A 64.9 kg student is riding a looping roller coaster. At the top of the loop the

Question

A 64.9 kg student is riding a looping roller coaster. At the top of the loop the student is moving with a speed of 19.6 m/s. The loop has radius of 25.4 m at the top.

Find the normal force from the seat on the student at the top of the loop.


Normal force (in N):
2.
A highway engineer wants to design a horizontal turn so that a car with mass 707 kg can go 16.4 m/s around curve. If she assumes the coefficient of static friction is 0.505, what is the smallest radius she can make the turn and not have the car skid?
Minimum radius (in m):
3.
A stunt man (67.8 kg) swings across a valley at the end of a 30.4 m long rope. He starts from a height of 14.3 m above the lowest point.

Find the tension in the rope at the bottom of the swing.


Tension at the bottom (in N):
4.
Consider a 783 kg satellite in a circular orbit around the earth with a period of 5.7 hours.

Determine the speed of the satellite in m/s.

Given information:
Mass of Earth = 6.0 x 1024 kg
Radius of Earth = 6.4 x 106 m
G = 6.67 x 10-11 N m2/kg2

Speed (in m/s):

Explanation / Answer

(1). Mass m = 64.9 kg Radius r = 25.4 m Speed v = 19.6 m / s The normal force from the seat on the student at the top of the loop = mg - (mv 2 / r)                                                                                                       = 636.02 - 981.57                                                                                                       = - 345.55 N (2). Mass m = 707 kg Speed v = 16.4 m/ s Coefficient of static friction = 0.505 Radius r = ? We know v = [ rg ] From this r = v 2 / g                    = 54.34 m

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