The roller coaster in Figure P6.36 starts with a velocity of 15.2 m/s. One of th

Question

The roller coaster in Figure P6.36 starts with a velocity of 15.2 m/s. One of the riders is a small girl of mass 38 kg. At points B and C, the track is circular with the radii of curvature given in the figure. The heights at points A, B, and C are hA= 24.35 m, hB = 34.45 m, and hC=0 m. You may assume the track is frictionless. Find the velocity of the roller coaster at point B. Incorrect. Tries 1/8 Previous Tries Find the velocity of the roller coaster at point C. Tries 0/8 Find her apparent weight at B Tries 0/8 Find her apparent weight at C

Explanation / Answer

Hi,

In this case we have to solve this problem applying the conservation of energy. Unfortunately, I don't have the image so there is a lack of information. Even though, I can tell you that the way to solve the exercise would be as follows:

In this problem you will have only two kinds of energy, the kinetic one and the gravitational potential one. The first depends on the velocity while the second depends on the relative height. As the track is frictionless, the sum of those energies is conserved.

For instance, if the starting point is the point A, then you have the mechanical energy of said point (as you have the height and the velocity) which would be equal to:

EA = MghA + (1/2)Mvo2 = M [ 9.8 m/s2 * 24.35 m + (1/2)*(15.2 m/s )2 ] = (354.2 m2/s2) M

Note: M is the total mass of the roller coaster, which is unknown.

This would be equal to the mechanical energy in any point (B or C) :

EB = (354.2 m2/s2) M = MghB + (1/2)MvB2 ::::::::: (1/2)vB2 + ghB = 354.2 m2/s2

vB = (2*(354.2 m2/s2 - 9.8 m/s2 * 34.45 m))1/2 = 5.76 m/s

EC = (2354.2 m2/s2) M = MghC + (1/2)MvC2 ::::::::: (1/2)vC2 + ghC = 354.2 m2/s2

vC = (2*354.2 m2/s2)1/2 = 26.62 m/s

This results are valid as long as the point A is the starting point.

In the case of the last question, I would need to know if the girl is vertical or upside down as well as the radius of curvature, but I can tell you that this part can be solve through Newton's Laws.

I hope it helps.

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