Recitation Worksheet Q Solutions

Recitation Worksheet Q Solutions - Worksheet Q Gravitation...

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Worksheet Q: Gravitation 1. Uranus has a radius of 25,560 km and a surface acceleration due to gravity of 8.86 m/s 2 . Its moon Miranda is in a circular orbit about Uranus at an altitude of 104,000 km above the planet’s surface. Miranda has a mass of 6.6×10 19 kg and a radius of 235 km. Calculate: a. The mass of Uranus The acceleration of gravity on the surface of any planet is 2 GM g R = where M and R are the mass and radius of the planet. Thus b. The acceleration of Miranda for its motion about Uranus. The distance between Miranda and the center of Uranus is Since the only force acting on Miranda is the gravitational pull from Uranus, the acceleration of Miranda is the gravitational acceleration by Uranus at that distance c. The acceleration due to Miranda’s gravity at the surface of Miranda. 19 11 2 2 2 2 2 M 6.6 10 kg 6.67 10 Nm /kg 0.080 m/s (235000 m) M M GM g R × = = × = d. Describe the motion of an object released 1 m above Miranda’s surface, on the side of Miranda that faces Uranus. 2 2 6 2 25 U U U 11 2 2 (8.86 m/s )(25.56 10 m) 8.86 10 kg 6.67 10 Nm /kg g R M G × = = = × × 6 6 6 104 10 m +25.56 10 m =129.56 10 m r = × × × M U M 2 25 11 2 2 2 U U 2 6 2 8.68 10 kg 6.67 10 Nm /kg 0.345 m/s (129.56 10 m) m M G m a r M a g G r = × = = = × = ×
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(Worksheet Q) This question can be tricky. If we draw a figure, it is pretty clear that the net acceleration of the object will be toward Uranus. But that does not mean that the object will really
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