1. A car drives straight down towards the bottom of a valley and up the other si

Question

1. A car drives straight down towards the bottom of a valley and up the other side on a road whose bottom has a radius of curvature of 115 m. At the bery bottom, the normal force of the driver is twice his weight. At what speed was the car traveling? Please show work.

2. Calculate the period of a satellite orbiting the Moon, 95 km above the Earth's surface. Ignore efffects of the Earth. The moons radius is 1740 km. Please show work.

3. Planet A and planet B are in circular orbits around a distant star. Planet A is 7.0 trimes farther from the star than is planet B. What is teh ratio of their speeds Va/Vb. Please show work.

Explanation / Answer

1.Normal force =w +mv^2/r =2w =>mv^2/r =w=mg =>v^2/r =g

=>v =(115*9.8)^0.5 =33.57m/s;

3.centripetal force =gravitation al forc=>

Ma(Va^2)/Ra =GMa*Ms/Ra^2 for planet A

Ma(Vb^2)/Rb =GMb*Ms/Rb^2 for planet B

=> (Va^2)*Ra =(Vb^2)*Rb => Va/Vb = 1/7^0.5 =0.377

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