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passphysics
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1a. Homework Statement
You are riding in a car over a hill that has a radius of curvature R. What speed should you be going if you want to feel one-third of your normal weight. Express your answer in terms of the radius R and the acceleration due to gravity g.
1b. You continue your journey at the same speed down the other side of the hill until you reach a valley that has a radius of curvature of two-thirds R. In terms of your true weight (mg) what is your apparent weight at the lowest point of the valley?
F=(GMm)/(r^2)
[tex]\sum[/tex]F=ma
a=(v^2)/(r)
v=(2[tex]\pi[/tex]r)/(T)
v=(2pi r)/(T(period))
1a.) I know that the sum of the forces in the y direction are F=(mg)(1/3)-N=mv^2/r
so v=[tex]\sqrt{rg/3-rN/m}[/tex]
1b.) Your weight should be more than your actual weight because mg-N=(mv^2)/r
I just don't know if i should put 2/3r in the equation. Then it would be mg=N-(mv^2)/(2/3r)
Sorry if i used the symbols incorrectly.
Thanks!
You are riding in a car over a hill that has a radius of curvature R. What speed should you be going if you want to feel one-third of your normal weight. Express your answer in terms of the radius R and the acceleration due to gravity g.
1b. You continue your journey at the same speed down the other side of the hill until you reach a valley that has a radius of curvature of two-thirds R. In terms of your true weight (mg) what is your apparent weight at the lowest point of the valley?
Homework Equations
F=(GMm)/(r^2)
[tex]\sum[/tex]F=ma
a=(v^2)/(r)
v=(2[tex]\pi[/tex]r)/(T)
v=(2pi r)/(T(period))
The Attempt at a Solution
1a.) I know that the sum of the forces in the y direction are F=(mg)(1/3)-N=mv^2/r
so v=[tex]\sqrt{rg/3-rN/m}[/tex]
1b.) Your weight should be more than your actual weight because mg-N=(mv^2)/r
I just don't know if i should put 2/3r in the equation. Then it would be mg=N-(mv^2)/(2/3r)
Sorry if i used the symbols incorrectly.
Thanks!