All High School Physics Resources
Example Questions
Example Question #51 : Specific Forces
A satellite orbits above the Earth. What is the tangential velocity of the satellite?
To solve this problem, first recognize that the force due to gravity of the Earth on the satellite is the same as the centripetal force acting on the satellite. That means .
Solve for for the satellite. To do this, use the law of universal gravitation.
Remember that is the distance between the centers of the two objects. That means it will be equal to the radius of the earth PLUS the orbiting distance.
Use the given values for the masses of the objects and distance to solve for the force of gravity.
Now that we know the force, we can find the acceleration. Remember that centripetal force is . Set our two forces equal and solve for the centripetal acceleration.
Now we can find the tangential velocity, using the equation for centripetal acceleration. Again, remember that the radius is equal to the sum of the radius of the Earth and the height of the satellite!
Example Question #63 : Forces
A satellite of mass orbits above the Earth. If the force due to gravity of the Earth on the satellite is , what is the mass of the satellite?
To solve this problem, use the law of universal gravitation.
Remember that is the distance between the centers of the two objects. That means it will be equal to the radius of the earth PLUS the orbiting distance.
Use the given values for the mass of the Earth, force of gravity, and distance to solve for the mass of the satellite.
Example Question #67 : Forces
A satellite of mass orbits above the Earth. It malfunctions and half of the satellite breaks off, leaving the satellite with only half the original mass. What is the resulting force due to gravity on the satellite in terms of , the original force due to gravity when the satellite was whole?
To solve this problem, we need to set up the law of universal gravitation.
When the satellite was whole:
After the satellite breaks:
We can now compare these two equations. Start by expanding the second equation.
We can substitute our first equation into the second.
and
This tells us that the final force of gravity is equal to one half the original force of gravity.
Example Question #32 : Universal Gravitation
A satellite orbits above the Earth. The satellite runs into another stationary satellite of equal mass and the two stick together. What is their resulting velocity?
We can use the conservation of momentum to solve. Since the satellites stick together, there is only one final velocity term.
We know the masses for both satellites are equal, and the second satellite is initially stationary.
Now we need to find the velocity of the first satellite. Since the satellite is in orbit (circular motion), we need to find the tangential velocity. We can do this by finding the centripetal acceleration from the centripetal force.
Recognize that the force due to gravity of the Earth on the satellite is the same as the centripetal force acting on the satellite. That means .
Solve for for the satellite. To do this, use the law of universal gravitation.
Remember that is the distance between the centers of the two objects. That means it will be equal to the radius of the earth PLUS the orbiting distance.
Use the given values for the masses of the objects and distance to solve for the force of gravity.
Now that we know the force, we can find the acceleration. Remember that centripetal force is . Set our two forces equal and solve for the centripetal acceleration.
Now we can find the tangential velocity, using the equation for centripetal acceleration. Again, remember that the radius is equal to the sum of the radius of the Earth and the height of the satellite!
This value is the tangential velocity, or the initial velocity of the first satellite. We can plug this into the equation for conversation of momentum to solve for the final velocity of the two satellites.
Example Question #33 : Universal Gravitation
A satellite orbits above the Earth. What is the period of the satellite's orbit?
The period describes how long it takes the satellite to make one full orbit. If you go back to the definition of velocity, , we can apply that to our new circular orbit, in which the distance is equal to the circumference of the circle and the time is equal to the period: . The circumference divided by the period will give us the average velocity.
The problem gives us the radius, but we need to find the tangential velocity. We can do this by first solving for the centripetal acceleration from the centripetal force.
Recognize that the force due to gravity of the Earth on the satellite is the same as the centripetal force acting on the satellite. That means .
Solve for for the satellite. To do this, use the law of universal gravitation.
Remember that is the distance between the centers of the two objects. That means it will be equal to the radius of the earth PLUS the orbiting distance.
Use the given values for the masses of the objects and distance to solve for the force of gravity.
Now that we know the force, we can find the acceleration. Remember that centripetal force is . Set our two forces equal and solve for the centripetal acceleration.
Now we can find the tangential velocity, using the equation for centripetal acceleration. Again, remember that the radius is equal to the sum of the radius of the Earth and the height of the satellite!
We now have a value for the tangential velocity, which we can use in the equation for velocity from the beginning to find the period.
Example Question #34 : Universal Gravitation
Two planets are apart. If the first planet has a mass of and the second has a mass of , what is the gravitational force between them?
To solve, use Newton's law of universal gravitation:
We are given the values for the mass of each planet, as well as the distance (radius) between them. Using these values and the gravitational constant, we can solve for the force of gravity.
Example Question #31 : Understanding Universal Gravitation
Two planets are apart. If the first planet has a mass of and the second has a mass of , what is the acceleration on the smaller planet?
Remember that Newton's second law states that . The force acting upon the planet in question will be the force due to gravity. Once we find that, we can find the acceleration.
To solve for the force, use Newton's law of universal gravitation:
We are given the values for the mass of each planet, as well as the distance (radius) between them. Using these values and the gravitational constant, we can solve for the force of gravity.
Now that we know the force of gravity, we can use Newton's second law and the mass of the smaller planet to solve for the acceleration of gravity.Example Question #75 : Forces
Two planets are apart. If the first planet has a mass of and the second has a mass of , what is the acceleration on the larger planet?
Remember that Newton's second law states that . The force acting upon the planet in question will be the force due to gravity. Once we find that, we can find the acceleration.
To solve for the force, use Newton's law of universal gravitation:
We are given the values for the mass of each planet, as well as the distance (radius) between them. Using these values and the gravitational constant, we can solve for the force of gravity.
Now that we know the force of gravity, we can use Newton's second law and the mass of the larger planet to solve for the acceleration of gravity.Example Question #642 : Newtonian Mechanics
An astronaut has a mass of . He travels to a new planet and observes his weight is on this planet's surface. If the radius of the planet is , what is the mass of the planet?
To solve, use Newton's law of universal gravitation:
Remember that the weight of the astronaut is the same as the gravitational force acting between the planet and the astronaut.
We are given the gravitational constant, the radius of the planet, the mass of the astronaut, and the magnitude of the force generated. Using these values in the universal gravitation equation, we can solve for the mass of the planet.
Example Question #4 : Universal Gravitation
Two satellites in space, each with equal mass, are apart from each other. If the force of gravity between them is , what is the mass of each satellite?
To solve this problem, use Newton's law of universal gravitation:
We are given the value of the force, the distance (radius), and the gravitational constant. We are also told that the masses of the two satellites are equal. Since the masses are equal, we can reduce the numerator of the law of gravitation to a single variable.
Now we can use our give values to solve for the mass.
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