Whether twirling a rock around your head or looking at the motion of a satellite as it orbits the Earth, both can be described using the terms centripetal force, tangential velocity, and period. Use your understanding of uniform circular motion and satellite motion to answer the following questions.
A car of mass 8.88 x 102 kg takes a turn of radius 20.0 meters with a speed of 10.0 m/s. What is the centripetal force acting on the car?
- 4.44 x 103 N
- 4.44 x 102 N
- 4.44 N
- 44.4 N
Use \(\small\mathsf{ F_c = \frac{mv^2}{r} }\) to solve for centripetal force.
Use \(\small\mathsf{ F_c = \frac{mv^2}{r} }\) to solve for centripetal force.
Use \(\small\mathsf{ F_c = \frac{mv^2}{r} }\) to solve for centripetal force.
Use \(\small\mathsf{ F_c = \frac{mv^2}{r} }\) to solve for centripetal force.
A satellite of mass 4500 kg orbits the Earth at the same orbital radius as a satellite of 6500 kg. Which of the following statements is true?
- The centripetal force on both are equal.
- The centripetal acceleration on both are equal.
- The velocity of the 4500 kg satellite must be greater than the 6500 kg satellite.
- The two satellites cannot be going the same speed.
The centripetal force depends on the mass of the objects: \(\small\mathsf{ F_c = \frac{mv^2}{r} }\).
Since the velocity and thus the centripetal acceleration of satellites at the same orbital radius do not depend on the mass, the two satellites will have the same centripetal speed and centripetal acceleration.
Since the velocity and thus the centripetal acceleration of satellites at the same orbital radius do not depend on the mass, the two satellites will have the same centripetal speed and centripetal acceleration.
Since the velocity and thus the centripetal acceleration of satellites at the same orbital radius do not depend on the mass, the two satellites will have the same centripetal speed and centripetal acceleration.
A car moves in a circle with radius of 22.5 meters at a constant speed of 4.50 m/s. The net force acting on the car is 810 meters. What is the car's mass?
- 4.05 x 103 kg
- 1.80 x 103 kg
- 8.10 x 103 kg
- 9.00 x 102 kg
Use \(\small\mathsf{ F_c = \frac{mv^2}{r} }\) to solve for the mass.
Use \(\small\mathsf{ F_c = \frac{mv^2}{r} }\) to solve for the mass.
Use \(\small\mathsf{ F_c = \frac{mv^2}{r} }\) to solve for the mass.
Use \(\small\mathsf{ F_c = \frac{mv^2}{r} }\) to solve for the mass.
What is the orbital period of a satellite orbiting Earth (m = 5.97 x 1024 kg) at an orbital radius of 4.22 x 107 m?
- 1 hour
- 12 hours
- 24 hours
- 1440 hours
Use \(\small\mathsf{ t_s = \frac{2\pi r^{\frac{3}{2}}}{\sqrt{GM}} }\) to solve for the period. Then, find out how many hours are in that number of seconds.
Use \(\small\mathsf{ t_s = \frac{2\pi r^{\frac{3}{2}}}{\sqrt{GM}} }\) to solve for the period. Then, find out how many hours are in that number of seconds.
Use \(\small\mathsf{ t_s = \frac{2\pi r^{\frac{3}{2}}}{\sqrt{GM}} }\) to solve for the period. Then, find out how many hours are in that number of seconds.
Use \(\small\mathsf{ t_s = \frac{2\pi r^{\frac{3}{2}}}{\sqrt{GM}} }\) to solve for the period. Then, find out how many hours are in that number of seconds.
What is the orbital speed of a satellite orbiting Earth (m = 5.97 x 1024 kg) at an orbital radius of 4.22 x 107 m?
- 55.3 m/s
- 3.03 x 103 m/s
- 8.63 x 104 m/s
- 9.36 x 106 m/s
Use \(\small\mathsf{ v_c = \sqrt{\frac{GM}{r}} }\) to find the orbital speed of the satellite.
Use \(\small\mathsf{ v_c = \sqrt{\frac{GM}{r}} }\) to find the orbital speed of the satellite.
Use \(\small\mathsf{ v_c = \sqrt{\frac{GM}{r}} }\) to find the orbital speed of the satellite.
Use \(\small\mathsf{ v_c = \sqrt{\frac{GM}{r}} }\) to find the orbital speed of the satellite.
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