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DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture12A.Danylov
Lecture 12
Chapter 8
Universal Law of Gravity
Physics I
Course website:https://sites.uml.edu/andriy-danylov/teaching/physics-i/
He is right. I don’t feel my weight.But how to deal with anxiety
about falling?
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture12A.Danylov
Today we are going to discuss:Chapter 8:
Some leftovers Universal law of Gravity: Section 6.3 Circular Orbits/Satellites: Section 8.3
ConcepTest Ferris Wheel
A) N remains equal to mg
B) N is smaller than mg
C) N is larger than mg
D) none of the above
You’re on a Ferris wheel moving in avertical circle. When the Ferris wheel is atrest, the normal force N exerted by yourseat is equal to your weight mg. How doesN change at the top of the Ferris wheelwhen you are in motion?
You are in circular motion, so there has to be a
centripetal force pointing inward. At the top, the
only two forces are mg (down) and N (up), so N
must be smaller than mg.
Follow-up: Where is N larger than mg?
RvmNmg
2
NRvmmg
2
N
RvmmgN
2
RvmmgN
2
Bottom
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture12A.Danylov
Example Car on a circular flat road
R
vFc points toward the center of the circle (i.e., downward in this case). The weight vectorpoints down and the normal force (exerted by the hill) points up. The magnitude of the net force, therefore, isFc = mg – N.
N
Askiergoesoverasmallroundhillwith
radiusR.Becausesheisincircularmotion,
therehastobeacentripetalforce. Atthetop
ofthehill,whatisFc oftheskierequalto?
ConcepTest Going in Circles
Follow-up: What happens when the skier goes into a small dip?
A)Fc =N +mg
B)Fc =mg – N
C)Fc =T +N –mg
D)Fc =N
E)Fc =mg
Fc = N ‐mg
mg
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture12A.Danylov
Law of Universal GravitationThe motion of Satellites
Section 6.3Section 8.3
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture12A.Danylov
universal gravitational constant
M
mF
Gravitational force is central, attractive, proportional to masses, and inversely proportional to the square of the distance
2rmMGF
Newton’s Law of Universal Gravitation
G 6.671011 N m2 kg2
A gravitational force of attraction exists between all objects that have mass
Gravitationalforcesbetweentwoobjectsareonlysignificantwhenatleastoneoftheobjectsisverymassive.
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture12A.Danylov
Gravity near the Earth’s Surface
WhatshouldwegetfortheaccelerationduetogravityattheEarth’ssurface?
MEARTH 5.981024 kg REARTH 6.38106 m G 6.671011 Nm2
kg2
mg
g GME
RE2 9.80 m/s2
2rmGMF E
2rmGM
F E
ME
mLet’s apply N.2nd law for gravitational force
maF 2rmGMma E
Denote the acceleration due to gravity as 2)(
rGMrga E
If r=RE (on the surface)
F
So, we can simplify our force: That is why we use mg
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture12A.Danylov
Variations in “g” on the surface
The acceleration due to gravity varies over the Earth’s surface due to altitude, localgeology, and the shape of the Earth, which is not quite spherical.
TheaccelerationduetogravityvariesovertheEarth’ssurface
duetoaltitude anditissmalleronMt.Everest.
ConcepTest Mt. Everest/AppleTwo apples are droppedsimultaneously from 2m abovethe ground at the top of MountEverest and at sea level.Which hits the ground first?
A) Apple at sea level B) Apple on Mt. Everest C) They hit simultaneously
End of Class
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture12A.Danylov
Newton’s Cannon on a Mountain
https://physics.weber.edu/schroeder/software/NewtonsCannon.html
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture12A.Danylov
SatelliteExample
AsatellitedoesnotcrashintoEarthbecauseofitshighspeed.Ifitstoppedmoving,itwould,ofcourse,falldirectlyintoEarth.ThesamehappenswiththeMoon
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture12A.Danylov
Weighlessness (Explanation)
The “weightlessness” ina freely falling elevatoris because everything isaccelerating equallyindependent of mass.So, there is no normalforce.
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture12A.Danylov
The satellite and all its contents are in free fall, except with a huge tangential velocity. So, there is no normal force. Everything is accelerating equally independent of mass.This is what leads to the experience of weightlessness.
“Weightlessness” (cont.)
They do have a gravitational force acting on them, though!
https://www.gozerog.com/
Zero gravity created in a plane
WeightlessnesscanbeexperiencedonEarthaswell,butonlybriefly:
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture12A.Danylov
Thank you
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture12A.Danylov
mg
Tz
Tr
ar
T
z
r
)1(0 mgTF zz
)2(2
RmvSinTTr
rrr maTF
r component of tension provides the centripetal acceleration
Example Conical pendulum
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture12A.Danylov
Examples. Banked curve
But sometimes, friction force is not enough to keep a car on a circular road.
Banking the curve can help to keep cars from skidding.
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture12A.Danylov
mg
Ncos
Nsin
Fz = Ncos mg = 0
Fr = Nsin = marar= v2/R
N
Nsin mv2/R
tan v2/gRIndependent of object mass !!!
Banked Curves (solution)
r component of normal force provides the centripetal accelerationhttp://phys23p.sl.psu.edu/phys_anim/mech/car_banked_new.avi
r
z
Ncos mg
z
r
Take a ratio
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