Universal Gravitation and Central Net Force. Gravity 12/21/2017. supplemental

Transcription

1 Universal Gravitation and Central Net Force Gravity supplemental Newton s Universal Law of Gravitation Inverse square law (all field forces are inverse squares) Why? Our universe has 3 dimensions of space, as you move outward you encounter 3 dimensional spheres of gravitational field the surface area of a sphere is 4πr, so each new sphere of field (influence) decreases by a r term. All massive objects put gravitational forces on other massive objects You have mass, and so does the person next you Yes, you are attracted to the person sitting next to you You are also attractive so someone living in another galaxy, but the force is so small it can t be measured 1

2 7 173 The equation is where little g comes from mg = GMm/r Cancel the little m s and you find g = GM/r where the mass of the Earth is 5.97 x 10 4 kg Where the radius of the Earth is x 10 6 m Big G is 6.67 x Multiple it out and g = 9.8 N/kg, tada!

3 Assignments on gravity Volume of a sphere: Density: m D = V V 4 = π r 3 3 The nature of orbits Throw a ball, projectile motion (a parabola) Throw it harder and the projectile motion is the same just a longer parabola Throw it so hard that it makes it to the horizon before it hits the ground that it will enter into a constant state of falling toward the center of the earth but never hitting it People in ISS are not floating, they are falling continuous state of sky-diving Centripetal vs centrifugal l In order to accelerate, you need an unbalanced force in the direction of acceleration. When you take the round-about at middle road too fast, you have to be accelerated into the circle (inward), but you feel like you are being thrown outward because of your inertia wanting to keep you in the path of your motion Centrifugal vs. centripetal motion (centrimeaning center and petal meaning seeking like a bee seeks a flower petal). Centrifugal is not real, it is the feeling of inertia. Silly Silo at Adventureland example Curves, Centrifugal, Centripetal Forces Going around a curve smushes you against window Understand this as inertia: your body wants to keep going straight but the car is accelerating towards the center of the curve Centripetal, Centrifugal Forces, continued The car is accelerated toward the center of the curve by a centripetal (center seeking) force The name for the net force toward the center of the circle that causes circular motion to occur NOT a separate force. Can use F net to represent it. In your reference frame of the car, you experience a fake, or fictitious centrifugal force Not a real force, just inertia relative to car s acceleration The Car accelerates you think you re being accelerated Centripetal Force on car velocity of car (and the way you d rather go) 3

4 Car Around a Curve - Friction Centripetal Force What provides it? If there isn t enough friction (icy or wet road), the car doesn t make the curve! Silly Silo the wall provides the centripetal force! Vertical drum rotates, you re pressed against wall Friction force against wall matches gravity Seem to stick to wall, feel very heavy Real Forces: Friction; up Centripetal; inwards Gravity (weight); down Lab How do mass, velocity and radius affect centripetal force? Three investigations Fc versus velocity Mass versus velocity Radius versus velocity Some values are filled in already Circular Motion w/ a sparkler How differentials work How do we create artificial gravity Circularly moving space stations The Martian (movie) Interstellar (movie) 001 Space Oddyssey(movie) Halo (video game) Elysium (movie) How differentials work Space Odyssey 4

5 How do trains turn? Baffling balloon behavior A Which direction does the net force (centripetal force) point for an object moving in a uniform circular motion? Which of the following is true for an object traveling in a circular path at constant speed? a) its speed is constant, so its acceleration is zero. b) both its speed and velocity are constant. c) its speed is constant, but its velocity is changing. d) both its velocity and acceleration are constant. F net 5

6 A 1500-kg car goes around a curve with a radius of 50.0-m at a speed of 8.0 m/s. a) How much Fc is needed? mv (1500)(8.0) Fc = = = 190 = 1900N r 50.0 A 50.0-g cork on a 1.00-m string twirls at 3.00 rev/s. The string can hold only 0.0-N. Will it break? Π(1) v = = 18.8m / s (18.8) F = = c 7 N IT WILL HOLD!!! A classmate swings a rock on a string in an overhead circle. Suppose that the string breaks at the point shown. Draw a line to show the path of the rock. Two identical boats race around a semi-circular turn, both are traveling at the same speed. a. Which boat takes longer to complete the turn? b. Which boat has a greater acceleration in the turn? c. Which boat has the greater net force on it? Unit 6 Universal Gravitation and Central Net Force Model Recap/Review 6

7 F net How do I figure this out? Try it out but make it easy on yourself. Substitute in easy #s to work with, like 1 and and find out! 7