Describe them.

two forces of different types: weight acting downward and normal force acting upward

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If the book in the previous question is in free fall, how many forces should be shown in a free-body diagram of the book? Describe them.

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Problems

A ball of mass m hangs at rest, suspended by a string. (a) Sketch all forces. (b) Draw the free-body diagram for the ball.

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A car moves along a horizontal road. Draw a free-body diagram; be sure to include the friction of the road that opposes the forward motion of the car.

A free body diagram shows a vector F subscript e pointing right, vector N pointing up, vector f pointing left and arrow w pointing down.

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A runner pushes against the track, as shown. (a) Provide a free-body diagram showing all the forces on the runner. ( Hint: Place all forces at the center of his body, and include his weight.) (b) Give a revised diagram showing the xy -component form.

A picture of a man running towards the right is shown. An arrow labeled F points up and right from the floor towards his foot.
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The traffic light hangs from the cables as shown. Draw a free-body diagram on a coordinate plane for this situation.

Figure shows a traffic light hanging from a horizontal cable by three other cables, T1, T2 and T3. T1 hangs down and right making an angle of 41 degrees with the horizontal cable. T2 hangs down and left, making an angle of 63 degrees with the horizontal cable. These meet at a point and T3 hangs vertically down from here. The light is attached to T3. A vector pointing down from the light is labeled w equal to 200 newtons.

Figure shows coordinate axes. Three arrows radiate out from the origin. T1, labeled 41 degrees points up and left. T2, labeled 63 degrees points up and right. T3 equal to w equal to 200 N is along the negative y axis.

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Additional problems

Two small forces, F 1 = −2.40 i ^ 6.10 t j ^ N and F 2 = 8.50 i ^ 9.70 j ^ N, are exerted on a rogue asteroid by a pair of space tractors. (a) Find the net force. (b) What are the magnitude and direction of the net force? (c) If the mass of the asteroid is 125 kg, what acceleration does it experience (in vector form)? (d) What are the magnitude and direction of the acceleration?

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Questions & Answers

what Is tidal wave
Pranay Reply
Specific heat capacity .....what is the formulae for solving the SHC of a substance in respect to its container
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Heat ÷ (change in temperature x Mass)
akshay
what is symbol of nano
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what is the symbol of nano
Iqra
n
Grant
n
Irtza
using dimensional analysis find the unit of gravitation constant G in F=G m1 m2/r
John Reply
Newton meter per kg square
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meter squre par second and kg swaure
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what are the possible sources of error in coefficient of static and dynamic friction and there precautions
GRACE
what is Bohr
Shcorah Reply
He is a physicist who formulated the atomic model of an Atom
Lily
And made 3 postulates
Lily
Check university physics vol 3 > Nuclear physics
Lily
Bohr model
kami
what is mean by Doppler effect
RAMANJI Reply
Good
Ahmad
increase or decrease in the frequency of sound and light.
Jhon
good
Eng
is it?
Vinayaka
actually it is apparent change in the frequency of light or sound as object move towards or away.
Vinayaka
state the basic assumption of kinetic theory of gases
FELIX Reply
state the characteristics of gases that differentiate them from solids
FELIX
identify the magnitude and direction a vector quantity
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Identify work done on an inclined plane given at angle to the horizontal
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formula for Velocity
Honey_and Reply
what is the value of x 6yx7y
Elijah Reply
what is the formula for frictional force
bassey Reply
I believe, correct me if I am wrong, but Ffr=Fn*mu
Grant
frictional force ,mathematically Fforce (Ffr) =K∆R where by K stands for coefficient of friction ,R stands for normal force/reaction NB: R = mass of a body ( m) x Acc.due gravity (g) The formula will hold the meaning if and only if the body is relatively moving with zero angle (∅ = 0°C)
Boay
What is concept associated with linear motion
Adeoye Reply
what causes friction?
Elijah
uneven surfaces cause friction Elijah
Shii
rough surfacea
Grant
what will happen to vapor pressure when you add solute to a solution?
shane Reply
how is freezing point depression different from boiling point elevation?
shane
how is the osmotic pressure affect the blood serum?
shane
what is the example of colligative properties that seen in everyday living?
shane
freezing point depression deals with the particles in the matter(liquid) loosing energy.....while boiling elevation is the particles of the matter(liquid)gaining energy
E-vibes
What is motion
Adeoye Reply
moving place to place
Addis
change position with respect to surrounding
Muhammad
to which
Addis
to where ?
Addis
the phenomenon of an object to changes its position with respect to the reference point with passage of time then it is called as motion
Shubham
it's just a change in position
festus
reference point -it is a fixed point respect to which can say that a object is at rest or motion
Shubham
yes
Shubham
A change in position
Lily
change in position depending on time
bassey
a change in the position of a body
E-vibes
Is there any calculation for line integral in scalar feild?
Sadia Reply

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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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