Circular Motion Basics
What direction does centripetal acceleration ALWAYS point?
Toward the center of the circle.
T/F: An object moving in a circle at a constant speed has zero acceleration.
False-- it has centripetal acceleration.
Where is the gravitational field stronger:
halfway inside the Earth or just outside the Earth's surface?
just outside the Earth's surface
Astronauts on the ISS feel "weightless" because...
A. They are in zero gravity
B. They are in free fall around the Eearth
C. They are moving at a constant speed around the Earth
D. None of the above. Astronauts do not feel weightless on the ISS.
B.
Astronauts feel weightless because they are falling freely around the Earth
What is the equation escape velocity?
sqrt((2GM)/R)
A car is driving at 10m/s around a circular track. Describe the change in acceleration when the car's speed is doubled.
The centripetal force quadruples.
What force acts as the centripetal force when I swing a bucket of water in a vertical circle?
Tension in the arm/bucket.
In orbit, is a satellite accelerating if it moves at a constant speed?
Yes, because it is constantly changing direction.
If Earth's mass doubled but it's radius stays the same, what would happen to your weight?
Your weight would double.
Look at the drawing. What h value is needed to ensure the cart stays on the track until the end?
h = 5/2 R
If static friction disappears while a car is turning, what happens?
The car slides straight off the curve (no centripetal force)
At the very top of a rollercoaster loop, what forces are acting on the rider? What direction are these forces facing?
Fgravity going downwards and Fnormal downwards.
What happens to the gravitational force between two objects if the distance between them doubles?
The force becomes 1/4 as big.
An object is moving in a circle at a constant speed. At some instant, what is the work done by the net force on the object during a short time interval?
Zero. The net force is perpendicular to velocity, and since work=Fdcos(x) and x=90o, cos(90)=0, there is no work done by the net force!
Name Tycho Brabe's 3 Laws of Planetary Motion
1. Orbits of our planets are ellipses with the sun at one foci (200pts)
2. Law of Equal Areas
A planet sweeps out equal times as it equal orbits. (200pts)
3. we don't need to know this one but if you get it, you get 1000pts
A biker turns in a circle of radius 50m at a speed of 10 m/s. What is the centripetal acceleration?
Ac= 10(10) / 50 = 2m/s(s)
In a vertical circle, where is the tension in the string greatest?
At the bottom, tension must over some both weight and provide centripetal force.
There are 3 planets orbiting the Sun. You are standing on Planet B. Planet A travels 5000m closer to the sun. Planet B travels 2000m closer to the sun. Planet C travels 1000m closer to the sun. From your position, in what direction will planets A and C be moving?
The planets will appear to be moving away from Planet B.
Order the planets by time it takes to orbit around the sun (shortest time to longest time)
1. Mercury
2. Venus
3. Earth
4. Mars
5. Jupiter
6. Saturn
7. Uranus
8. Neptune
How long does it take for Neptune to order the sun?
165 Earth years
within 5 years: 500pts
within 10 years: 400pts
within 30 years: 300 pts
within 50 years: 150 pts
within 100 years: 50pts
Over 100 years: no points awarded
A ball is attached to a string and swung in a horizontal circle at a constant height. If the string breaks at a certain instant, what path will the ball follow immediately after the string breaks?
The ball will move in a straight line tangent to the circle at the point of release, because no net force acts to change it's direction anymore (Newton's 1st Law).
NOTE: a common trap, do NOT say "outwards" --the ball moves tangentially outwards, not radially outwards!
A 2.0kg object moves at 6.0m/s in a vertical circle of radius 1.5m. What is the maximum tension in the string?
T = 67.6 N
Tension must overcome gravity and provide centripetal force.
T- mg = (mv2/r)
T= (2.0)(9.8) + (2.0)(6.0)2/1.5
A satellite orbits very close to the Earth's surface. If the orbital speed is about 8,000 m/s, how many minutes does it take to go once around the Earth (circumference = 40,000km)?
83 minutes.
40,000m/ 8,000m/s = 5000seconds
A small block of mass m=0.50kg slides without friction along a track that includes a vertical loop of radius r=1.2m.
The block is released from rest at a height h above the bottom of the loop. What is the minimum height h above the bottom of the loop so that the block stays in contact with the track all the way around the loop?
h = 3.0m
Energyinitial= mgh
Energyfinal= mg(2r) + (1/2)mv2
set equal: gh = 5/2(rg)
solve for h.
Tides on Earth are caused by....
Spring tides are...
Neap tides are...
...difference in Fg on different sides of the Earth.
...when tidal forces overlap, higher high tide and lower low tide during a full/new moon.
...when tidal forces contradict during 1st/3rd quarter.