A satellite of mass Ms = 2x10' kg is attached to a point on the equator of the Earth (MẸ= 6x1024 kg) by a long, ideal spring with spring constant k= 10$ N/m so that it is moving in a circular trajectory of radius r= 7x10' m from the center of the Earth. Recall that G 7x10' Nm²/kg?. a) Draw and clearly label a free body diagram indicating all of the forces acting on the satellite, from the perspective shown in the diagram. Assume that the spring is stretched, not compressed, compared to its natural length. b) What is the direction and magnitude of the force of gravity on the satellite as viewed in the diagram? c) The satellite maintains its position over the same spot on the Earth's equator, so that its orbital period is T = 1 day = 9x10 s. What is the magnitude of the acceleration a of the satellite?
A satellite of mass Ms = 2x10' kg is attached to a point on the equator of the Earth (MẸ= 6x1024 kg) by a long, ideal spring with spring constant k= 10$ N/m so that it is moving in a circular trajectory of radius r= 7x10' m from the center of the Earth. Recall that G 7x10' Nm²/kg?. a) Draw and clearly label a free body diagram indicating all of the forces acting on the satellite, from the perspective shown in the diagram. Assume that the spring is stretched, not compressed, compared to its natural length. b) What is the direction and magnitude of the force of gravity on the satellite as viewed in the diagram? c) The satellite maintains its position over the same spot on the Earth's equator, so that its orbital period is T = 1 day = 9x10 s. What is the magnitude of the acceleration a of the satellite?
Related questions
Question
PM2: please answer question and explain each step with reasoning
Transcribed Image Text:A satellite of mass Ms = 2x10 kg is attached to a point on the equator of the Earth (ME= 6x10²4 kg) by a long, ideal
spring with spring constant k = 10 N/m so that it is moving in a circular trajectory of radius r = 7x10' m from the
center of the Earth. Recall that G= 7x10-" Nm²/kg?.
a) Draw and clearly label a free body diagram indicating all of the forces acting on the satellite, from the
perspective shown in the diagram. Assume that the spring is stretched, not compressed, compared to its natural
length.
b) What is the direction and magnitude of the force of gravity on the satellite as viewed in the diagram?
c) The satellite maintains its position over the same spot on the Earth's equator, so that its orbital period is T= 1
day = 9x10* s. What is the magnitude of the acceleration a of the satellite?
d) What is the natural length Lnat (unstretched length) of the spring? You may approximate the Earth's radius as RE
= 10' m.
e) How much potential energy is stored in the stretched spring?
f) If the satellite breaks free from the spring, it will then follow
an open orbit. What will the satellite's kinetic energy be
when it has traveled very far from the Earth?
Earth
Ms
Satellite
spring
ME
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
