calculating the amount of torque (a confusing task)
TRANSCRIPT
![Page 1: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/1.jpg)
Calculating the amount of torque
(A confusing task)
![Page 2: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/2.jpg)
A door
Hinge
Hinge
Knob
![Page 3: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/3.jpg)
Door (Top View)
Hinge
knob
knob
![Page 4: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/4.jpg)
How much torque?(Zero, a Little, or Large?)
![Page 5: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/5.jpg)
How much torque?(Zero, a Little, or Large?)
![Page 6: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/6.jpg)
How much torque?(Zero, a Little, or Large?)
![Page 7: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/7.jpg)
How much torque?(Zero, a Little, or Large?)
![Page 8: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/8.jpg)
How much torque?(Zero, a Little, or Large?)
![Page 9: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/9.jpg)
How to calculate torqueMethod One
(“Adjust the force”)
F
![Page 10: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/10.jpg)
F
Draw a vector from the axis to the point of application of force.
d
![Page 11: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/11.jpg)
F
Extend the vector to make an angle between the force and d.
d
![Page 12: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/12.jpg)
F
Complete the triangle to find the component of F that is perpendicular to d. This is the
only part of F that makes the torque.
F = Fsin d
![Page 13: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/13.jpg)
F
= d·F = d·Fsin
F = Fsin d
![Page 14: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/14.jpg)
F
How to calculate torqueMethod Two
{“Adjust the distance”} (more handy than you might think)
![Page 15: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/15.jpg)
F
Draw the usual distance vector.
d
![Page 16: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/16.jpg)
F
Extend the ForceVector to see the “Line of Force”
d
![Page 17: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/17.jpg)
Fd
How far is the Line of Force from the pivot?
(We call this distance the ‘Lever Arm’ or “Moment Arm’)
d = dsin()
![Page 18: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/18.jpg)
Fd
= F·d = F·dsin = d Fsin
dsin
![Page 19: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/19.jpg)
Numerical Examples.For each, the force is 20 N, and the dimensions of the door are:
0.8 meters
0.3 m
Note: The diagonal distance is 0.854 meters.
![Page 20: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/20.jpg)
Numerical Example A (Method One - Adjust Force)
F40˚
d = 0.8 m
![Page 21: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/21.jpg)
Numerical Example A (Method One - Adjust Force)
50˚40˚
d = 0.8 mF = 20 N = 50˚
![Page 22: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/22.jpg)
Numerical Example A (Method One - Adjust Force)
50˚40˚
d = 0.8 m
F = 20 N·sin(50˚) = 15.3N
F
![Page 23: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/23.jpg)
Numerical Example A (Method One - Adjust Force)
50˚40˚
d = 0.8 mF = 20 N·sin(50˚) = 15.3N
F
= d·F= (0.8 m)·(15.3 N) = 12.3 Nm
![Page 24: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/24.jpg)
Numerical Example A(Method Two - Adjust Distance)
F40˚
50˚40˚
90˚
d = 0.8 m
d = ?
![Page 25: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/25.jpg)
Numerical Example A(Method Two - Adjust Distance)
F40˚
50˚40˚
d = (0.8 m)sin(˚) = 0.61 m
d = 0.8 m
![Page 26: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/26.jpg)
Numerical Example A(Method Two - Adjust Distance)
F40˚
50˚40˚
d = (0.8 m)sin(˚) = 0.61 m
d = 0.8 m
= d·F= (0.61 m)·(20 N) = 12.3 Nm
![Page 27: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/27.jpg)
Numerical Example BWill this be: More, Less, or the Same
amount of Torque?
d = 0.8 mF = 20 N
![Page 28: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/28.jpg)
Numerical Example BMethod One - Adjust Force
90˚
Why is F = 20 N?
![Page 29: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/29.jpg)
Numerical Example BMethod One - Adjust Force
90˚
= d·F= (0.8 m)·(20 N) = 16 NmIs this more, less, or the same?
![Page 30: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/30.jpg)
Numerical Example B Method Two - Adjust Distance
d = 0.8 mF = 20 N
![Page 31: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/31.jpg)
Numerical Example B Method Two - Adjust Distance
d = 0.8 mF = 20 N
Why is d = 0.8 m?
![Page 32: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/32.jpg)
Numerical Example B Method Two - Adjust Distance
d = 0.8 mF = 20 N
= d·F= (0.8 m)·(20 N) = 16 Nm
![Page 33: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/33.jpg)
Numerical Example C(shows why Method 2 is useful)
![Page 34: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/34.jpg)
Numerical Example C(Method One - Adjust Force)
WARNING: This is a bad method for this problem.
20 N
0.8 m
0.3 m
Just sit back and see how much work this method is for this problem, and then how easy the othermethod is for the same problem.
![Page 35: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/35.jpg)
Numerical Example CIn Method One, we find F.Draw in the component of
F that is to d.
d
D = √(0.82 + 0.32) = 0.854 m
![Page 36: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/36.jpg)
Extend d. Find F.
d
![Page 37: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/37.jpg)
Extend d. Find F.
d
F
= InvTan(Opp/Adj) = tan-1(0.8m/0.3m) = 69.4˚
![Page 38: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/38.jpg)
Find F.
d
F
F = (20 N)sin(69.4˚) = 18.7 N
![Page 39: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/39.jpg)
= d·F= (0.854m)·(18.7N)
= 16 Nm
d
F
This was a tough way to get the answer.
![Page 40: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/40.jpg)
Numerical Example C(Method Two - Adjust Distance)
20 N
0.8 m
0.3 m
![Page 41: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/41.jpg)
= F·dSo, find the distance from
the ‘Line of force’ to the pivot.20 N
0.8 m
0.3 m
![Page 42: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/42.jpg)
d
20 N
0.8 m
0.3 m
![Page 43: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/43.jpg)
= F·d
= (20 N)·(0.8 m) = 16 Nm
20 N
0.8 m
0.3 m
That was much better.
![Page 44: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/44.jpg)
Addendum (skippable)A closer look at Method 1 in Example C
• In the next slide notice that the distance (d) comes from the width (W) of the door and the thickness (T) of the door:
€
d = W 2 + T 2
![Page 45: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/45.jpg)
d
W
T
d = square root of …
![Page 46: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/46.jpg)
In the previous slide, notice that
• The sine of the angle is Opp/Hyp• So
€
sinθ =W
W 2 + T 2
![Page 47: Calculating the amount of torque (A confusing task)](https://reader035.vdocuments.mx/reader035/viewer/2022070413/5697bfd61a28abf838cae0ba/html5/thumbnails/47.jpg)
Calculate the torqueand see the simplification to the
old result• = d•F•sin
€
=FW€
= W 2 + T 2 ⋅F ⋅W
W 2 + T 2