# 5.7 Drawing free-body diagrams  (Page 3/6)

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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.

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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 ${\stackrel{\to }{F}}_{\text{net}}=\sum \stackrel{\to }{F}={\stackrel{\to }{F}}_{1}+{\stackrel{\to }{F}}_{2}+\text{⋯}$ Newton’s first law $\stackrel{\to }{v}=\phantom{\rule{0.2em}{0ex}}\text{constant when}\phantom{\rule{0.2em}{0ex}}{\stackrel{\to }{F}}_{\text{net}}=\stackrel{\to }{0}\phantom{\rule{0.2em}{0ex}}\text{N}$ Newton’s second law, vector form ${\stackrel{\to }{F}}_{\text{net}}=\sum \stackrel{\to }{F}=m\stackrel{\to }{a}$ Newton’s second law, scalar form ${F}_{\text{net}}=ma$ Newton’s second law, component form $\sum {\stackrel{\to }{F}}_{x}=m{\stackrel{\to }{a}}_{x}\text{,}\phantom{\rule{0.2em}{0ex}}\sum {\stackrel{\to }{F}}_{y}=m{\stackrel{\to }{a}}_{y},\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}\sum {\stackrel{\to }{F}}_{z}=m{\stackrel{\to }{a}}_{z}.$ Newton’s second law, momentum form ${\stackrel{\to }{F}}_{\text{net}}=\frac{d\stackrel{\to }{p}}{dt}$ Definition of weight, vector form $\stackrel{\to }{w}=m\stackrel{\to }{g}$ Definition of weight, scalar form $w=mg$ Newton’s third law ${\stackrel{\to }{F}}_{\text{AB}}=\text{−}{\stackrel{\to }{F}}_{\text{BA}}$ Normal force on an object resting on a horizontal surface, vector form $\stackrel{\to }{N}=\text{−}m\stackrel{\to }{g}$ Normal force on an object resting on a horizontal surface, scalar form $N=mg$ Normal force on an object resting on an inclined plane, scalar form $N=mg\text{cos}\phantom{\rule{0.2em}{0ex}}\theta$ Tension in a cable supporting an object of mass m at rest, scalar form $T=w=mg$

## 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?

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

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.

## 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.

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 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.

The traffic light hangs from the cables as shown. Draw a free-body diagram on a coordinate plane for this situation.

Two small forces, ${\stackrel{\to }{F}}_{1}=-2.40\stackrel{^}{i}-6.10t\stackrel{^}{j}$ N and ${\stackrel{\to }{F}}_{2}=8.50\stackrel{^}{i}-9.70\stackrel{^}{j}$ 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?

is the eye the same like the camera
I can't understand
Suraia
Josh
I think the question is that ,,, the working principal of eye and camera same or not?
Sardar
yes i think is same as the camera
what are the dimensions of surface tension
samsfavor
why is the "_" sign used for a wave to the right instead of to the left?
why classical mechanics is necessary for graduate students?
classical mechanics?
Victor
principle of superposition?
principle of superposition allows us to find the electric field on a charge by finding the x and y components
Kidus
Two Masses,m and 2m,approach each along a path at right angles to each other .After collision,they stick together and move off at 2m/s at angle 37° to the original direction of the mass m. What where the initial speeds of the two particles
MB
2m & m initial velocity 1.8m/s & 4.8m/s respectively,apply conservation of linear momentum in two perpendicular directions.
Shubhrant
A body on circular orbit makes an angular displacement given by teta(t)=2(t)+5(t)+5.if time t is in seconds calculate the angular velocity at t=2s
MB
2+5+0=7sec differentiate above equation w.r.t time, as angular velocity is rate of change of angular displacement.
Shubhrant
Ok i got a question I'm not asking how gravity works. I would like to know why gravity works. like why is gravity the way it is. What is the true nature of gravity?
gravity pulls towards a mass...like every object is pulled towards earth
Ashok
An automobile traveling with an initial velocity of 25m/s is accelerated to 35m/s in 6s,the wheel of the automobile is 80cm in diameter. find * The angular acceleration
(10/6) ÷0.4=4.167 per sec
Shubhrant
what is the formula for pressure?
force/area
Kidus
force is newtom
Kidus
and area is meter squared
Kidus
so in SI units pressure is N/m^2
Kidus
In customary United States units pressure is lb/in^2. pound per square inch
Kidus
who is Newton?
scientist
Jeevan
a scientist
Peter
that discovered law of motion
Peter
ok
John
but who is Isaac newton?
John
a postmodernist would say that he did not discover them, he made them up and they're not actually a reality in itself, but a mere construct by which we decided to observe the word around us
elo
how?
Qhoshe
Besides his work on universal gravitation (gravity), Newton developed the 3 laws of motion which form the basic principles of modern physics. His discovery of calculus led the way to more powerful methods of solving mathematical problems. His work in optics included the study of white light and
Daniel
and the color spectrum
Daniel
what is a scalar quantity
scalar: are quantity have numerical value
muslim
is that a better way in defining scalar quantity
Peter
thanks
muslim
quantity that has magnitude but no direction
Peter
upward force and downward force lift
upward force and downward force on lift
hi
Etini
hi
elo
hy
Xander
Hello
Jux_dob
hi
Peter
Helo
Tobi
Daniel
what's the answer? I can't get it
what is the question again?
Sallieu
What's this conversation?
Zareen
what is catenation? and give examples
sununu
How many kilometres in 1 mile
Nessy
1.609km in 1mile
Faqir
what's the si unit of impulse
The Newton second (N•s)
Ethan
what is the s. I unit of current
Amphere(A)
imam
thanks man
Roland
u r welcome
imam
the velocity of a boat related to water is 3i+4j and that of water related to earth is i-3j. what is the velocity of the boat relative to earth.If unit vector i and j represent 1km/hour east and north respectively
what is head to tail rule?
kinza