Session 25 HW1 A level highway curve of radius 100 m is banked for cars travelin

Question

Session 25 HW1 A level highway curve of radius 100 m is banked for cars traveling at a speed of 20 m/s. What is the bank angle? (b) If a car rounds the above curve at 40 m/s what is the minimum coefficient of friction that will keep it on the road? Session 2.6 MW? (a) Io, a small moon of Jupiter, has an orbital period of 1.77 days and an orbital radius of 4.22x10^5 km. From these data, determine the mass of Jupiter. (b) Ganymede, Jupiter?s largest moon, has an orbital period of 7.16 days. What is its orbital radius?

Explanation / Answer

1)

Here , let the banking angle is theta ,

then ,

Fc   = mg*sin(theta)

mv^2/r   = mg*sin(theta)

20^2 /100 = 9.8 * sin(theta)

theta = 24.1 degree

the banking angle is 24.1 degree

b)

for 40 m/s , and considering friction

Fc   = mg*sin(theta) + u*mg*cos(theta)

40^2 /100 = 9.8 *(sin(24.1) + u*cos(24.1))

solving for u

u = 1.34

the minimum coefficient of friction is 1.34

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