Two horizontal curves on a bobsled run are banked at the same angle, but one has twice the radius of the other. The safe speed (no friction needed to stay on the run) for the smaller radius curve is v. What is the safe speed on the larger radius curve? A) v/2
B) v /√ 2
C) 2v
D) v√2

I shall answer it here so this can help other students out
First, FN = mg/cos
On a banked curve, FNx is the only acceleration force
FNx = mv^2/r
FNx = FNsin
mg/cos * sin = mv^2/r
cancel out the mass (m) and sin*1/cos is tan
gtan = v^2/r
rgtan = v^2
√(rgtan) = v (this is the velocity for the smaller radius.)
call larger radius velocity X

for larger radius, it becomes 2r, so √(2rgtan) = X

understand you can do √xy = √x * √y

√(rgtan) * √2 = X (√(rgtan) = v)
v * √2 = X (where X is velocity with larger radius)

As shown in fig. p3.64, a closed, rigid tank fitted with a fine-wire electric resistor is filled with refrigerant 22, initially at 2108c, a quality of 80%, and a volume of 0.01 m3. a 12-volt battery provides a 5-amp current to the resistor for 5 minutes. if the final temperature of the refrigerant is 408c, determine the heat transfer, in kj, from the refrigerant.

Ogle–2013–blg–0723 is an exoplanet that is similar to earth in size and proximity to its star. this exoplanet has mass m=4.18×1024kg and radius r=5.66×106m. an astronaut whose weight on earth is w=735n lands on the planet. a. calculate m, the mass of the astronaut. b. calculate gp? , the acceleration due to gravity on the surface of ogle–2013–blg–0723. c. calculate wp? , the weight of the astronaut on the surface of ogle–2013–blg–0723. d. calculate v, the minimum velocity required to put an object into orbit above ogle–2013–blg–0723. e. calculate t, the time required to complete an orbit around ogle–2013–blg–0723.

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