6) A car initially traveling eastward turns north by traveling in a circular pat

Question

6) A car initially traveling eastward turns north by traveling in a circular path at uniform speed as shown in the figure below. The length of the arc ABC is 217 m, and the car completes the turn in 38.0 s.

(b) What is the magnitude and direction of the acceleration when the car is at point B?

what is the magnitude : m/s^2

what is the Direction :

8) A satellite has a mass of 213 kg and is located at 1.95 106 m above the surface of Earth.

(a) What is the potential energy associated with the satellite at this location?

J

10) An artificial satellite circling the Earth completes each orbit in 138 minutes.

(a) Find the altitude of the satellite.
m

(b) What is the value of g at the location of this satellite?
m/s2

11)A satellite of Mars, called Phobos, has an orbital radius of 9.4 106 m and a period of 2.8 104 s. Assuming the orbit is circular, determine the mass of Mars.
kg

Explanation / Answer

6) L = 2pi*r

217 = 2pi*r

r = 34.54m

ac = rw^2 = 34.54*(2pi/38)^2

ac = 0.944 m/s^2

(b) towards center

8) m = 213 kg , h = 1.95*10^6 m

potenital energy U =GMm/(R+h)

U = 6.67*10^-11*5.98*10^24*213/(6371000+1950000)

U = 1.02*10^10 J

10) T = 138 min

from Keplers third law

T^2 = 4pi^2(R+h)^3/GM

(138*60)^2 = 4*3.14^2*(6371000+h)^3/(6.67*10^-11*5.98*10^24)

h = 2.48*10^6 m

(b) g= GM/(R+h)^2

g = (6.67*10^-11*5.98*10^24)/(6371000+2480000)^2

g = 5.09 m/s^2

11) r = 9.4*10^6 m , T = 2.8*10^4 s

from Keplers third law

T^2 = 4pi^2(R+h)^3/GM

(2.8*10^4)^2 = 4*3.14^2*(6371000+9400000)^3/(6.67*10^-11*M)

M = 2.958*10^24 kg

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