Download circular motion

CIRCULAR MOTION
HOW DO YOU GET SOMETHING TO MOVE IN A CIRCLE?
• Name one thing that travels in a circular path. (not something that spins) • What are some things we could measure about its motion?
• Consider the bowling ball lab (borling), when was the bowling ball moving in a circle or part of a circle. IMAGINE PUSHING A BOWLING BALL…
DIRECTION OF ACCELERATION?
In both cases:
• You have to stop the bowling ball from traveling upwards.
• You have to start the ball traveling to the right.
FORCE PERPENDICULAR TO MOTION
• A force perpendicular to an objects velocity causes a change in direction, NOT speed.
• Think of it as constantly accelerating sideways.
• http://www.youtube.com/watch?v=3tNVOhtvPEw
FORCE DIAGRAM:
CENTRIPETAL ACCELERATION
• If there is a net force towards the inside of the circle then there must be an acceleration.
• Where v is the linear velocity of the object around the circle and r is the radius of the circle. • Using Newton’s 2nd Law the Centripetal Force becomes:
CENTRIPETAL FORCE
BECAUSE THIS IS A NET FORCE YOU CANNOT
DRAW IT ON A FORCE DIAGRAM. It is always made up of other forces.
WHAT FORCE(S) ARE CAUSING THE CENTRIPETAL ACCELERATION?
A ball tied to a string in swung around in a circle above your head.
WHAT FORCE(S) ARE CAUSING THE CENTRIPETAL ACCELERATION?
A car goes around a sharp corner.
WHAT FORCE(S) ARE CAUSING THE CENTRIPETAL ACCELERATION?
A satellite orbits around the Earth.
WHAT FORCE(S) ARE CAUSING THE CENTRIPETAL ACCELERATION?
A roller coaster travels up the side of a circular loop.
WHAT FORCE(S) ARE CAUSING THE CENTRIPETAL ACCELERATION?
A roller coaster travels upside‐down at the top of a circular loop.
A 18 kg lawn mower has a linear speed of 2 m/s. What is the tension in 6 meter long rope attaching it to the pole? 2 m/s
6.0 m
How fast can a 1200 kg car travel around a corner with a radius of 20 m if the coefficient of friction is µ = 0.9?
A 3000 kg wrecking ball swings down with a speed with a speed of 28 m/s. What is the tension in the 30 m long cable at the bottom of the swing?
A 500 kg roller coaster is upside‐down at the top of a loop with a radius of 20 m. What is the normal force if the roller coaster is traveling 18 m/s?
CRITICAL VELOCITY
The minimum velocity for an object to travel in vertical circle and maintain its circular path against the force of gravity.
https://www.youtube.com/watch?v=‐TbpgZ2Dt0A
A 500 kg roller coaster is upside‐down at the top of a loop with a radius of 20 m. What is the critical velocity?
GRAVITY
The equation , works great for smaller objects at or near the surface of a planet. However the force of gravity really depends on the mass of the two objects.
Any two objects are attracted to each other simply because they have mass.
6.67
10
Girl, Brandy (42.5 kg), sits 1.50 m from boy (63.0 kg), George. What is force of gravity between them?
The Sun has a mass of 1.99 x 1030 kg and Venus has a mass of 4.87 x 1024 kg. Venus is 1.08 x 1011 m from the Sun. What is the force of gravity between them?
Find mass of earth. re = 6.38 x 106 m. 10.0 kg mass, other mass is earth’s mass.
The International Space Station has a mass of 450,000 kg and orbits the earth at a radius of 6.78 x 106 m (250 miles above the surface of the earth).
What is the force of gravity on it if the mass of the Earth is 5.97 x 1024 kg?
How fast is the ISS traveling?
How long does it take to orbit the Earth once? NEWTON’S 1ST LAW AND CIRCULAR MOTION
• What is Newton’s 1st Law?
• What direction is the lawn mower going in the diagram?
• If the rope to the lawnmower was cut, which direction would it go?
OH NO!!! ICE!!!!
Which direction will the car go when it hits the frictionless patch of ice?
A
ICE
B
C
D
MISCONCEPTIONS OF CIRCULAR MOTION AND THE FICTIONAL CENTRIFUGAL FORCE
DEBUNKING THE CENTRIFUGAL FORCE
Imagine you are riding in a fast car. The driver steps on the accelerator and the car speeds up
• Which direction do you feel like you are being pushed?
• Which direction are you actually accelerating and being pushed?
A LITTLE THOUGHT EXPERIMENT:
•
A passenger in a car wants to travel in a straight line path at a constant speed (Newton’s 1st Law)
•
Car makes a left turn.
•
Side of car pushes her to center of spin. •
She feels a push to the center ‐ she exerts an equal and opposite force on the door. (Newton’s 3rd Law)
•
She can't tell the difference between her pushing on the side of the car or the side of the car pushing on her. •
She thinks that she is being pushed outward. (This is where the false idea of an outward centrifugal force comes from.)
SATELLITES
https://www.youtube.com/watch?v=51mxBkwwSB8
GRAVITY IN ORBIT:
FREEFALL
Astronauts  "weightless"
distance to the center of the earth is only about 10 % greater force of gravity only slightly less
Falling endlessly around the earth
Gravity doesn't seem to work while falling.
weightlessness is caused by being in a constant state of free fall.
Warm Up
1. How can something be constantly falling towards Earth, but never actually hit it?
2. A satellite with a mass of 1500 kg is orbiting the Earth (m = 5.97 x 1024) at a radius of 8 x 106 m. What is the force?
3. How fast is the satellite orbiting?
A popular ride at amusement parks is illustrated below. In this ride, people sit in a swing that is suspended from a long rotating pole. A 45 kg rider is a distance 12 m from the pole and moves with a speed of 12 m/s. 1. Find the centripetal force on the rider.
2. Find the vertical component on tension.
3. Find the tension of the cable.
4. Find the angle θ.
Child twirls a yo yo with mass 0.25 kg. The angle of cord with vertical is 30.0.
1. What is the vertical component of tension?
0
2. What is the tension in the string?
3. What is the speed of the yo yo?