# Desperate need of help

1. Nov 22, 2004

### fizziksplaya

These two are toughies for a first year rookie like me. I survived kinematics, and I thought I survived circular motion. But the work-energy chapter just threw 2 curveballs in my face. Any help would be more than appreciated:

1) The drawing shows a version of the loop-the-loop trip for a small car (the picture sucks. its basically a real circle, car goes straight ahead then up and around the loop and out the other side) If the car is given an inital speed of 4.0 m/s. What is the largest value that the radius can have if the car is to remain in contact with the circular track at all times?

2) A skier starts from rest at the top of a hill. The skier coasts down the hill and up a second hill, as the drawing illustrates (the skier starts from an unkown height above a horizontal, the slope goes downward under the horizontal, and comes back up on the second "circular" crest). The crest of the second hill is circular, with a radius of 36m. Neglect friction and air resistance. What must be the height of the first hill so that the skier just loses contact with the crest of the second hill?

The first one I've been struggling with for hours. The second one, i'm not sure i understand the question, so if you explained it to me, I could probably figure it out myself

2. Nov 22, 2004

### Galileo

1) You have to look at the highest point piont the loop. Recall that the centripetal acceleration on the car when it is in circular motion is $v^2/R$, where R is the radius of the loop.
If the car is to remain in the loop, this must be greater than the gravitational acceleration g.
To find the speed of the car at the top, use conservation of energy.