Newton's Laws - Physics
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Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the Earth? Which accelerates more?
Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the Earth? Which accelerates more?
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.
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.
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An asteroid with a mass of 
approaches the Earth. If they are 
apart, what is the asteroid's resultant acceleration?
An asteroid with a mass of 
The relationship between force and acceleration is Newton's second law:
We know the mass, but we will need to find the force. For this calculation, use the law of universal gravitation:
We are given the value of each mass, the distance (radius), and the gravitational constant. Using these values, we can solve for the force of gravity.
Now that we know the force, we can use this value with the mass of the asteroid to find its acceleration.
The relationship between force and acceleration is Newton's second law:
We know the mass, but we will need to find the force. For this calculation, use the law of universal gravitation:
We are given the value of each mass, the distance (radius), and the gravitational constant. Using these values, we can solve for the force of gravity.
Now that we know the force, we can use this value with the mass of the asteroid to find its acceleration.
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Two asteroids exert a gravitational force on one another. By what factor would this force change if one asteroid doubles in mass, the other asteroid triples in mass, and the distance between them is quadrupled?
Two asteroids exert a gravitational force on one another. By what factor would this force change if one asteroid doubles in mass, the other asteroid triples in mass, and the distance between them is quadrupled?
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.
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.
We can use our first calculation to see the how the force has changed.
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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?
A 
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.
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 
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.
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Two satellites in space, each with a mass of 
, are 
apart from each other. What is the force of gravity between them?
Two satellites in space, each with a mass of 
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.
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.
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An astronaut lands on a planet with the same mass as Earth, but twice the radius. What will be the acceleration due to gravity on this planet, in terms of the acceleration due to gravity on Earth?
An astronaut lands on a planet with the same mass as Earth, but twice the radius. What will be the acceleration due to gravity on this planet, in terms of the acceleration due to gravity on Earth?
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.
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.
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Two satellites are a distance r from each other in space. If one of the satellites has a mass of m and the other has a mass of 2m, which one will have the smaller acceleration?
Two satellites are a distance r from each other in space. If one of the satellites has a mass of m and the other has a mass of 2m, which one will have the smaller acceleration?
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.
The formula for force and acceleration is Newton's 2nd law: 
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:
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 
As you can see, the acceleration for 
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In the International Space Station, which orbits the Earth, astronauts experience apparent weightlessness for what reason?
In the International Space Station, which orbits the Earth, astronauts experience apparent weightlessness for what reason?
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.
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.
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An astronaut lands on a new planet. She knows her own mass, 
, and the radius of the planet, 
. What other value must she know in order to find the mass of the new planet?
An astronaut lands on a new planet. She knows her own mass, 
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.
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.
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Which of these is not an example of Newtonian mechanics?
Which of these is not an example of Newtonian mechanics?
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.
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.
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Which of the following is not a part of Newton's second law?
Which of the following is not a part of Newton's second law?
Newton's 2nd law states 
. Therefore, all we need is a force, a mass, and an acceleration!
Newton's 2nd law states
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A block is pushed with 
newtons of force. What other information do we need in order to find the acceleration of the block?
A block is pushed with
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 states that
If we know the force,
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A 
ball rests on a flat table. What is the normal force exerted on the ball by the table?
A
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.
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.
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A 
orange falls from a tree. What is the force of gravity on the orange?
A
Newton's second law states that:
We are given the mass of the orange and the acceleration; since we are looking at the force due to gravity, the acceleration will be the acceleration due to gravity. Use these given values to calculate the force.
Keep in mind that the force will be negative, since gravity acts in the downward direction.
Newton's second law states that:
We are given the mass of the orange and the acceleration; since we are looking at the force due to gravity, the acceleration will be the acceleration due to gravity. Use these given values to calculate the force.
Keep in mind that the force will be negative, since gravity acts in the downward direction.
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Which of these is necessary for there to be a non-zero net force?
Which of these is necessary for there to be a non-zero net force?
Newton's second law states that force is a mass times an acceleration.
In order for a force to exist, there must be an acceleration applied to a mass. A force cannot exist on a massless object, nor can it exist without a net acceleration.
Newton's third law states that for every force on an object, there is an equal and opposite force from the object. These force frequently cancel out, however, and produce a net force of zero.
Newton's second law states that force is a mass times an acceleration.
In order for a force to exist, there must be an acceleration applied to a mass. A force cannot exist on a massless object, nor can it exist without a net acceleration.
Newton's third law states that for every force on an object, there is an equal and opposite force from the object. These force frequently cancel out, however, and produce a net force of zero.
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A person jumps from the roof of a house 
high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 
. If the mass of his torso (excluding legs) is 
, find the average force exerted on his torso by his legs during deceleration.
A person jumps from the roof of a house 
To solve this problem we need to divide up the situation into two parts. During the first part the person is jumping from the roof of a house and is therefore undergoing freefall and accelerated motion due to the force of gravity. Therefore we will need to use kinematic equations to solve for the final velocity as the person lands. In the second part of the problem, the person decelerates their torso through a specific distance and comes to a stop. We will then need to calculate the acceleration of the torso during this second part to determine the average force applied.
Let us start with kinematics to determine the speed of the torso as it hits the ground.
Knowns
We can use the kinematic equation
This is the velocity of the torso as it hits the ground. We will know use the same equation with new variables to determine the acceleration of the torso as it comes to a stop.
Knowns
Rearrange to get the acceleration by itself
We can now plug this into Newton’s 2nd Law to find the average force acting on the object.
To solve this problem we need to divide up the situation into two parts. During the first part the person is jumping from the roof of a house and is therefore undergoing freefall and accelerated motion due to the force of gravity. Therefore we will need to use kinematic equations to solve for the final velocity as the person lands. In the second part of the problem, the person decelerates their torso through a specific distance and comes to a stop. We will then need to calculate the acceleration of the torso during this second part to determine the average force applied.
Let us start with kinematics to determine the speed of the torso as it hits the ground.
Knowns
We can use the kinematic equation
This is the velocity of the torso as it hits the ground. We will know use the same equation with new variables to determine the acceleration of the torso as it comes to a stop.
Knowns
Rearrange to get the acceleration by itself
We can now plug this into Newton’s 2nd Law to find the average force acting on the object.
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A pair of fuzzy dice is hanging by a cord from your rearview mirror. While you are decelerating at a constant rate from 
to rest in 
, what angle does the string make with the vertical and in what direction (toward or away from the windshield)?
A pair of fuzzy dice is hanging by a cord from your rearview mirror. While you are decelerating at a constant rate from 
When you are slowing down the car, the fuzzy dice want to keep moving forward. Therefore the angle they make will be toward the windshield. The force of tension on the fuzzy dice is what is holding them back with the car, keeping them from going through the windshield. This tension force is comprised of two components. The y-component of the tension is equal to the force of gravity acting on the fuzzy dice. The x-component of the tension is equal to the force of the car slowing down.
The angle of the fuzzy dice is related to these two components through the trigonometric function tangent.
We can then use in the inverse tan function to determine the angle acting on the fuzzy dice.
Notice how the mass of the dice falls out of the equation
We can now plug in our values and solve.
When you are slowing down the car, the fuzzy dice want to keep moving forward. Therefore the angle they make will be toward the windshield. The force of tension on the fuzzy dice is what is holding them back with the car, keeping them from going through the windshield. This tension force is comprised of two components. The y-component of the tension is equal to the force of gravity acting on the fuzzy dice. The x-component of the tension is equal to the force of the car slowing down.
The angle of the fuzzy dice is related to these two components through the trigonometric function tangent.
We can then use in the inverse tan function to determine the angle acting on the fuzzy dice.
Notice how the mass of the dice falls out of the equation
We can now plug in our values and solve.
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Suppose your car was stuck deep in the mud and you wanted to use the method above to pull it out. What force would you have to exert perpendicular to the center of the rope to produce a force of 12,000 N on the car if the angle that the rope is bent from the horizontal is 3 degrees?
Suppose your car was stuck deep in the mud and you wanted to use the method above to pull it out. What force would you have to exert perpendicular to the center of the rope to produce a force of 12,000 N on the car if the angle that the rope is bent from the horizontal is 3 degrees?
To determine this we would first need to determine the vertical component of the 
force acting on the car. To do this we would use the sine trigonometric function.
The pull in the vertical direction must be at least 
to pull the car. However, we also know there is another equal force on the tree on the other side of the pull. Therefore the total pull must be double this value in order to pull both the tree and the car equally.
To determine this we would first need to determine the vertical component of the 
The pull in the vertical direction must be at least 
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A 
ball rests on a flat table. What is the normal force exerted on the ball by the table?
A 
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.
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.
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Two dogs pull on a 
bone in opposite directions. If the first dog pulls with a force of 
to the left and the other pulls with a force of 
in the opposite direction, what will be the acceleration on the bone?
Two dogs pull on a 
First we need to find the net force, which will be equal to the sum of the forces on the bone.
Since the forces are going in opposite directions, we know that one force will be negative (since force is a vector). Conventionally, right is assigned a positive directional value. The force to the left will be negative.
From here we can use Newton's second law to expand the force and solve for the acceleration, using the mass of the bone.
First we need to find the net force, which will be equal to the sum of the forces on the bone.
Since the forces are going in opposite directions, we know that one force will be negative (since force is a vector). Conventionally, right is assigned a positive directional value. The force to the left will be negative.
From here we can use Newton's second law to expand the force and solve for the acceleration, using the mass of the bone.
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