Centripetal Motion Problems

[Stephanie]

I have a few homework problems do tommorrow and I have tried and can't figure out these few problems. Thanks for the help. Oh and I don't just want the answers. I have those...I need help forming the equations. Thanks.

73. A curve of radius 60m is banked for a design speed of 100km/hr. If the coefficient of static friction is .30 (wet pavement), at what range of speeds can a car safely make the curve?

75. Two equal-mass stars maintain a constant distance apart of 8.0 x 10^10m and rotate about a point mid-way between them at a rate of one revolution every 12.6yrs. What must be the mass of each star?

76. A train traveling at a constant speed rounds a curve of radius 275m. A chandelier suspended from the ceiling swings out to an angle of 17.5degrees throughout the turn. What is the speed of the train?

78. Astronomers using the Hubble Space Telecope have recently deduced the presence of an extremely massive core in the distant galazy M87, so dense that it could well be a black hole. They did this by measuring the speed of gas clouds orbiting the core to be 780km/s at a distance of 60Lightyears (5.7x10^17m) from the core. Deduce the mass of the core and compare it to the mass of our sun.

**I think that 78 is just Velocity^2 divided by radius, is that right?

 

[berkeman]

-73- looks familiar. I think it came up a few days ago, but my quick search didn't find it. Here's a related thread with a long discussion of friction and banked tracks, though:

https://www.physicsforums.com/showthread.php?t=135880

-78- no, I don't think you have the correct approach (and I don't understand your approach). What do you use to calculate the mass of the Earth or another large body in space, given the orbital distance and speed? Do you need the mass of the orbiting object? (Hint -- remember that you can put satellites in geostationary orbit, independent of their mass.)

 

[radou]

...75. Two equal-mass stars maintain a constant distance apart of 8.0 x 10^10m and rotate about a point mid-way between them at a rate of one revolution every 12.6yrs. What must be the mass of each star?

Which is the force that crosses your mind when rotation is mentioned? Further on, what force crosses your mind when two celestial objects are mentioned? What is the relation between these two forces?