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**1a. The problem statement, all variables and given/known data**

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?

**2. Relevant 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))

**3. 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!

**1. The problem statement, all variables and given/known data**

**2. Relevant equations**

**3. The attempt at a solution**

**1. The problem statement, all variables and given/known data**

**2. Relevant equations**

**3. The attempt at a solution**