# 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?

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