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Goals Equilibrium Weight The End
Physics 2514Lecture 13
P. Gutierrez
Department of Physics & AstronomyUniversity of Oklahoma
P. Gutierrez (University of Oklahoma) Physics 2514 February 23, 2011 1 / 14
Goals Equilibrium Weight The End
Goal
Goals for today’s lecture:Application of Newton’s second law continue
Equilibrium Static and Dynamic.
Gravity and weight.
Continue with the application of friction Static and Kinetic
P. Gutierrez (University of Oklahoma) Physics 2514 February 23, 2011 2 / 14
Goals Equilibrium Weight The End
Clicker
An elevator suspended by a cable is moving downwards andslowing to a stop. Which free-body diagram is correct?
P. Gutierrez (University of Oklahoma) Physics 2514 February 23, 2011 3 / 14
Goals Equilibrium Weight The End
Equilibrium
Newton’s Second Law.
An object of mass m subjected to forces ~F1, ~F2, . . . will undergoan acceleration ~a given by
~a =~Fnet
m
where ~Fnet =∑n
i=1~Fi is the vector sum of all forces acting on
the object. The acceleration vector ~a points in the samedirection as the force vector ~Fnet.
Condition for equilibrium.∑
i
~Fi = 0 ⇒ ~a = 0
P. Gutierrez (University of Oklahoma) Physics 2514 February 23, 2011 4 / 14
Goals Equilibrium Weight The End
Equilibrium
Equilibrium∑
i~Fi = 0.
Static equilibrium system is at rest.
Dynamic equilibrium system moves with a constantvelocity; ~a = 0.
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Goals Equilibrium Weight The End
Example
A 50 kg steel box is in the back of a dump truck. The truck’sbed, also made of steel, is slowly tilted. At what angle will thefile cabinet begin to slide?
Brief description: A 50 kg steel box is on a steel incline plane.What is the maximum angle the incline can have for the box toremain in static equilibrium?
P. Gutierrez (University of Oklahoma) Physics 2514 February 23, 2011 6 / 14
Goals Equilibrium Weight The End
Example
A 50 kg steel box is in the back of a dump truck. The truck’sbed, also made of steel, is slowly tilted. At what angle will thefile cabinet begin to slide?
Brief description: A 50 kg steel box is on a steel incline plane.What is the maximum angle the incline can have for the box toremain in static equilibrium?
P. Gutierrez (University of Oklahoma) Physics 2514 February 23, 2011 6 / 14
Goals Equilibrium Weight The End
Solution
Knownµs = 0.80, m = 50 kg
Unknownangle θ of inclineNormal force n
Newton’s second law:
mg sin θ − µsn = 0
n − mg cos θ = 0
}
⇒ µs = tan θ ⇒ θ = tan−1 µs = 38.7◦
P. Gutierrez (University of Oklahoma) Physics 2514 February 23, 2011 7 / 14
Goals Equilibrium Weight The End
Solution
Knownµs = 0.80, m = 50 kg
Unknownangle θ of inclineNormal force n
Newton’s second law:
mg sin θ − µsn = 0
n − mg cos θ = 0
}
⇒ µs = tan θ ⇒ θ = tan−1 µs = 38.7◦
P. Gutierrez (University of Oklahoma) Physics 2514 February 23, 2011 7 / 14
Goals Equilibrium Weight The End
Solution
Knownµs = 0.80, m = 50 kg
Unknownangle θ of inclineNormal force n
Newton’s second law:
mg sin θ − µsn = 0
n − mg cos θ = 0
}
⇒ µs = tan θ ⇒ θ = tan−1 µs = 38.7◦
P. Gutierrez (University of Oklahoma) Physics 2514 February 23, 2011 7 / 14
Goals Equilibrium Weight The End Example
Gravity and Weight
Mass is an intrinsic property of an object (objects inertia).
Gravity is a long range force acting between any twomasses. (Newton’s law of gravity.)
~FG =Gm1m2
r2r̂
Gravity near Earth’s surface (Newton’s second law.)
m~a = ~FG =GmMe
R2e
r̂ ⇒ g ≡ a =GMe
R2e
= 9.8 m/s2
G = 6.67 × 10−11 N · m2/kg2
Me = 5.98 × 1024 kg Re = 6.37 × 106 m
P. Gutierrez (University of Oklahoma) Physics 2514 February 23, 2011 8 / 14
Goals Equilibrium Weight The End Example
Gravity and Earth
m~a =GmMe
(Re + y)2r̂ ⇒ g ≡ a =
GMe
(Re + y)2
y ⇒ distance above the earth’s surface
y (km) g (m/s2)
0 9.830 Earth’s surface
10 9.799 Cruising altitude of a commercial aircraft
100 9.528 60 miles up
400 8.703 Height of space shuttle
400,000 0.003 Height of the moon
P. Gutierrez (University of Oklahoma) Physics 2514 February 23, 2011 9 / 14
Goals Equilibrium Weight The End Example
Weight
Weight is a measurement
An objects weight results from the force exerted on aspring scale could be a pulling or pushing contact force.
If the system is in static equilibrium (rest frame) w = mg.
P. Gutierrez (University of Oklahoma) Physics 2514 February 23, 2011 10 / 14
Goals Equilibrium Weight The End Example
Weight
Weight is a measurement
An objects weight results from the force exerted on aspring scale could be a pulling or pushing contact force.
If the system is in static equilibrium (rest frame) w = mg.
P. Gutierrez (University of Oklahoma) Physics 2514 February 23, 2011 10 / 14
Goals Equilibrium Weight The End Example
Example
You are standing on a scale inside an elevator. When theelevator is stationary, you find your weight is 680 N. What isyour weight if the elevator is moving downward with a velocityof 10 m/s, but the accleration is upward at 3 m/s2?
P. Gutierrez (University of Oklahoma) Physics 2514 February 23, 2011 11 / 14
Goals Equilibrium Weight The End Example
Example
You are standing on a scale inside an elevator. When theelevator is stationary, you find your weight is 680 N. What isyour weight if the elevator is moving downward with a velocityof 10 m/s, but the accleration is upward at 3 m/s2?
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Goals Equilibrium Weight The End Example
Solution
P. Gutierrez (University of Oklahoma) Physics 2514 February 23, 2011 12 / 14
Goals Equilibrium Weight The End Example
Solution
∑
i
Fyi = Fsp − mg = ma
w = N = Fsp
⇒ w = ma+mg = m(a+g) = 888 N
P. Gutierrez (University of Oklahoma) Physics 2514 February 23, 2011 12 / 14
Goals Equilibrium Weight The End Example
Solution
∑
i
Fyi = Fsp − mg = ma
w = N = Fsp
⇒ w = ma+mg = m(a+g) = 888 N
P. Gutierrez (University of Oklahoma) Physics 2514 February 23, 2011 12 / 14
Goals Equilibrium Weight The End Example
Clicker
In the example the elevator is moving downwards at 10 m/s,accelerating upwards at 3 m/s2 and the weight is found to be888 N. Now assume that the elevator is moving upwards at10 m/s and accelerating upwards at 3 m/s2, what is the weight?(Recall that for the stationary elevator the weight was 680 N.)
A) 888 N
B) 680 N
C) 471 N
D) 0 N
C) -888 N
P. Gutierrez (University of Oklahoma) Physics 2514 February 23, 2011 13 / 14
Goals Equilibrium Weight The End
Announcements
Read chapter 6.
Reading quiz on chapter 5 and 6; due by 11:59 PM today.
New homework available.
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