Flowers in Liquid Nitrogen
Energy
Levers give you a 'mechanical advantage'
1st gear requires a small force and a lot pedaling, while 10th gear requires little pedaling but larger force.
An Incline Plane is a Simple Machine
I) Work - Product of F and displacement in which force acts
Work and Energy
**Scalar**
A) Equation W done by a specific force on an object
F = Force Δd - displacement Ө = angle between F and d Other units for work (Joule) or Kg m2/sec2
If you have Multiple Forces
Work done by all the forces on object
Finding Wnet
Finding Fnet
W and F negative if acting against d (A car braking, friction, catching baseball)
If Ө between
Ex) Object pushed at angle Ө, f=0, mass M, Force F, distance d
Ex) Object pushed at angle, f≠0, Mass M, Force F, μ, Fn Find Net Work done on mower
Wnet = Fcosqd - μFnd Wnet = work by mower - work against Why is Wf negative? When finding Wnet
Challenge Question: Two people exert a 10 Newton force on a block for 2 meters. One person exerts her force at a 50-degree angle. (frictionless)
Person 2 does more work
Ex) Find minimum work needed to push a 950 kg car 810 m up a 9.0 degree incline, a) no friction b) friction μ = 0.25
Work is minimum W = [mgsinq]d
W = [950 kg x 9.8m/s2]sin9]810m
1.2 x 106 J
b) Find minimum work needed to push a 950 kg car 810 m up a 9.0 degree incline, friction μ = 0.25
W = [mg(sinӨ+μcosӨ]d
= 3.0 x 106 J
Textbook p. 162) 8
8. 330 kg piano, slides down 3.6 m, 28° incline uk = .40 keep from accel. down ramp by man
(a) Force exerted by man?
Since a = 0 so Fnet = 0 down ramp Free body Diagram on piano Fdown = Fup
mgsinӨ = fk + Fman
mgsinӨ = ukFn + Fman
mgsinӨ = ukmgcosӨ + Fman
mgsinӨ - ukmgcosӨ = Fman
Fman = 3.8 x 102 N
b) Work done by man on piano?
Work + or - ?
W = -3.8 x 102 N(3.6m)
= -1.4 x 103 J c) Work done by friction
Work + or -?
Wf = -[ukFn]d
= - ukmgcosӨ[d]
Wf = -4.1 x 103 J
d) Work done by force of gravity?
Work + or -?
W = mgsinӨ[d]
5.5 x 103 J e) Net work done on piano?
Wnet = Fnetd
Since constant v then a = 0 then Fnet = 0
W = 0 Or Wnet = Wman + Wfr + Wg
Wnet = Wman + Wfr + Wg 2 forces opp. direction of d, one F with d Wnet = -1400 J + -4100J + 5500 J Wnet = 0 J
B) Work and F vs. d diagram (plot)
W = Area Under Plot = 1/2bh
= 1/2(5 m)(3 N)
7.5 Nm
p. 162) 14
Sketch Graph Area under plot = W W = 1/2[b1 + b2]h W = 1/2[13m+5m]24 N
W = 216 J
ŠTony Mangiacapre., - All Rights Reserved
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