In this problem, use g = 9.80 m/s2.
Bizarro, located at Six Flags New England, in Agawam, MA, is the name of one of the top-rated roller coasters in the country. The first drop on the roller coaster brings you down 67 meters.
There are some resistive forces acting as the roller coaster comes down, of course, so let's say you actually reach the bottom of the hill with a speed of merely 75.0 miles per hour. In addition, let's say that the bottom of the hill is a vertical circular arc with a radius of 50.0 m. Figure out the size of the upward normal force acting on you at the bottom of the hill, and then divide by the force of gravity acting on you - this will give you the "g-force" (in units of g, the acceleration due to gravity), you experience at the bottom of the hill.
I thought it would be F=ma=[(m*v^2)/r]-mg and the m's could be factored out since it is not given and to get g force I would divide by g= 9.8 and got ~11.3, but it is not right. Is my reasoning flawed somewhere?
The force acting at the bottom of the loop is [(m*v^2)/r] + mg
You got the sign wrong. There may be another error as well.
75 mph = 110 ft/s = 33.53 m/s
v^2/r = 22.5 m/s^2
(v^2/r + g)/g = 3.29
Your reasoning is mostly correct, but there is a minor mistake in the equation you used. The correct equation to calculate the net force at the bottom of the hill is:
F_net = (m * v^2) / r + mg
Where:
- F_net is the net force at the bottom of the hill
- m is the mass of the person riding the roller coaster
- v is the velocity of the person at the bottom of the hill
- r is the radius of the circular arc at the bottom of the hill
- g is the acceleration due to gravity
To find the upward normal force at the bottom of the hill, subtract the weight force (mg) from the net force (F_net):
F_normal = F_net - mg
To calculate the g-force, divide the upward normal force by the weight force:
g-force = F_normal / mg
In your calculation, you only subtracted the weight force (mg) from the net force, but you did not calculate the actual net force correctly. By correcting this error and following the steps mentioned above, you should be able to find the correct answer.