Ch 06: Centripetal Forces & GravitationWorksheetSee all chapters
All Chapters
Ch 01: Units & Vectors
Ch 02: 1D Motion (Kinematics)
Ch 03: 2D Motion (Projectile Motion)
Ch 04: Intro to Forces (Dynamics)
Ch 05: Friction, Inclines, Systems
Ch 06: Centripetal Forces & Gravitation
Ch 07: Work & Energy
Ch 08: Conservation of Energy
Ch 09: Momentum & Impulse
Ch 10: Rotational Kinematics
Ch 11: Rotational Inertia & Energy
Ch 12: Torque & Rotational Dynamics
Ch 13: Rotational Equilibrium
Ch 14: Angular Momentum
Ch 15: Periodic Motion (NEW)
Ch 15: Periodic Motion (Oscillations)
Ch 16: Waves & Sound
Ch 17: Fluid Mechanics
Ch 18: Heat and Temperature
Ch 19: Kinetic Theory of Ideal Gasses
Ch 20: The First Law of Thermodynamics
Ch 21: The Second Law of Thermodynamics
Ch 22: Electric Force & Field; Gauss' Law
Ch 23: Electric Potential
Ch 24: Capacitors & Dielectrics
Ch 25: Resistors & DC Circuits
Ch 26: Magnetic Fields and Forces
Ch 27: Sources of Magnetic Field
Ch 28: Induction and Inductance
Ch 29: Alternating Current
Ch 30: Electromagnetic Waves
Ch 31: Geometric Optics
Ch 32: Wave Optics
Ch 34: Special Relativity
Ch 35: Particle-Wave Duality
Ch 36: Atomic Structure
Ch 37: Nuclear Physics
Ch 38: Quantum Mechanics

Concept #1: Universal Law of Gravitation

Practice: (a) How hard does the Earth (5.98 x 1024 kg) pull on the Moon (7.35 x 1022 kg) if they are 3.85 x 108 m apart? (b) How hard does the Sun (1.99 x 1030 kg) pull on the Moon if they are 1.50 x 1011 m apart?

Practice: Calculate the net force acting on the Moon when it is aligned with the Sun and the Earth, as shown below. Use the values given and forces found in EXAMPLE 1 (above). 

EXTRA: What acceleration (magnitude and direction) does the Moon have as a result of this net force?

Example #1: Gravitational Force

Additional Problems
Which of the following is true about the gravitational force? a. The closer two object get, the larger the force gets but the smaller the speed gets b. The closer two objects get, the smaller the force gets but the larger the acceleration gets c. The further two objects get, the smaller the force gets and the smaller the acceleration gets d. The further two objects get, the larger the force gets and the larger the speed gets
A 15 kg mass lies at rest on a table with a coefficient of static friction of 0.4. If you were to place a second mass 5 cm away from the first, what would that mass have to be to cause the 15 kg mass to move towards it?
Let there be two planets X and Y with masses M X and MY . The radius of planet X is twice that of planet Y. If an object weighs 4 times as much on the surface of planet X as it does on the surface of planet Y, then MX/MY is given byA. 1/8 B. 16 C. 1/4 D. 8 E. 1 F. 1/16 G. 1/2 H. 2 I. 4
Consider the six equally-spaced objects shown in the diagram below. The points A, B, C and D represent locations in empty space and the large circles represent planets with masses m and 2m.  1. At which location(s) would the magnitude of the net gravitational force on an object be a maximum? 2. At which location(s) would the magnitude of the net gravitational force on an object be a minimum? Separate your answers by a semicolon. 1. A and D; B and C 2. C; A 3. B and C; A 4. B; D 5. D; B 6. A; C 7. B and C; A and D 8. B; A and D 9. A; B and C 10. D; B and C  
What is the difference in the force of gravity on a 1.0-kg mass at the bottom of the deepest ocean trench and that at the top of the highest mountain? Assume that g = 9.8 m/s2 at sea level. The radius of Earth at sea level is 6.37 × 106 m. The deepest trench is the Marianas Trench, south of Guam, which has a depth d = 1.103 × 104 m below sea level. The highest mountain is Everest in Nepal, which has a height of h = 8.847 × 103 m above sea level. The difference is A. 0.0062 N B. 0.061 N C. 0.034 N D. 0.0067 N E. 0.027 N
A certain object weighs 22.2 N on the surface of Earth. If the radius of the moon is 0.276 times the radius of Earth and the mass of the moon is 0.0123 times the mass of Earth, the object's weight on the surface of the moon is approximately A. 9.79 N B. 133 N C. 3.58 N D. 22.2 N E. 0.365 N
One day a human being will land on Mars. Mars has a diameter of 6786 km and a mass of 6.42×1023 kg. If you weighed 834 N on Earth, how much would you weigh on Mars? A. 1270 N B. 316 N C. 224 N D. 834 N E. None of the above
A 15 kg mass and a 7 kg mass are separated by 10 cm. Where should you place a 4 kg mass in between the two masses so that the net gravitational force on it is zero?
If you have a mass of 60 kg, answer the following questions:a. What is your weight on Earth?b. What is your mass on the Moon?c. What is your weight on the Moon? Note that the mass of the moon is 7.34 x 10  22 kg and the radius is 1.74 x 103 km. 
Two masses, separated by a distance d, experience a gravitational force F. In order to drop the force to F/3, the distance has to be changed toa) d√(3)b) 3dc) d / 3d) d / √(3)