Lecture 2-Chapter 4-Making Sense of the Universe (Motion, Energy, and Gravity)

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Published on 4 Aug 2010
School
UTSG
Department
Astronomy & Astrophysics
Course
AST201H1
Chapter 4 ± Making Sense of the Universe (Motion, Energy, and Gravity)
Describing Motion
There are 3 basic terms to describe how an object is moving:
1. Speed tells us how far an object will go in a certain amount of time.
x ie, 100km/hr is a speed, which tells us that the car will cover 100 km in an
hour.
2. Velocity tells us both the speed and direction of an object.
x ie, 100km/hr going due north.
1. Acceleration is when there is a changing velocity in any way, whether in speed or
direction or both.
x You can often feel the effects of acceleration Æ speeding up in a car would push you
back into your seat, and slowing down in a car would pull you forward from the seat,
and around a curve would push you away from the direction of your turn.
x However, when in constant velocity\RXGRQ¶WIHHOVXFKHIIHFWVLHDVPRRWKIOLJKWRQ
an airplane.
The Acceleration of Gravity
x Gravity accelerates all objects by the same amount, regardless of their mass.
x However, air resistance can cause a difference in acceleration.
o ie, a feather floats gently to the ground, while a rock plummets.
x The acceleration of a falling object is called the acceleration of gravity and is equal to
9.8m/s^2 Æ downward velocity increases by 9.8m/s with each passing second.
Momentum and Force
x $QREMHFW¶Vmomentum is its combination of mass and velocity (Momentum = Mass X
Velocity).
x 7KHRQO\ZD\WRFKDQJHDQREMHFW¶VPRPHQWXPLVWRDSSO\Dforce.
x The net force (overall force) acting on an object represents the combined effect of all
the individual forces put together.
o ie, when driving at a constant velocity, the force generated by the engine to
turn the wheels precisely offsets the forces of air resistance and road friction;
thus, there is no net force on your car.
x A change in momentum occurs only when the net force is not zero.
x &KDQJLQJDQREMHFW¶VPRPHQWXPPHDQVFKDQJLQJLWVYHORFLW\ZKLOHLWVPDVVEHLQJ
constant. Thus, the presence of a net force causes an object to accelerate.
x In other words, anytime an object accelerates, a net force must be causing the
acceleration (causing the feelings of pushes forward, backward, or to the side in a car).
Moving in Circles
x An ice skater spins in place with zero velocity and hence with zero momentum.
Simply, her spin gives her angular momentum (circling momentum or turning
momentum).
x Any object that is either spinning or moving along a curved path has angular
momentum.
o ie, Earth has angular momentum due both to its rotation (rotational angular
momentum) and to its orbit around the Sun (orbital angular momentum).
x The tySHRIIRUFHWKDWFDQFKDQJHDQREMHFW¶VDQJXODUPRPHQWXPLVFDOOHGDtorque
(twisting force).
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o ie, opening the door means making it rotate on its hinges, and to change tire
turning the bolts on a tire means making them rotate, both require giving them
some angular momentum.
The Difference between Mass and Weights
x Your mass is the amount of matter in your body.
x Your weight describes a force that is acting on your mass. It is what a scale measures
when standing on it.
o ie, your mass will be the same no matter how the elevator is moving. When
the elevator is stationary or moving at constant velocity, the scale reads your
normal weight. However, when the elevator accelerates upward or downward,
the floor exerts a greater or weaker force which makes you heavier or lighter
respectively.
Free-Fall and Weightlessness
x If you are in free-fall ± falling without any resistance to slow you down ± then you
are weightless.
o ie, you are in free-fall when the elevator cable breaks, and when you jump off
a chair or spring.
Weightlessness in Space
x Astronauts are weightless the entire time they are orbiting Earth because they are in a
constant state of free-fall.
x The Space Shuttle, the Space Station, and all other orbiting objects stay in orbit
because they are coQVWDQWO\³IDOOLQJDURXQG´WKH(DUWK7KHLUFRQVWDQWVWDWHRIIUHH-
fall makes these spacecraft and everything in them weightless.
1HZWRQ¶V/DZVRI0RWLRQ
1. 1HZWRQ¶VILUVWODZRIPRWLRQ: an object moves at constant velocity unless a net force
acts to change its speed or direction.
x ie, a spaceship needs no fuel to keep moving in space.
2. 1HZWRQ¶VVHFRQGODZRIPRWLRQ: force = mass X acceleration
x ie, a baseball accelerates as the pitcher applies a force by moving his arm.
(Once the ball is released, the force frRPWKHSLWFKHVDUPFHDVHVDQGWKH
EDOO¶VSDWKFKDQJHVRQO\EHFDXVHRIWKHIRUFHVRIJUDYLW\DQGDLUUHVLVWDQFH
3. 1HZWRQ¶VWKLUGODZRIPRWLRQ: for any force, there is always an equal and opposite
reaction force.
x ie, a rocket is propelled upward by a force equal and opposite to the force with
which gas is expelled out its back.
DIAGRAM
Conservation Laws in Astronomy
1. Conservation of momentum states that the total momentum of interacting objects
cannot change as long as no external force is acting on them ± their total momentum is
conserved.
- 0RPHQWXPRIDQREMHFWFDQRQO\EHJDLQHGRUORVWLIVRPHRWKHUREMHFW¶V
momentum changes by the opposite amount.
- The total momentum of you and the rest of Earth remains the same at all times.
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