AST201H1 Study Guide - Midterm Guide: Weightlessness, Gravitational Time Dilation, Electromagnetic Spectrum

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violetdinosaur460

10 Feb 2014

School

UTSG

Department

Astronomy & Astrophysics

Course

AST201H1

Professor

Michael Reid

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AST201H1 Full Course Notes

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S2. 1 einstein"s revolution special relativity: an object is travelling relative to sth, no object can travel faster than the speed of light. 2 people share the same reference frame when they"re not moving relative to each other. Thought experiments 1-9 - see slides for length contraction & time dilation. Jackie is moving relative to you & her twin sister, you"ll see jackie"s time running more slowly than yours & her sister"s. 1 light-year: therefore, the round trip takes only 2 years to you but people on earth will be 50 years older. S3. 1 einstein"s 2nd revolution - general relativity: matter shapes the fabric" of spacetime in a matter analogous to the way heavy weights distort a rubber sheet. 1: the equivalence principle, the effects of gravity are exactly equivalent to the effects of acceleration. According to the equivalence principle, all orbits must represent the straightest possible path through spacetime. Shapes & speeds of orbits reveal the geometry of spacetime.

Related Questions

Theoretical question here on relativity and lengthcontraction:

If a neutron star of upper-limit mass is moving at a highlyrelativistic speed when viewed by an observer, then we know thatthe neutron star will appear to contract in the direction ofmotion.

Is it possible for the neutron star to appear to contractsufficiently enough so that its density becomes large enough to beconsidered a black hole (satisfies Schwarzschild radius) relativeto a stationary observer?

That is to say, is it possible for a stellar object to be a neutronstar in its rest frame but a black hole in the another frame ofreference? If so, what implications could that hold, would light beunable to escape it from the observer's frame (but possible toescape it from its rest frame)?

Learning Goal: To understand length contraction and timedilation.

An inertial frame of reference is one in which Newton's laws hold.Any frame of reference that moves at a constant speed relative toan inertial frame of reference is also an inertial frame. Theproper length l_0 of an object is defined to be the length of theobject as measured in the object's rest frame. If the length of theobject is measured in any other inertial frame, moving with speed urelative to the object's rest frame (in a direction parallel tol_0), the resulting length l is given by the length contractionequation

l = l_0\sqrt{1-\frac{u^2}{c^2}} ,

where c is the speed of light. Similarly, if two events occur atthe same spatial point in a particular reference frame, and anobserver at rest in this frame measures the time interval betweenthese two events, the time interval so measured is defined to bethe proper time Delta t_0. When the time interval is measured inany other inertial frame, again moving with speed u relative to thefirst frame, the resulting time interval Delta t is given by thetime dilation equation

\Delta t = \frac{\Delta t_0}{\sqrt{1-\frac{u^2}{c^2}}} .

a. Suppose that you measure the length of a spaceship, at restrelative to you, to be 400 \rm m. How long will you measure it tobe if it flies past you at a speed of u = 0.75c?
Express the length l in meters to three significant figures.

b. The spaceship from Part A has a large clock attached to itsside. This clock ran at the same rate as your watch when you werein the same reference frame. How much time Delta t will pass onyour watch as 80 \rm s passes on the clock attached to theship?
Express your answer in seconds to three significant figures.

c. Two spaceships, named A and B, are flying toward each other withrelative speed 0.800c. If the captain of ship A fires a missile,counts 10.0 \rm s on his watch, and then fires a second missile,how much time Delta t will the captain of ship B measure to havepassed between the firing of the two missiles?
Express your answer in seconds to three significant figures.

d. The captain of ship B knows that ship A uses 2-m-long missiles.She measures the length of the first missile, once it has finishedaccelerating, and finds it to be only 0.872 \rm m long. What is thespeed u of the missile, relative to ship B?
Express your answer in meters per second to three significantfigures. Use c = 3 \times 10^8 \; \rm m/s.

Please answer fully... thank you

1. Which of the following describes an object with a non-zero netforce acting on it? Choose all that apply.
The moped accelerated while making a left turn.
The motorcycle traveled at a constant speed while making au-turn.
The truck slowed down while making a right turn.
The spaceship traveled at a constant speed in a straightline.
The car sped up from 50 mph to 65 mph while moving in a straightline.

2. If you observe that an object is accelerating, what should youconclude?
A non-zero net force is acting on it. Only forces causeacceleration. As such, if an object is accelerating it must bebecause a non-zero net force is acting on it.
It must be in free fall.
It must be changing direction. Acceleration is a vector and vectorshave both magnitude and direction. Thus if an object isaccelerating it must be changing direction.
The forces acting on the object must be greater than the forces theobject is exerting.
It must be speeding up. If an object is accelerating that means itis speeding up.

3. Which of the following are true according to Newton's 2nd Law?Choose all that apply.

If the acceleration is zero, then the net force is zero.
If you apply the same force to 2 objects, the one with more masswill have a greater acceleration.
If you apply the same force to 2 objects, the one with less masswill have a greater acceleration.
If two objects have the same acceleration, the one with less masswill have a larger net force exerted on it.
If two objects have the same acceleration, the one with more masswill have a larger net force exerted on it.
The larger the net force on an object is, the larger theacceleration.
The larger the net force on an object is, the smaller theacceleration.

4. A box is on the Moon. The box weighs 152 lb and is in free fall.How much force is the box exerting on the Moon and in whatdirection?

lb
Up
Down
Right
North
East
West
Left
South

5. Which of the following are the correct units for mass? Chooseall that apply.
slugs
u
kgÂ·m/s2
g
N
m/s2
oz
lb

6. If an object is traveling in a circle, which of the followingmust be TRUE? Choose all that apply.
The object is slowing down.
The object is speeding up.
The object has a net force acting on it.
The object has a constant velocity.
The object is accelerating.

AST201H1 Study Guide - Midterm Guide: Weightlessness, Gravitational Time Dilation, Electromagnetic Spectrum

AST201H1 Full Course Notes

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