Soulutuons to problems assigned 1/10

Problems from handout:
17. a) Towards center of circle
b) Towards center of circle
c) Static friction

61.
a) Since the car is moving in a circle you now the acceleration must be a_c=v²/r. You have been given the radius (r=50m) of the circle but you have to find the velocity. The car's lap time is 14.3s and since the track goes around the circumference of a circle the distance the car travels each lap is 2π(r). The velocity (distance/time) is then 2π(50m)/14.3s=22m/s.Now just plug in: a_c=(22m/s)²/50m = 9.68 m/s²
b) If you know the acceleration then finding the force is just a matter of multiplying the mass: F_c=ma_c (or F_c=mv²/r).
67. If the pilot is moving at the right speed the only force that will be acting on him at the top of the loop will be gravity -- because that's the only force needed to maintain his motion. The pilot will feel this as a sensation of weightlessness. In this special situation centripetal acceleration is exact provided by gravitational acceleration so that g=v²/r (remember g=9.8m/s²). This problem tells you the pilot's speed and asks you to find the radius:

g=v²/r rearrange and you get: r=v²/g= (120m/s)²/(9.8m/s²)=141.2.


Thats it!