PHYSICS 7C Final: PHYSICS7C Final Exam 2011 Fall Solutions

89 views10 pages

turquoisegnu128

2 Oct 2018

School

Department

Course

Professor

For unlimited access to Study Guides, a Grade+ subscription is required.

anishka.fernandopulle1 and 38345 others unlocked

PHYSICS 7C Full Course Notes

Verified Note

35 documents

Document Summary

Suddenly the right-hand ball becomes detached and falls off but the left-hand ball remains. ( ibar = ml2/12: find the angular acceleration of the bar just after the ball falls off. 0 = (ibar + iball) 2 / 2 + mg(-l/2) = 5. 7 rad/s: two spheres mass m and radius r each are set in deep space at distance. They accelerate towards each other because of their mutual gravitational attraction: find the speed of each sphere when their centers of mass are x meters apart (solve in terms of x). When the force of gravity is equal to the spring forces. Fspring = 2 * k (x-2r-2) (2* for two springs) (x=2r+2 is the point when the springs are touching but apply no force) This is a hard problem to solve exactly. 1 2mvi2 +1 2i i2= mgh + 1 2mvf2 +1 2i f2 use i =2mr2/5 and v= r.

Related Questions

Assume a hole is drilled through the center of the Earth. It can be shown that an object of the mass m at a distance r from the center of the Earth is pulled toward the center only by the material in the shaded portion of Figure P13.73. Assume Earth has a uniform density ρ. Write down Newton's law of gravitation for an object at a distance r from the center of the Earth and show that the force on it is of the form of Hooke's law, F= -kr, with an effective force constant of k = (4/3) πρGm, where G is the gravitational constant.

brownmole943

1. Mail Chute Through the Earth (40 points total)
Assume the Earth is sphere of radius R, has uniform density, massM,
and tunnel dug through the Earth from pole to pole. A box of massm
(very well wrapped!) is held just above the North Pole openingand
dropped from rest (see diagram). Assume:
Â· You can ignore friction and all effects due to the various
motions of the Earth
Â· The tunnel is so thin it has no measurable effect on the
gravitational field of the Earth.
a) Use Gaussâ law to find an expression for F(r), the magnitude ofthe gravitational force felt by mass
m at distance r from the center of the Earth, where r < R. (10points)
b) Show that m will move through the Earth in simple harmonicmotion. Find T, the period of that
motion. Use: MEarth = 5.98x1024 kg, REarth = 6.37x106 m, and G =6.67x10-11 N-m2/kg2 to get a
numerical answer. (8 points)
c) Use a computer program to draw a graph of a(r), (magnitude only,so it is positive at all points),
showing points from r = 0 to r = 2R outside the Earth). (10points)
NOTE: You do not have to show a derivation for F(r) for r >R.
d) Find a numerical value for vmax, the maximum speed of m, usingthe values for the constants given in
part b. (Initial conditions: ro = R, vo = 0.) (12 points)
HINT: One method is to use conservation of energy.

In the example 12.5 (Section 12.3) in the textbook we ignored thegravitational effects of the moon on a spacecraft en route from theearth to the moon. In fact, we must include the gravitationalpotential energy due to the moon as well. For this problem, you canignore the motion of the earth and moon.

Part A
If the moon of mass m_{\rm M} has radius R_{\rm M} and the distancebetween the centers of the earth and the moon is R_{\rm EM}, findthe total gravitational potential energy of the particle-earth andparticle-moon systems when a particle with mass m is between theearth and the moon, and a distance r from the center of the earth.Take the gravitational potential energy to be zero when the objectsare far from each other. Take the mass of earth as m_{\rm E}.

Part B
There is a point along a line between the earth and the moon wherethe net gravitational force is zero. Use the expression derived inpart (a) to find the distance of this point from the center of theearth.

Part C
With what speed must a spacecraft be launched from the surface ofthe earth just barely to reach this point?

Part D
If a spacecraft were launched from the earth's surface toward themoon with an initial speed of 11.2 {\rm km/s}, with what speedwould it impact the moon?

PHYSICS 7C Final: PHYSICS7C Final Exam 2011 Fall Solutions

PHYSICS 7C Full Course Notes

Document Summary

Get access

Related textbook solutions

Physics: Principles with Applications

Related Documents

PHYSICS 7C Study Guide - Final Guide: Orbital Speed, Isotopes Of Nitrogen, Angular Acceleration

PHYSICS 135 Chapter Notes - Chapter 12: Gm-1, Ellipse, Orbital Speed

PH 125 Midterm: ph125_s14_exam4-SOLN

Related Questions