Net Force - High School Physics
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Jerry pushes a 
box with 
of force. What is the resultant acceleration?
Jerry pushes a
Newton's second law states that 
.
In this problem, 
and 
.
Plug these into the equation to solve for acceleration.
Newton's second law states that
In this problem,
Plug these into the equation to solve for acceleration.
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A 
ball rolls forward with a net acceleration of 
. What is the net force on the ball?
A
Newton's second law states that 
.
Plug in the values given to us and solve for the force.
Newton's second law states that
Plug in the values given to us and solve for the force.
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Louisa rolls a ball with 
of force. She observes that it has a constant linear acceleration of 
. What is the mass of the ball?
Louisa rolls a ball with
Newton's second law states that 
.
Plug in the given values to solve for the mass.
Newton's second law states that
Plug in the given values to solve for the mass.
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Derek pushes a 
crate along a rough surface with 
of force. He observes that it is only accelerating at a rate of 
. What must the value of the force of friction be?
(Assume the only two forces acting on the object are friction and Derek).
Derek pushes a
(Assume the only two forces acting on the object are friction and Derek).
Newton's second law states that 
.
If Derek is pushing with 
of force, then we should be able to solve for the acceleration of the 
crate.
Derek observes that the crate is acceleration at a rate of 
, rather than the expected 
. An outside force is acting upon it to slow the acceleration.
The equation for the net force on the object is: 
. We also know, from Newton's second law, that 
, where the resultant force and acceleration are the values actually observed.
Plug in the information we've been given so far to find the force of friction.
Subtract 
from both sides to find the force of friction.
Friction will be negative because it acts in the direction opposite to the force of Derek.
Newton's second law states that
If Derek is pushing with
Derek observes that the crate is acceleration at a rate of
The equation for the net force on the object is:
Plug in the information we've been given so far to find the force of friction.
Subtract
Friction will be negative because it acts in the direction opposite to the force of Derek.
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A hammer exerts a 
force on a nail. What is the force the nail exerts on the hammer?
A hammer exerts a
Newton's third law states that when one object exerts a force on a second object, the second object exerts a force equal in size, but opposite in direction to the first. That means that the force of the hammer on the nail and the nail on the hammer will be equal in size, but opposite in direction.
Since the hammer exerts 
of force on the nail, the nail must exert 
of force on the hammer.
Newton's third law states that when one object exerts a force on a second object, the second object exerts a force equal in size, but opposite in direction to the first. That means that the force of the hammer on the nail and the nail on the hammer will be equal in size, but opposite in direction.
Since the hammer exerts
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Michael pushes a 
box with 
of force to the left. Annie pushes the same box with 
of force to the right. What is the net force on the box?
Michael pushes a
For the net force, we add up all the forces: 
.
Since force is a vector, the direction of the action matters. We will make leftward motion negative and rightward motion positive. Michael is pushing with 
to the left, making his force equal to 
. Annie was pushing with 
to the right, so her force will remain 
.
We can find the net force by adding the individual force together.
For the net force, we add up all the forces:
Since force is a vector, the direction of the action matters. We will make leftward motion negative and rightward motion positive. Michael is pushing with
We can find the net force by adding the individual force together.
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Franklin lifts a 
weight vertically. If he lifts it so that way the velocity of the weight is constant, how much force is he using?
Franklin lifts a
If the object has a constant velocity, that means that the net acceleration must be zero.
In conjunction with Newton's second law, we can see that the net force is also zero. If there is no net acceleration, then there is no net force.
Since Franklin is lifting the weight vertically, that means there will be two force acting upon the weight: his lifting force and gravity. The net force will be equal to the sum of the forces acting on the weight.
Since we just proved that the net force will equal zero, we can say 
.
We know the mass of the weight and we know the acceleration, so we can solve for the lifting force.
If the object has a constant velocity, that means that the net acceleration must be zero.
In conjunction with Newton's second law, we can see that the net force is also zero. If there is no net acceleration, then there is no net force.
Since Franklin is lifting the weight vertically, that means there will be two force acting upon the weight: his lifting force and gravity. The net force will be equal to the sum of the forces acting on the weight.
Since we just proved that the net force will equal zero, we can say
We know the mass of the weight and we know the acceleration, so we can solve for the lifting force.
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A 
box starts at rest and reaches a velocity of 
after traveling a distance 
. What was the force on the box?
A
The formula for force is 
.
We are given the mass, but we will need to calculate the acceleration to use in the formula.
We know the initial velocity (zero because the box starts from rest), final velocity, and distance traveled. Using these values, we can find the acceleration using the formula 
.
Plug in our given values and solve for acceleration.
Divide both sides by 
.
Now we know both the acceleration and the mass, allowing us to solve for the force.
The formula for force is
We are given the mass, but we will need to calculate the acceleration to use in the formula.
We know the initial velocity (zero because the box starts from rest), final velocity, and distance traveled. Using these values, we can find the acceleration using the formula
Plug in our given values and solve for acceleration.
Divide both sides by
Now we know both the acceleration and the mass, allowing us to solve for the force.
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An airplane has a mass of 
. What is the minimum necessary lift force to get the airplane off the ground?
An airplane has a mass of
In this problem there will be two forces acting upon the airplane: the weight of the plane (force of gravity) and the lifting force. Since we are looking for the minimum force to lift the plane, we can set the two forces equal to each other: 
.
We can calculate the gravitational force using the mass.
Returning to the original equation, we see that the lifting force must be 
.
In this problem there will be two forces acting upon the airplane: the weight of the plane (force of gravity) and the lifting force. Since we are looking for the minimum force to lift the plane, we can set the two forces equal to each other:
We can calculate the gravitational force using the mass.
Returning to the original equation, we see that the lifting force must be
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A dog bites down on a chew toy with 
of force. What is the force of the chew toy on the dog?
A dog bites down on a chew toy with
Use Newton's third law to solve this question. The force of the dog on the chew toy is equal in magnitude, but opposite of direction, to the force of the chew toy acting on the dog.
That means that 
.
Using our given values for find the force of the chew toy.
Use Newton's third law to solve this question. The force of the dog on the chew toy is equal in magnitude, but opposite of direction, to the force of the chew toy acting on the dog.
That means that
Using our given values for find the force of the chew toy.
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If the mass of the object is 
and 
, what is the normal force on the object?
If the mass of the object is
The normal force is always perpendicular to the surface upon which the object is moving, and is pointed away from said surface. That means we are looking for the value for Z in the diagram.
Observe that Z and Y are equal, but opposite forces.
If we can solve for Y, then we can find Z.
We can use our understanding of trigonometry to find an equation for Y.
If we plug in 
for the angle, we see:
Since we are solving for Y, we can multiply both sides by W.
Now that we know an equation for Y, we can return to our original equation to solve for Z.
From here, we can use Newton's second law to find the value of W, the total force of gravity.
Substitute this into our equation for Z.
Now we can solve for Z using the values given in the question for the angle, mass, and gravity.
The normal force is always perpendicular to the surface upon which the object is moving, and is pointed away from said surface. That means we are looking for the value for Z in the diagram.
Observe that Z and Y are equal, but opposite forces.
If we can solve for Y, then we can find Z.
We can use our understanding of trigonometry to find an equation for Y.
If we plug in
Since we are solving for Y, we can multiply both sides by W.
Now that we know an equation for Y, we can return to our original equation to solve for Z.
From here, we can use Newton's second law to find the value of W, the total force of gravity.
Substitute this into our equation for Z.
Now we can solve for Z using the values given in the question for the angle, mass, and gravity.
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If the mass of the object is 
and 
, what is the normal force on the object?
If the mass of the object is
The normal force is always perpendicular to the surface upon which the object is moving, and is pointed away from said surface. That means we are looking for the value for Z in the diagram.
Observe that Z and Y are equal, but opposite forces.
If we can solve for Y, then we can find Z.
We can use our understanding of trigonometry to find an equation for Y.
If we plug in 
for the angle, we see:
Since we are solving for Y, we can multiply both sides by W.
Now that we know an equation for Y, we can return to our original equation to solve for Z.
From here, we can use Newton's second law to find the value of W, the total force of gravity.
Substitute this into our equation for Z.
Now we can solve for Z using the values given in the question for the angle, mass, and gravity.
The normal force is always perpendicular to the surface upon which the object is moving, and is pointed away from said surface. That means we are looking for the value for Z in the diagram.
Observe that Z and Y are equal, but opposite forces.
If we can solve for Y, then we can find Z.
We can use our understanding of trigonometry to find an equation for Y.
If we plug in
Since we are solving for Y, we can multiply both sides by W.
Now that we know an equation for Y, we can return to our original equation to solve for Z.
From here, we can use Newton's second law to find the value of W, the total force of gravity.
Substitute this into our equation for Z.
Now we can solve for Z using the values given in the question for the angle, mass, and gravity.
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How much force is required to acclerate a 
crate at 
?
How much force is required to acclerate a
The formula for force is 
. Plug in our given values and solve:
The formula for force is
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Miguel pushes a box with 
of force to the left. His sister Alexis pushes with 
of force to the right. What is the net force on the box?
Miguel pushes a box with
We need to look at the net force, which is the sum of the other forces:
Since Alexis and Miguel are pushing with the same value but in opposite directions, make one of these forces negative:
Therefore, the net force upon the object is 
.
We need to look at the net force, which is the sum of the other forces:
Since Alexis and Miguel are pushing with the same value but in opposite directions, make one of these forces negative:
Therefore, the net force upon the object is
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The force acting upon a crate is 
. If the mass of the crate is 
, what is the acceleration?
The force acting upon a crate is
For this problem use Newton's second law:
We are given the total force and the mass, allowing us to solve for the acceleration.
For this problem use Newton's second law:
We are given the total force and the mass, allowing us to solve for the acceleration.
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Two dogs pull on a bone. One pulls with 
of force to the right and one pulls with 
of force to the left. What is the net force on the bone?
Two dogs pull on a bone. One pulls with
Force is a vector quantity, meaning that both magnitude and direction are important factors. Net force is calculated by summing all of the forces acting on an object.
For this question, we will assign "to the right" as the positive direction and "to the left" as the negative direction. Under these conditions, we can add the given forces to find the net force.
This means that it has a net force of 
to the left.
Force is a vector quantity, meaning that both magnitude and direction are important factors. Net force is calculated by summing all of the forces acting on an object.
For this question, we will assign "to the right" as the positive direction and "to the left" as the negative direction. Under these conditions, we can add the given forces to find the net force.
This means that it has a net force of
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Which of the following represents the force due to gravity?
Which of the following represents the force due to gravity?
Remember, in a force diagram, forces come from the center of the object. The force of gravity will always be straight down from the center of the object.
In this diagram, W is pointed directly downward.
Remember, in a force diagram, forces come from the center of the object. The force of gravity will always be straight down from the center of the object.
In this diagram, W is pointed directly downward.
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Which of the following represents the force due to friction?
Which of the following represents the force due to friction?
The force due to friction will always be parallel to the surface upon which the object is traveling. It will come directly from the center of the object, and be pointed in the opposite direction to the motion of the object.
In this diagram, V is pointed parallel to the surface and opposite to the direction of motion.
The force due to friction will always be parallel to the surface upon which the object is traveling. It will come directly from the center of the object, and be pointed in the opposite direction to the motion of the object.
In this diagram, V is pointed parallel to the surface and opposite to the direction of motion.
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What is the value of angle 
within the triangle made by X, W, and Y?
What is the value of angle
When working in an inclined plane, when we break our force due to gravity into components, the angle at the top that triangle will be equal to the angle of the inclined plane.
In the diagram, the total force due to gravity is given by W. X represents the horizontal component, and is parallel to the surface of the plane. Y represents the vertical component, and is perpendicular to the surface of the plane. X and Y thus create a right angle, with W as the hypotenuse. By turning this triangle such that the right angle aligns with the right angle of the inclined plane (between Q and P), we can see that W aligns with the incline surface and Y aligns with the base, P. Based on these alignments, the angle between W and Y must be equal to the angle between the surface and P; thus, 
.
When working in an inclined plane, when we break our force due to gravity into components, the angle at the top that triangle will be equal to the angle of the inclined plane.
In the diagram, the total force due to gravity is given by W. X represents the horizontal component, and is parallel to the surface of the plane. Y represents the vertical component, and is perpendicular to the surface of the plane. X and Y thus create a right angle, with W as the hypotenuse. By turning this triangle such that the right angle aligns with the right angle of the inclined plane (between Q and P), we can see that W aligns with the incline surface and Y aligns with the base, P. Based on these alignments, the angle between W and Y must be equal to the angle between the surface and P; thus,
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Which of the following represents the normal force?
Which of the following represents the normal force?
The normal force is always perpendicular to the surface on which the object is placed, and is pointed away from said surface.
In this diagram, Z is the only force that is perpendicular to the surface and in the upward direction. This force must counteract the vertical force of gravity, which will be perpendicular to the surface in the downward direction (Y).
The normal force is always perpendicular to the surface on which the object is placed, and is pointed away from said surface.
In this diagram, Z is the only force that is perpendicular to the surface and in the upward direction. This force must counteract the vertical force of gravity, which will be perpendicular to the surface in the downward direction (Y).
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