Paul Hewitt Explain How Gravity Pulls on a Moving Object
These notes are to supplement the reading of Chapter two pages 38-69 in the Holt Text Physics Text Book by Serway and Faughn.
Additionally the following are helpful.
Paul Hewitt explain how gravity pulls on a moving object.
Projectiles launched at different angels.
several descriptions, click on links below.
VA SOL’s covered:
PH.1The student will plan and conduct investigations in which
a)the components of a system are defined;
information is recorded and presented in an organized format;
c)metric units are used in all measurements and calculations;
PH.2The student will investigate and understand how to analyze and interpret data. Key concepts include
a)a description of a physical problem is translated into a mathematical statement in order to find a solution;
e)analysis of systems employs vector quantities utilizing trigonometric and graphical methods.
PH.3The student will investigate and understand how to demonstrate scientific reasoning and logic. Key concepts include
a)analysis of scientific sources to develop and refine research hypotheses;
b)analysis of how science explains and predicts relationships;
c)evaluation of evidence for scientific theories;
e)construction and defense of a scientific viewpoint (the nature of science).
PH.4The student will investigate and understand how applications of physics affect the world. Key concepts include
a)examples from the real world; and
b)exploration of the roles and contributions of science and technology.
PH.5The student will investigate and understand the interrelationships among mass, distance, force, and time through mathematical and experimental processes. Key concepts include
b)uniform circular motion;
c)projectile motion;
e)gravitation;
f)planetary motion;
2- Dimensional Motion Notes
Projectile Motion
A projectile is an object that is moving while the force of weight is the only force acting on it.
The center of mass (c-m) of a projectile follows a parabola.
An objects c-m is located at the point the object will balance on.
An object will fall over if the c-m exceeds the base.
Females typically have a lower center of mass than males do.
Experiment:
Take your physics book to a wall. Back away from the wall the distance of two of your feet, by placing one foot behind the other. Then bend at the waist and rest your head against the wall w/o moving your feet. The physics book should still be in your hand. From this position most females (not all) can stand back up, while most males (not all) cannot.
Objects projected with the same initial velocity will
Travel the furthest in the horizontal “x” direction (often called range) if it is launched at 45⁰.
Travel the highest if it is launched at 90⁰.
Equal angles from 45⁰ land at the same spot. (For example 40⁰ and 50⁰ are both 5⁰ from 45⁰ so they land at the same spot.)
Horizontal and vertical Velocities are independent of each other.
This means that if an object is projected horizontally, while another object is dropped from the same height, they will land at the same time.
Horizontal velocity vx is constant while vertical velocity is experiencing an acceleration of -9.8m/s2.
Example Problem number 1
An airplane is flying horizontally at 200.mi/hr while it is 40.0m up in the air. If a box is drop out of the plane, how far will the box move horizontally before it hits the ground?
Example problem number 2
A golf ball is hit 35m/s at 20⁰, how high will the ball go, and how far away will it land?
First, read the question and then diagram sketch what is happening.
Next , use SOH-CAH-TOA to find the components of the vi.
Notice that in the vertical direction it is viy (velocity intial in the “Y” direction) b/c vertically the velocity is changing (there is acceleration.)
In the horizontal direction it is just vx b/c the velocity is constant.
The next thing is to find the amount of time. In order to do this we will remember that at the highest point the velocity in the “Y” direction is zero. We will temporarily call that our final velocity in the “Y” direction (Vfy.)
Vfy=viy+ayt
0.00m/s=12.0m/s + (-9.80m/s2) (t)
-12.0m/s = (-9.80m/s2) (t)
t = 1.22 s
Remember by using 0.00m/s as the final velocity, we only calculated the time going up, the total time would be twice that or 2.44s.
Now that time has been calculated, we can solve for the displacement. When we solve for (how high) vertical displacement, dy, we will only use the time going up or 3.27s because that is how long it took to reach the highest spot.
dy = viy t+ ½ a t2
dy = (12.0 m/s)(1.22 s) + ½ (-9.80 m/s2) (1.22s)2
dy =7.35m
When we calculate (how far) horizontal displacement, dx, we must use the constant velocity formula. Also, since the ball will be travelling for the total time we will use the 6.54s.
dx = vx t
dx = (32.9m/s) (2.44s)
dx = 80.3m
______Circular and PeriodicMotion
SHM- simple harmonic motion
•It’s a motion that repeats itself without any external energy.
•It is created when there is an equilibrium point (where forces are balanced); and when forces push the object back toward the equilibrium point when it’s moved from the equilibrium.
•Pendulums, springs, guitar strings, and bobble head dolls all exhibit SHM.
•Resonance- When something is in SHM and a force is added at exact intervals to increase the movement.
•Period (T) – is the amount of time for one complete cycle. (unit: second (s))
Example
- What is period of minute hand on a clock? What is period of Earth’s, rotation and revolution?
- 1 hr1 day1 year
Circular Motion
•This section deals with objects that move in a circle, not an object that is rotating. A record on a record player is rotating. A lady bug on top of the record is moving in circular motion. The big difference is with circular motion there is no point that is fixed, with rotation, there is a spot that does not move location, just changes direction.
• Velocity used to be v=d/t with circular motion it becomesvc=2r/T known as tangential (b/c its direction is along the circles’ tangent) or centripetal velocity
•Centripetal velocity can be used to calculate our speed around the earth. The radius (earth)= 6.38 x 106 m, find vc
R=6.38 x 106 m
T=24hrs (3600s/hr)=86,400s
V=2πr/T= (2π(6.38 x 106 m))/86,400s =464 m/s That’s over 900 mph!
There is ancentripetal acceleration ac even when vc is constant, remember Newton’s first law. Which says “. . . objects in motion stay in straight line motion unless acted on by a net force.”
•The acceleration (ac) pulls toward the center, w/o ac object will go tangent.
•ac=v2/r= 42r/T2
•If ac> 9.8m/s2 things can go upside down and not fall. Amusement parks use this with rides that go upside down. Also, you can put water in a bucket and spin it over your head and the water will not come out b/c it is already accelerating downward at 9.8m/s2.
•One of the ways to produce artificial gravity in a space station is to spin the space station. People inside will be accelerated toward the center felling like gravity is pulling them toward the outside of the circle.
Centripetal vs. Centrifugal
•Centrifugal force is an imaginary force that pulls out. It does not actually exists, (Newton’s First Law. . . objects are simply trying to go in a straight line), however many people are confused (ie. Faith Hill – This Kiss) called a misnomer.
•Centripetal force is a real force that pulls toward the center of a circle.
• Ex. Washing machine, gravity for the planets, force of tires on the road
Centripetal Force (Fc)
• Fc= m42r/T2
•Fc= mv2/r
•Fc = mac
example.
Find the FC of an 80.0 kg person at the equator?
Fc= m42r/T2
Fc= (80.0kg)42(6.38 x106m) /(86,400s )2
Fc= 2.70 N
•Would you weigh more at the equator or the poles?
Pendulums – A string with a weight on the end (called a bob)
•Galileo first figured out how to quantify the period of a pendulum while watching the chandeliers sway at church.
•T= 2(l/g)
•This means that the length of the string and gravity are the only two things that affect the period of a pendulum. (The mass of the bob and how far its pulled back have no effect!)
•Pendulums where the most accurate and dependable way to keep time before quartz crystal. It is still used in grandfather clocks.
•A Foucault pendulum shows the rotation of the earth