remember - nevis laboratoriessciulli/physics1401/...top of a wall of height h = 3.05 m. the plank...
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slide 1Physics 1401 - L 16 Frank Sciulli
Remember
l Midterm 2 to be taken one week from today
l Will cover mainly chapter 7 – 13u But understanding previous chapters may be
neededl Check website at **Exam Specifics for
midterm 2u Practice exam and solutions u Exam Guide
l Important issue is to be able to do problems
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slide 2Physics 1401 - L 16 Frank Sciulli
Today
l Hand in HW 7l Finish chapter 13 … u Ch 7 – 13 emphasized in midterm 2
l Go on to gravity
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slide 3Physics 1401 - L 16 Frank Sciulli
Problem 13-25 (not assigned)
l Strut Ms= 45kgu Take length s
l Findu tension, Tu Force components
at the hinge
Fy Fxs
The system is in equilibrium. A concrete block of mass 225 kg hangs from the end of the uniform strut whose mass is 45.0 kg. Find
(a) the tension T in the cable and the (b) horizontal and(c) vertical force components on the strut from the hinge.
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slide 4Physics 1401 - L 16 Frank Sciulli
Problem 13-29 (not assigned)
l Frictionless at the rollerl Find that if θ<θ0, the
plank slipsl What is µs for the plank
contact with ground?
Wf
n
Nθ
0
3.056.1044570
h mL mW Nθ
=
=
=
= °
A uniform plank, with a length L of 6.10 m and a weight of 445 N, rests on the ground and against a frictionless roller at the top of a wall of height h = 3.05 m. The plank remains in equilibrium for any value of θ > 70° but slips if θ < 70°. Find the coefficient of static friction between the plank and the ground.
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slide 5Physics 1401 - L 16 Frank Sciulli
Ch 14 - Gravitationl Newton’s great achievements of late 17th century
scienceu 3 laws of motion
o To some extent, were re-statements by Galileo and othersu law of universal gravitation
o unique and important essential to complete the picture
l Thus far, we have only seen the utility of Newton’s Laws in describing everyday laws (on Earth’s surface) u investigated by many: Galileo, Toricelli, …
l Truly earthshaking discovery was supplementing this with the Universal Law of Gravitationu lots of competition: Hooke, …u explained astronomical descriptions of Solar system +
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slide 6Physics 1401 - L 16 Frank Sciulli
What is Gravity? (Newton)l Attractive force between any two mass
elements of the universe; force is:u always attractiveu proportional to massesu inversely proportional to square of separationu dependent on a new universal constant, G
o G = 6.67× 10-11 N-m2/kg2
1 22
m mF Gr
=
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slide 7Physics 1401 - L 16 Frank Sciulli
Gravity Potential Energy
r
mmU Gr
dU mmF Gdr r
= −
= − = −
1 2
1 22
l This must be the right potential … it gives the right force
l Note path independence …
l Note text examples
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slide 8Physics 1401 - L 16 Frank Sciulli
Energies of Any Bodyand Escape Velocity
l Note that E<0corresponds to boundbody (planet, etc)
l E>0 is unbound bodyl Escape from surface of
Earth requires E > 0
212
const.
K mvMmU Gr
E K U
=
= −
= + = 212
0
0
2
esc
esc
EMmmv GR
GMvR
>
− =
=M
vr
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slide 9Physics 1401 - L 16 Frank Sciulli
Applicability of Newton’s Gravity
l Still (with modifications from General Relativity) accepted as the basic force law
l Applies in all known circumstancesu Earth’s surfaceu Inside the Earthu Solar Systemu Grand Universe…
1 22
m mF Gr
=
l Important general law of forcel Similar form for electricity, …
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slide 10Physics 1401 - L 16 Frank Sciulli
Gravity at surface of the Earth
l Many subtletiesuDensity vs r (look into here)u Rotation of Earth (small)u slightly nonspherical shapeu …
l ALL SMALL!!
2
2
MmG mgR
Mg GR
=
=
M = Earth mass R = Earth radius G = universal gravitational constant
l AssertionK All mass of Earth can be considered to be at the center when seen from outsideK Can be proven!K Unexpected result for force on object inside Earth
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slide 11Physics 1401 - L 16 Frank Sciulli
Shell of Mass from OUTSIDE
l Force on m is as if all the mass M were concentrated at the center of the sphereuie, at center of mass
2mMF Gr
=
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slide 12Physics 1401 - L 16 Frank Sciulli
Shell of Mass from INSIDE
l cone through m intercepts the sphere in two places
l Area on shell surface intercepted by cone ~ r2
l Magnitudes of forces on m by pieces of surface 1, 2
r1
r2
A2
A1
A Ar AA rr r
A rA r
FF
=
= = =2 222 1
21 22 21 1
22 2
21 1
2
1
1
1,21,2 2
1,2
mmF G
r=
l Forces on m from opposite pieces of surface cancell No net force on mINSIDE shell!
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slide 13Physics 1401 - L 16 Frank Sciulli
Shell of Mass from INSIDE and OUTSIDE
l Summarize: for a uniform shell of mass uAny mass inside feels no
forceuAny mass outside feels a
force as if all of M were concentrated at center of the sphere (shell)
l Can be proven in each case mathematically by integrating over all the mass in the shellu Try if you like!
F 0=
2mMF Gr
=
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slide 14Physics 1401 - L 16 Frank Sciulli
Consider Earth as continuous, uniform set of shells
2
343
2 3 343
inside m
tottot
mMF G
rr mMmF G M G r
r R R
=
= =
ππ
l Shells outside ( r>R ) contribute NOnet force on m
l Shells inside ( r<R ) act as if all their mass concentrated at the center
l Only that part of the Earth mass inside r is relevant to the force on m
l Check out problem 14-23
attractive to center … like spring force
Actually Earth not uniform (next slide) but general point valid
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slide 15Physics 1401 - L 16 Frank Sciulli
Earth Structure and Empirical “Gravity”
l Radial dependence of densityl Earth rotation reduces effective “weight”
but this effect is tiny (<.034m/s2)l More important: gravitational force (and
acceleration) decrease with R -- but need to go very high to see effect.
Altitude(km)
ag (m/s2) Altitude Example
0 9.83 Mean Earth surface8.8 9.8 Mt. Everest36.6 9.71 Highest manned balloon400 8.7 Space shuttle orbit
35 700 0.225 Communications satellite
6370 kmEarthR =
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slide 16Physics 1401 - L 16 Frank Sciulli
Gravity at surface of the Earth
l Many subtleties (see text)uDensity vs ru Rotation of Earthu slightly nonspherical shapeu …
l ALL SMALL!!
2
2
MmG mgR
Mg GR
=
=
M = Earth mass R = Earth radius G = universal gravitational constant
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slide 17Physics 1401 - L 16 Frank Sciulli
Remember
l Midterm 2 to be taken one week from todayl Will cover mainly chapters 7 – 13u But understanding previous chapters may be
neededl Check website at **Exam Specifics for
midterm 2u Practice exam and solutionsu Exam Guide
l Important issue is to be able to do problemsl Recitation session tomorrow will go over the
sample midterm