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  5. Drawing free-body diagrams

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.

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

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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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