work ap physics c mrs. coyle. work the work done on an object by an external constant force: w = f r...
TRANSCRIPT
![Page 1: Work AP Physics C Mrs. Coyle. Work The work done on an object by an external constant force: W = F r cos is the angle between the displacement, r,](https://reader030.vdocument.in/reader030/viewer/2022032803/56649e2e5503460f94b1e6e0/html5/thumbnails/1.jpg)
Work
AP Physics CMrs. Coyle
![Page 2: Work AP Physics C Mrs. Coyle. Work The work done on an object by an external constant force: W = F r cos is the angle between the displacement, r,](https://reader030.vdocument.in/reader030/viewer/2022032803/56649e2e5503460f94b1e6e0/html5/thumbnails/2.jpg)
Work• The work done on an object by an external
constant force:
W = F r cos
• is the angle between the displacement, r, and the force F.
![Page 3: Work AP Physics C Mrs. Coyle. Work The work done on an object by an external constant force: W = F r cos is the angle between the displacement, r,](https://reader030.vdocument.in/reader030/viewer/2022032803/56649e2e5503460f94b1e6e0/html5/thumbnails/3.jpg)
Products of two Vectors A and B
• Dot Product: – A·B =A B cos Scalar
• Cross Product: – AxB = AB sin Vector
![Page 4: Work AP Physics C Mrs. Coyle. Work The work done on an object by an external constant force: W = F r cos is the angle between the displacement, r,](https://reader030.vdocument.in/reader030/viewer/2022032803/56649e2e5503460f94b1e6e0/html5/thumbnails/4.jpg)
Work is a dot product
• Work is the dot product of Force and displacement.
W= F·r
![Page 5: Work AP Physics C Mrs. Coyle. Work The work done on an object by an external constant force: W = F r cos is the angle between the displacement, r,](https://reader030.vdocument.in/reader030/viewer/2022032803/56649e2e5503460f94b1e6e0/html5/thumbnails/5.jpg)
Units of Work• Is a scalar quantity.• Unit: Joule 1 J = 1 N m∙• James Prescott Joule, English, 19thCentury
• Other units of work: British system:
foot-pound cgs system:
erg=dyne ·cm Sub-atomic level:
electron-Volt (eV)
![Page 6: Work AP Physics C Mrs. Coyle. Work The work done on an object by an external constant force: W = F r cos is the angle between the displacement, r,](https://reader030.vdocument.in/reader030/viewer/2022032803/56649e2e5503460f94b1e6e0/html5/thumbnails/6.jpg)
Meaning of Sign of Work
When the work done by an external force onto the system is:
+ : the system gains energy - : the system loses energy
![Page 7: Work AP Physics C Mrs. Coyle. Work The work done on an object by an external constant force: W = F r cos is the angle between the displacement, r,](https://reader030.vdocument.in/reader030/viewer/2022032803/56649e2e5503460f94b1e6e0/html5/thumbnails/7.jpg)
• When the force is in the direction of thedisplacement, =0o:cos 0= 1 => W= F r and work is positive
Which force acting on the sled does positive work?
![Page 8: Work AP Physics C Mrs. Coyle. Work The work done on an object by an external constant force: W = F r cos is the angle between the displacement, r,](https://reader030.vdocument.in/reader030/viewer/2022032803/56649e2e5503460f94b1e6e0/html5/thumbnails/8.jpg)
When the force acts opposite to the direction ofthe displacement, =180o:cos 180 = -1 => W= F r and work is negative
Which force acting on the sleddoes negative work?
![Page 9: Work AP Physics C Mrs. Coyle. Work The work done on an object by an external constant force: W = F r cos is the angle between the displacement, r,](https://reader030.vdocument.in/reader030/viewer/2022032803/56649e2e5503460f94b1e6e0/html5/thumbnails/9.jpg)
When the force acts perpendicular to thedisplacement,
then the work done by that force is zero.
What force(s) acting on the sled does no work?
![Page 10: Work AP Physics C Mrs. Coyle. Work The work done on an object by an external constant force: W = F r cos is the angle between the displacement, r,](https://reader030.vdocument.in/reader030/viewer/2022032803/56649e2e5503460f94b1e6e0/html5/thumbnails/10.jpg)
Question
• Does the centripetal force do work?
![Page 11: Work AP Physics C Mrs. Coyle. Work The work done on an object by an external constant force: W = F r cos is the angle between the displacement, r,](https://reader030.vdocument.in/reader030/viewer/2022032803/56649e2e5503460f94b1e6e0/html5/thumbnails/11.jpg)
Example 1• How much work was done by
the 30N applied tension force to move the 6kg box along the floor by 20m? (A: 300J)
• How much work did the weight do in the same case?
• If µ=0.2, how much work did the friction do? (Hint: Use Fxnet to calculate N)(A: -136J)
![Page 12: Work AP Physics C Mrs. Coyle. Work The work done on an object by an external constant force: W = F r cos is the angle between the displacement, r,](https://reader030.vdocument.in/reader030/viewer/2022032803/56649e2e5503460f94b1e6e0/html5/thumbnails/12.jpg)
Work done by Resultant
W= W1+ W2+ Wn
Since work is a scalar, the net work done by a resultant force is equal to the sum of theindividual works done by each individualforce acting on the object.
net by individual forcesW W
![Page 13: Work AP Physics C Mrs. Coyle. Work The work done on an object by an external constant force: W = F r cos is the angle between the displacement, r,](https://reader030.vdocument.in/reader030/viewer/2022032803/56649e2e5503460f94b1e6e0/html5/thumbnails/13.jpg)
Work is the area under an F vs d graph.
![Page 14: Work AP Physics C Mrs. Coyle. Work The work done on an object by an external constant force: W = F r cos is the angle between the displacement, r,](https://reader030.vdocument.in/reader030/viewer/2022032803/56649e2e5503460f94b1e6e0/html5/thumbnails/14.jpg)
Work Done by a Variable Force
• For a small displacement, x, W ~ F x
• Over the total displacement:
f
i
x
xx
W F x
![Page 15: Work AP Physics C Mrs. Coyle. Work The work done on an object by an external constant force: W = F r cos is the angle between the displacement, r,](https://reader030.vdocument.in/reader030/viewer/2022032803/56649e2e5503460f94b1e6e0/html5/thumbnails/15.jpg)
Work Done by a Variable Force
• The work done is equal to the area under the curve.
lim0
ff
ii
xx
x x xxx
F x F dx
f
i
x
xxW F dx
![Page 16: Work AP Physics C Mrs. Coyle. Work The work done on an object by an external constant force: W = F r cos is the angle between the displacement, r,](https://reader030.vdocument.in/reader030/viewer/2022032803/56649e2e5503460f94b1e6e0/html5/thumbnails/16.jpg)
Work
W = F r cos
W = F(x) dx
W = F • dr
![Page 17: Work AP Physics C Mrs. Coyle. Work The work done on an object by an external constant force: W = F r cos is the angle between the displacement, r,](https://reader030.vdocument.in/reader030/viewer/2022032803/56649e2e5503460f94b1e6e0/html5/thumbnails/17.jpg)
Example 2 – Work by a Variable Force
The force acting on a particle is F(x)= (9x2 +3) N.Find the work done by the force on the particle
as it moves it from x1 =1.5m to x 2=4m.
Ans: 199 J
![Page 18: Work AP Physics C Mrs. Coyle. Work The work done on an object by an external constant force: W = F r cos is the angle between the displacement, r,](https://reader030.vdocument.in/reader030/viewer/2022032803/56649e2e5503460f94b1e6e0/html5/thumbnails/18.jpg)
Example 3 Work as dot product of vectors
A particle is pushed by a constant force of F=(4i +5j)N and undergoes a displacement ofr= (3i+ 2j)m.Find the work done by the force.
Ans: (12 +10)J= 22J (Scalar Quantity)
![Page 19: Work AP Physics C Mrs. Coyle. Work The work done on an object by an external constant force: W = F r cos is the angle between the displacement, r,](https://reader030.vdocument.in/reader030/viewer/2022032803/56649e2e5503460f94b1e6e0/html5/thumbnails/19.jpg)
Hooke’s Law
Force exerted by spring: Fs = - kx–equilibrium position is x = 0–k : spring constant (force constant)
(k increases as stiffness of the spring increases)
![Page 20: Work AP Physics C Mrs. Coyle. Work The work done on an object by an external constant force: W = F r cos is the angle between the displacement, r,](https://reader030.vdocument.in/reader030/viewer/2022032803/56649e2e5503460f94b1e6e0/html5/thumbnails/20.jpg)
• because it always acts to bring the object towards equilibrium
• the minus sign in Hooke’s law indicates that the Fs always acts opposite the displacement form equilibrium.
Fs is a Restoring Force
![Page 21: Work AP Physics C Mrs. Coyle. Work The work done on an object by an external constant force: W = F r cos is the angle between the displacement, r,](https://reader030.vdocument.in/reader030/viewer/2022032803/56649e2e5503460f94b1e6e0/html5/thumbnails/21.jpg)
![Page 22: Work AP Physics C Mrs. Coyle. Work The work done on an object by an external constant force: W = F r cos is the angle between the displacement, r,](https://reader030.vdocument.in/reader030/viewer/2022032803/56649e2e5503460f94b1e6e0/html5/thumbnails/22.jpg)
Work Done by a Spring
max
0 2max
1
2
f
i
x
s xx xW F dx kx dx kx
![Page 23: Work AP Physics C Mrs. Coyle. Work The work done on an object by an external constant force: W = F r cos is the angle between the displacement, r,](https://reader030.vdocument.in/reader030/viewer/2022032803/56649e2e5503460f94b1e6e0/html5/thumbnails/23.jpg)
Example #16
An archer pulls her bowstring back 0.4m by exerting a force that increases uniformly from 0 to 230N.
a)What is the equivalent spring constant of the bow?b)How much work does the archer do in pulling the
bow?
Ans: a) 575N/m, b) 46.0J