Newton's Laws - High School Physics

The equation for the force of gravity between two objects is:

Using this equation, we can select arbitrary values for our original masses and distance. This will make it easier to solve when these values change.

is the gravitational constant. Now that we have a term for the initial force of gravity, we can use the changes from the question to find how the force changes.

We can use our first calculation to see the how the force has changed.

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 r 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 Fc=m∗ac. 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.

To solve this problem, use Newton's law of universal gravitation:

We are given the constant, as well as the satellite masses and distance (radius). Using these values we can solve for the force.

For this comparison, we can use the law of universal gravitation and Newton's second law:

We know that the force due to gravity on Earth is equal to mg. We can use this to set the two force equations equal to one another.

Notice that the mass cancels out from both sides.

This equation sets up the value of acceleration due to gravity on Earth.

The new planet has a radius equal to twice that of Earth. That means it has a radius of 2r. It has the same mass as Earth, mE. Using these variables, we can set up an equation for the acceleration due to gravity on the new planet.

Expand this equation to compare it to the acceleration of gravity on Earth.

We had previously solved for the gravity on Earth:

We can substitute this into the new acceleration equation:

The acceleration due to gravity on this new planet will be one quarter of what it would be on Earth.

The formula for force and acceleration is Newton's 2nd law: . We know the mass, but first we need to find the force:

For this equation, use the law of universal gravitation:

We know from the first equation that a force is a mass times an acceleration. That means we can rearrange the equation for universal gravitation to look a bit more like that first equation:

can turn into: respectively.

We know that the forces will be equal, so set these two equations equal to each other:

The problem tells us that

Let's say that to simplify.

As you can see, the acceleration for is twice the acceleration for . Therefore the mass 2m will have the smaller acceleration.

Newton’s 3rd law states that for every force there is an equal and opposite force. In other words, the force with which the moon pulls on the Earth is the same force that the Earth pulls on the moon.

Newton’s 2nd law states that the acceleration of an object is directly related to the force applied and inversely related to the mass of the object. Since both the earth and the moon have the same force acting on it, it is their masses that will determine who will accelerate more. Since there is an inverse relationship between the mass and acceleration, the object with the smaller mass will accelerate more. Therefore the moon will accelerate more.

The space station and the astronauts inside are in a constant state of free fall toward the center of the Earth. However, because they have such a high horizontal velocity and because the Earth is curved they will always be falling toward the earth as the Earth curves away from them. IF the space station were to slow down, they would land on the Earth. The high speed in the horizontal direction, keeps them in a parabolic flight path that aligns with the curvature of the Earth.

To find the relationship described in the question, we need to use the law of universal gravitation:

The question suggests that we know the radius and one of the masses, and asks us to solve for the other mass.

Since G is a constant, if we know the mass of the astronaut and the radius of the planet, all we need is the force due to gravity to solve for the mass of the planet. According to Newton's third law, the force of the planet on the astronaut will be equal and opposite to the force of the astronaut on the planet; thus, knowing her force on the planet will allows us to solve the equation.

Newton's first law says that an object in motion will remain in motion in the same direction unless acted upon by an outside force; an object at rest will remain at rest unless acted upon by an outside force.

In the example of the car hitting the wall, the passenger continues travelling at the same speed that the car was moving directly before impact. He does not stop his forward motion until an outside force (his seatbelt) stops him.

In the example of the satellite, the rotation of the satellite can only change rate if an outside force interferes. Because there are no forces to affect the satellite's spinning, it will continue to do so as per Newton's first law.

In the example of the construction worker, the box was at rest and therefore resisted any change to being at rest. Once it is in motion, it will continue in motion in the same direction. This principle is the same reason why static coefficients of friction are generally greater than kinetic coefficients of friction.

In the example of the child on the merry-go-round, the important part of Newton's first law to recall is that objects will remain in motion in the same direction. The rotational motion of the child will result in a constantly changing velocity in the direction tangent to the edge of the ride. Once the child lets go, she will move in a straight line directly off of the ride.

The hammer and nail example illustrates Newton's third law, but has no bearing on the principle of inertia.

This is an example of Newton's first law: an object at rest will remain at rest, and an object in motion will remain in motion in that direction, unless acted upon by an outside force.

Inertia is effectively nature's way of trying to avoid change. This explains why the box is hard to move while it is still; it requires change to get it to move from rest to moving. It is easier to continue motion when it is moving because it requires much less change to keep it moving in the same direction.

Mathematically, this principle dictates that the coefficient of static friction will always be greater than the coefficient of kinetic friction.

While the bus in moving forward, you move forward with the bus at the same velocity.

When the bus stops, your body continue to move forward with the original velocity at which you had been traveling. Since you are not attached to the bus, you will not stop at the same rate as the bus and will fall forward as your body continues to move.

This is the reason why seatbelts are so important as it keeps you fixed to the car so that you undergo the same forces that are acting on the car.

While the truck in moving forward, the carte moves forward with the truck at the same velocity.

When the trucks stops, the crate continues to move forward with the original velocity at which it had been traveling since there is no friction to stop the crate from moving. Since the crate is not attached to the truck, it will not stop at the same rate as the truck and will slide toward the cab of the truck as the truck slows down.

This is the reason why tie-downs are so important as it keeps objects fixed to the truck so that they undergo the same forces that are acting on the truck.

Newton's first law says that an object in motion will remain in motion in the same direction unless acted upon by an outside force; an object at rest will remain at rest unless acted upon by an outside force.

In the example of the car hitting the wall, the passenger continues travelling at the same speed that the car was moving directly before impact. He does not stop his forward motion until an outside force (his seatbelt) stops him.

In the example of the satellite, the rotation of the satellite can only change rate if an outside force interferes. Because there are no forces to affect the satellite's spinning, it will continue to do so as per Newton's first law.

In the example of the construction worker, the box was at rest and therefore resisted any change to being at rest. Once it is in motion, it will continue in motion in the same direction. This principle is the same reason why static coefficients of friction are generally greater than kinetic coefficients of friction.

In the example of the child on the merry-go-round, the important part of Newton's first law to recall is that objects will remain in motion in the same direction. The rotational motion of the child will result in a constantly changing velocity in the direction tangent to the edge of the ride. Once the child lets go, she will move in a straight line directly off of the ride.

The hammer and nail example illustrates Newton's third law, but has no bearing on the principle of inertia.

This is an example of Newton's first law: an object at rest will remain at rest, and an object in motion will remain in motion in that direction, unless acted upon by an outside force.

Inertia is effectively nature's way of trying to avoid change. This explains why the box is hard to move while it is still; it requires change to get it to move from rest to moving. It is easier to continue motion when it is moving because it requires much less change to keep it moving in the same direction.

Mathematically, this principle dictates that the coefficient of static friction will always be greater than the coefficient of kinetic friction.

According to Newton’s First law, an object in motion will remain in motion until there is an external force acting on this. This is observable in the real world as marbles will continue to roll until they are slowed down by friction or stopped by a wall or a person or some other external force.

Newtonian mechanics apply to all objects of substantial mass travelling at significantly slower than the speed of light.

Newton's law of universal gravitation, Newton's second law, momentum, and the equation for mechanical energy all fall under Newtonian mechanics.

The mass-energy equivalence suggests that mass can change as the speed of an object (such as an electron) approaches the speed of light. Newtonian mechanics assume that mass is constant, and do not apply to objects approaching the speed of light.

Newton's 2nd law states . Therefore, all we need is a force, a mass, and an acceleration!

Newton's second law states that .

If we know the force, , then we only need to know the mass, , in order to find acceleration.

Newton's second law allows us to solve for the force of gravity on the ball:

Newton's third law tells us that the force of the ball on the table, due to gravity, will be equal and opposite to the normal force of the table on the ball.

Substitute the equation for force of gravity.

Now we can use the mass of the ball and the acceleration of gravity to solve for the normal force. First, convert the mass to kilograms. Then, use the equation to find the normal force.