The mass of the rollercoaster car is 180 kg. Dimension A is 32 m. Dimension B is
ID: 2065856 • Letter: T
Question
The mass of the rollercoaster car is 180 kg.
Dimension A is 32 m.
Dimension B is 27 m
The coaster is already moving when it gets to point 1. The coaster rolls down the first hill, and a photogate measures its speed passing point 2. For the 2.94 m long coaster the photogate near point 2 is blocked for 0.079 seconds. The coaster then continues down the second hill to point 4.
a. If the rollercoaster has no friction, find the following, taking the ground as the reference point for potential energy: (i)Speed of the coaster as measured by the photogate near point 2: m/sec
(ii)Potential energy at point 2: J
(iii)Kinetic energy at point 2: J
(iv)Total energy at point 2: J
(v)Total energy at point 1: J
(vi)Potential energy at point 1: J
(vii)Kinetic energy at point 1: J
(viii) Speed of the coaster at point 1: m/sec b. Using the same concept as you used for part a (conservation of energy), find the speed of the coaster at point 4...
m/sec
Explanation / Answer
Total energy = Kinetic + Potential
(i) Speed of coaster: 2.94m/0.079s = 37.2m/s
(ii) Potential energy: mgh = 180kg * 9.8 * 27m = 47600J
(iii) (1/2)mv^2 = (.5)*(180kg)*(37.2m/s)^2 = 124546 J
(iv) 47600J + 124546 J = 172146 J = 1.72 x 105 J
(v) Tot. Energy At 1 = 1.72 x 105 J (Energy is not lost because there is no friction)
(vi) mgh = (180kg)*(9.8m/s^2)*32m = 56400J
(vii) To find the kinetic energy, we must first calculate the velocity at point 1.
1/2mvA^2 + mghA = 1/2mvB^2 + mghB
(.5)(180kg)VA^2 + (vi answer) = (iii answer) + (ii answer)
(.5)(180)(vA^2) + 56400J = 172146 J
VA^2 = [172146 J - 56400J ] / [(.5)(180)] = 35.86m/s
So, the kinetic energy is
(.5)(180kg)VA^2
(.5)(180kg)(35.86m/s)^2 = 115735 J
(viii) Found during the previous step: 35.86m/s
Speed of coaster at point 4 (I'm calling it "D"):
(.5)*m*vA^2 + mghA = (.5)m(vD)^2 + mghD
(vii answer) + (vi answer) = (.5)m(vD)^2 + 0
115735 J +56400J = (.5)m(vD)^2 + 0
VD^2 = (115735 J +56400J)/(.5*180)
VD = 43.73m/s
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