college and engineering physics free-body diagrams 1 toc steps to solving the problem drawings...
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College and Engineering Physics
Free-Body Diagrams
1
TOC
Steps to Solving the Problem
Drawings
Calculations
College and Engineering Physics
Free-Body Diagrams
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Using a free-body diagram…
1. Draw a picture of the problem.2. Draw the object on which the force is being
sought.3. Draw and label the forces and the acceleration.4. Choose and draw your axes.5. Determine the magnitude of the known forces and
the acceleration if it is known.6. Determine the angle of all of the forces and the
acceleration (from the x-axis going counterclockwise).
7. Determine the components of each force and the acceleration.
8. Add the components of all of the forces.9. Use Newton’s second law to solve the problem.
College and Engineering Physics
Free-Body Diagrams
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An example…
Bailey-the-Wonder-Dog is walking down a 20o slope with a constant acceleration of 1m/s2. Bailey herself has a mass of 35 kg. What is the coefficient of friction acting between each of Bailey’s legs and the slope?
College and Engineering Physics
Free-Body Diagrams
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TOC
θ
College and Engineering Physics
Free-Body Diagrams
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TOC
θw
N
f
w
N
f
w
N
f
a
a
a
College and Engineering Physics
Free-Body Diagrams
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TOC
y
x
θw
N
f
w
N
f
w
N
f
a
a
a
y
x
College and Engineering Physics
Free-Body Diagrams
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y
x
θw
N
f
w
N
f
w
N
f
w mgLaw) Second sNewton' (use N
Nf k
o270w
θ
o90N
o180f
2m/s 1a
a
a
a
o0a
35 kgm
College and Engineering Physics
Free-Body Diagrams
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y
x
w
N
f o270cosmgwx
Weight
o270sinmgwy
Law) Second sNewton' (use N
Nf k2m/s 1a
a
o270w
o90N
o180f
o0a
w mg 35 kgm
College and Engineering Physics
Free-Body Diagrams
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y
x
w
N
f 090cos o NN x
NNN y o90sin
Law) Second sNewton' (use N
Nf k2m/s 1a
a
o270w
o90N
o180f
o0a
Normal Force
w mg 35 kgm
College and Engineering Physics
Free-Body Diagrams
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y
x
w
N
f NNf kkx o180cos
0180sin o Nf ky
Law) Second sNewton' (use N
Nf k2m/s 1a
a
o270w
o90N
o180f
o0a
Friction
w mg 35 kgm
College and Engineering Physics
Free-Body Diagrams
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y
x
w
N
f aaax o0cos
00sin o aay
Law) Second sNewton' (use N
Nf k2m/s 1a
a
o270w
o90N
o180f
o0a
Acceleration
w mg 35 kgm
College and Engineering Physics
Free-Body Diagrams
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NmgF kx 0270costotal o
0270sintotal o NmgF y
o270cosmgwx o270sinmgwy
0xN NN y
Nf kx 0yf
College and Engineering Physics
Free-Body Diagrams
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NmgF kx o270costotal
NmgF y o270sintotal
aax
0ya
maNmg k o270cos
0270sin o Nmg
College and Engineering Physics
Free-Body Diagrams
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maNmg k o270cos
0270sin o Nmg
o270sinmgN
mamgmg k oo 270sin270cos
o
o
270sin
270cos
g
gak
o
o
270sin
270cos
mg
mgmak
College and Engineering Physics
Free-Body Diagrams
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o2
o22
290sinm/s 81.9
290cosm/s 81.9m/s 1 k
255.0k
o
o
270sin
270cos
g
gak
College and Engineering Physics
Free-Body Diagrams
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m
? ?
m
? ?
Rope 1 Rope 2
Rope 3
Rope 1 Rope 2
Rope 3
Figure A Figure B
120º
Sample Problem: Does the rope 1 in Figure A or B have greater tension?
L L
College and Engineering Physics
Free-Body Diagrams
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m m
? ? ? ?
Rope 1 Rope 2
Rope 3
Figure A Figure B
120º
Rope 1 Rope 2
Rope 3
L L
Sample Problem: Does the rope 1 in Figure A or B have greater tension?
College and Engineering Physics
Free-Body Diagrams
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m
ℓ
Sample Problem: Determine an algebraic expression for the spring constant of the spring in terms of the mass of the block (m), the displacement from equilibrium (ℓ) and the acceleration due to gravity (g).
College and Engineering Physics
Free-Body Diagrams
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