- #1
RoyceB
- 9
- 0
1.
A roller coaster is designed with a clothoid loop that has a radius of 12 m at the top. For comfort, the apparent weight of a rider at the top of the loop must be 0.400 normal weight. What is the speed of the car at the top of the loop?
2.
Fn = 0.400(Fg)
Fn = 0.400(mg)
mv2 / r = Fn + Fg (Since the Fn and the Fg face the same direction.)
3. The Attempt at a Solution
So my attempt at this was to draw a FBD, and I noticed that the Fn and the Fg face the same direction. From that I could come up with the equation ΞFy = Fn + Fg and then using things I could sub in I came up with;
mv2 / r = 0.400(mg) + mg
mv2 / 12.0m = 1.400mg
v = √((1.400mx9.81m/s2)(12.0m) / m)
v = 12.8m/s
My question along with if this is correct. Is why is there no force in the positive direction? I understand that the cart is resting on the tracks and is held in there. But shouldn't there be a force going upward? Wondering if someone could explain that and tell me if/where I went wrong.
A roller coaster is designed with a clothoid loop that has a radius of 12 m at the top. For comfort, the apparent weight of a rider at the top of the loop must be 0.400 normal weight. What is the speed of the car at the top of the loop?
2.
Fn = 0.400(Fg)
Fn = 0.400(mg)
mv2 / r = Fn + Fg (Since the Fn and the Fg face the same direction.)
3. The Attempt at a Solution
So my attempt at this was to draw a FBD, and I noticed that the Fn and the Fg face the same direction. From that I could come up with the equation ΞFy = Fn + Fg and then using things I could sub in I came up with;
mv2 / r = 0.400(mg) + mg
mv2 / 12.0m = 1.400mg
v = √((1.400mx9.81m/s2)(12.0m) / m)
v = 12.8m/s
My question along with if this is correct. Is why is there no force in the positive direction? I understand that the cart is resting on the tracks and is held in there. But shouldn't there be a force going upward? Wondering if someone could explain that and tell me if/where I went wrong.