091613
Laws of motion (I)
1) What is a Force? (or, why things move)
2) More on Reference Frames and Newtons 1st Law
3) Mass
4) Newtons 2nd Law
Why do Things Move?
Up until now we have been discussing Kinematics, or, how to describe the motion of objects
D
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D. We calculate work to find mechanical energy:
= = ( + ) (. ) + . ) ( )(. ) = . =
C. He performs the same amount of work. However, with a small rear sprocket the force is higher but the
distance he pedals is less, while the reverse is true if us
1) B: 11.4 h
t = d/v = (630 mi)/(55.3 mi/hr) = 11.4 hr
2) A: increase
g increases as you get closer to the surface of the Earth, as is approximately 9.8 m/s2 at the Earths surface.
3) C: instantaneous speed
The speedometer does not show direction, so it d
3)
a)
At r > r2, the entire charge Q is enclosed. Thus the potential is:
=
=
b)
By Gausss law, we get that:
=
=
=
( ( )
( )
= () =
( )
( + )
=
Where is the charge density
c)
At r < r1, qenc = 0, so s V(r) is constant and equal to V(r1)
( + )
=
a)
We apply Keplers third law:
=
(. + . ) (. )(. )
=
= .
b)
We apply the formula for gravitation:
=
(. )(. )
=
= . /
(. + . )
c)
Weight is equal to mass times acceleration due to gravity:
= = ( ) (.
) =
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a) We sum the forces in the horizon
1. Suppose we built a base on one of jupiter's small moons (a distance of 5AU from the Sun). How
fast would you have to launch a rocker from there to reach a moon of Saturn (10 AU away)?
(assume the speed to escape the small moon can be ignored, and we're
a)
We use an equation that relations angular velocity to angular acceleration:
= +
= (
) + (. )
= . /
b)
We use an equation that relations angular displacement to angular acceleration and velocity:
= + ( ) = (
) (. ) + ( ) (. ) (. ) = =
a)
W
Here we want to find the area under the curve from t = 0 to t = 4 sec, since the integration of
angular velocity with respect to time gives angular displacement:
= (
) ( ) + (
) ( ) = = .
a)
We use an equation that relations angular velocity to angular
091313
2D Motion (II)
1) More Projectiles
2) Uniform Circular Motion
3) Relative Motion
A Note on Notation
Y(t) = yi + vyit + (1/2)gt^2
G= -9.8
Y(t) = yi + vyit - (1/2)gt^2
G=9.8
Projectiles
X direction
Constant velocity
Xf= xi + vxit
Xf = 0 + vo cos thet
090913
Physics 151
Vectors
1) Coordinate Systems
X,y graph
-(x1,y1)
-any coordinate system is composed of orthogonal (perpendicular) directions
-Cartesian coordinates
-Polar Coordinates
- We use r and theta
-r = distance from the origin
-theta is the dist
1. the speed of galaxies can be measured by using
a. hubbles constant
b. speed of light
c.doppler shift
d. parallax
2. the reddish skies during a "sunset" can be explained by the wave effect:
a. red shift
b. blue shift
c. refraction
d. diffraction
e. disp