I've been doing extra questions for physics, but these four are still giving me trouble. Please help me solve them, including Free Body Diagrams if possible.
1. If a curve with a radius of 60m is properly banked for a car traveling at 60km/hr, what must the coefficient of static friction be for a car not to skid when traveling at 90km/hr?
2. A satellite of mass "m" moves in a circular orbit about the earth at a height "h" above its surface. If the radius of the earth is R and the accel due to gravity at the earth's surface is "g" show that the period of the satellite can be expressed as T=2pi*route((R+h)^3 / gR^2)
3. Calculate the mass of the sun using the fact that the period of the earth is 3.16x10^7 seconds and its mean distance from the sun is 1.5x10^11m. (G=6.67x10^-11 Nm^2/kg^2)
4. Conical pendulum question-
An amusement park ride consists of a rotating circular platform 8m in diameter from which seats are suspended at the end of 2.5m chains. When the system rotates the chains holding the seats make an angle theta=28degrees with the vertical a) what is the speed of the seat? b) If a child of mass 40kg sits in the 10kg seat, what is the tension in the chain?
Thanks huge guys, if I can see how these questions are done, i should be set for my midterm tomorrow.
EDIT:
I've attempted the questions a few times, and here are my conclusions so far.
1. I know i have to get the horizontal component of acceleration, and I think I have to use Click to see the LaTeX code for this imageFr=ma but I don't know how?
2. I'm completely confused on this one as I wasn't given any numbers, and it completely throws me when I just have to work with variables.
3. First you have to get Velocity using a=4pi^2r / T^2
so therefore Accel=5.93x10^-3
After that, i know I have to use accel somehow to get mass, but i'm not sure how exactally to do that.
4. I was sick the day this was taught, and my teacher was not much of a help trying to explain how to do conical pendulum questions. I did get the notes for that day, but I still have no idea how to even start this one :(
Did you get a copy of Schaum's Outline Series, as I suggested?
1. You are on the right track, equate centripetal force with the horizontal component of the force of friction at the new angle.
2. Set centripetal force equal to the force of gravity at distance (R+h) from the center of Earth. Remember the gravitational field at that altitude is
g'= g (R/(R+h))^2
and that period = 2PI(R+h)/velocity
3. Same procedure, the force of gravity is G Ms Me/R^2
4. This has nothing to do with pendulum. Set the horizontal component of chair equal to centripetal force. On the seat, you know mg, and the angle, that will give you the horizonal force to set equal to centripetal force.