Table of contents

0. Math Review31m
- Math Review
  31m
1. Intro to Physics Units1h 29m
2. 1D Motion / Kinematics3h 56m
3. Vectors2h 43m
4. 2D Kinematics1h 42m
5. Projectile Motion3h 6m
6. Intro to Forces (Dynamics)3h 22m
7. Friction, Inclines, Systems2h 44m
8. Centripetal Forces & Gravitation7h 26m
9. Work & Energy1h 59m
10. Conservation of Energy2h 54m
11. Momentum & Impulse3h 40m
12. Rotational Kinematics2h 59m
13. Rotational Inertia & Energy7h 4m
14. Torque & Rotational Dynamics2h 5m
15. Rotational Equilibrium3h 39m
16. Angular Momentum3h 6m
17. Periodic Motion2h 9m
18. Waves & Sound3h 40m
19. Fluid Mechanics4h 27m
20. Heat and Temperature3h 7m
21. Kinetic Theory of Ideal Gases1h 50m
22. The First Law of Thermodynamics1h 26m
23. The Second Law of Thermodynamics3h 11m
24. Electric Force & Field; Gauss' Law3h 42m
25. Electric Potential1h 51m
26. Capacitors & Dielectrics2h 2m
27. Resistors & DC Circuits3h 8m
28. Magnetic Fields and Forces2h 23m
29. Sources of Magnetic Field2h 30m
30. Induction and Inductance3h 38m
31. Alternating Current2h 37m
32. Electromagnetic Waves2h 14m
33. Geometric Optics2h 57m
34. Wave Optics1h 15m
35. Special Relativity2h 10m

8. Centripetal Forces & Gravitation

Energy of Circular Orbits

Physics

8. Centripetal Forces & Gravitation

Energy of Circular Orbits

Previous problemNext problem

Struggling with Physics?

Join thousands of students who trust us to help them ace their exams!Watch the first video

Multiple Choice

a) How much work do you have to do on a 100-kg payload to move it from Earth's surface to a height of 1000 km?
b) How much additional work must you do to put this payload into orbit at this altitude?

(a) $W_{AB}=3.37\times10^8$ J;

(b) $W_{B C} = 1.99 \times 1 0^{9}$ J

(a) $W_{AB}=8.48\times10^8$ J;

(b) $W_{B C} = 2.7 \times 1 0^{9}$ J

(a) $W_{AB}=3.37\times10^8$ J;

(b) $W_{B C} = 5.97 \times 1 0^{9}$ J

(a) $W_{AB}=8.48\times10^8$ J;

(b) $W_{BC}=8.1\times10^9$ J

Previous problemNext problem

Verified step by step guidance

Step 1: Understand the problem. We need to calculate the work done to move a 100-kg payload from Earth's surface to a height of 1000 km and then the additional work to put it into orbit at that altitude.

Step 2: Use the formula for gravitational potential energy change, which is given by ΔU = U_final - U_initial = -G * (M_earth * m) * (1/r_final - 1/r_initial), where G is the gravitational constant, M_earth is the mass of the Earth, m is the mass of the payload, r_initial is the initial distance from the center of the Earth, and r_final is the final distance from the center of the Earth.

Step 3: Calculate the initial and final distances from the center of the Earth. The initial distance (r_initial) is the radius of the Earth, approximately 6371 km. The final distance (r_final) is the radius of the Earth plus the altitude, which is 6371 km + 1000 km.

Step 4: Substitute the known values into the gravitational potential energy change formula to find the work done to move the payload to the height of 1000 km.

Step 5: To find the additional work to put the payload into orbit, calculate the kinetic energy required for orbit using the formula KE = 0.5 * m * v^2, where v is the orbital velocity. The orbital velocity can be found using v = sqrt(G * M_earth / r_final). The additional work is the kinetic energy required minus any initial kinetic energy (if applicable).