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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

Can any one give me the definition for Bending moment plz...
Prema Reply
I need a question for moment
paul Reply
what is charge
Zarshad
An attribution of particle that we have thought about to explain certain things like Electomagnetism
Nikunj
please what is the formula instantaneous velocity in projectile motion
Isaiah Reply
A computer is reading from a CD-ROM that rotates at 780 revolutions per minute.What is the centripetal acceleration at a point that is 0.030m from the center of the disc?
Rapqueen Reply
change revolution per minute by multiplying from 2pie and devide by 60.and take r=.030 and use formula centripital acceleration =omega sqare r.
Kumar
OK thank you
Rapqueen
observation of body boulded
Anwer Reply
a gas is compressed to 1/10 0f its original volume.calculate the rise temperature if the original volume is 400k. gamma =1.4
Celine Reply
the specific heat of hydrogen at constant pressure and temperature is 14.16kj|k.if 0.8kg of hydrogen is heated from 55 degree Celsius to 80 degree Celsius of a constant pressure. find the external work done .
Celine
hi
shaik
hy
Prasanna
g
Ahmad
what is imaginary mass and how we express is
Yash Reply
what is imaginary mass how we express it
Yash
centre of mass is also called as imaginary mass
Lokmani
l'm from Algeria and fell these can help me
Khlil Reply
Many amusement parks have rides that make vertical loops like the one shown below. For safety, the cars are attached to the rails in such a way that they cannot fall off. If the car goes over the top at just the right speed, gravity alone will supply the centripetal force. What other force acts and what is its direction if: (a) The car goes over the top at faster than this speed? (b) The car goes over the top at slower than this speed?
English Reply
how can I convert mile to meter per hour
Folorunsho Reply
1 mile * 1609m
Boon
hey can someone show me how to solve the - "Hanging from the ceiling over a baby bed ...." question
Shrushti Reply
i wanted to know the steps
Shrushti
sorry shrushti..
Rashid
which question please write it briefly
Asutosh
Olympus Mons on Mars is the largest volcano in the solar system, at a height of 25 km and with a radius of 312 km. If you are standing on the summit, with what initial velocity would you have to fire a projectile from a cannon horizontally to clear the volcano and land on the surface of Mars? Note that Mars has an acceleration of gravity of 3.7 m/s2 .
Eloisa Reply
what is summit
Asutosh
highest point on earth
Ngeh
पृथवी को इसके अक्ष पर कितने कोणीय चाल से घूमाऐ कि भूमधय पे आदमी का भार इसके वासतविक भार से 3/5अधिक हो
Vasudev Reply
best
Murari
At a post office, a parcel that is a 20.0-kg box slides down a ramp inclined at 30.0° 30.0° with the horizontal. The coefficient of kinetic friction between the box and plane is 0.0300. (a) Find the acceleration of the box. (b) Find the velocity of the box as it reaches the end of the plane, if the length of the plane is 2 m and the box starts at rest.
Kaitlin Reply
As an IT student must I take physics seriously?
Akaare Reply
yh
Bernice
hii
Raja
IT came from physics and maths so I don't see why you wouldn't
Brad
conditions for pure rolling
Md

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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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