Understanding Newton's Second Law - Physics
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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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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 F resultant=ma resultant, 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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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 forces 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 forces frequently cancel out, however, and produce a net force of zero.
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If you push a 
mass with the same force that you push a 
mass from rest.
If you push a 
Newton's second law states that force is a mass times an acceleration.
Since both masses have the same force acting on it, we can look at the relationship between mass and acceleration. These two things are inversely proportional to one another. As one increases, the other decreases. Therefore the larger mass will have a smaller acceleration. The smaller mass will have a larger acceleration.
Suppose that the force acting on both objects is 
. We can confirm this by solving for the acceleration.
The smaller mass will accelerate 6 times faster than the smaller mass.
Newton's second law states that force is a mass times an acceleration.
Since both masses have the same force acting on it, we can look at the relationship between mass and acceleration. These two things are inversely proportional to one another. As one increases, the other decreases. Therefore the larger mass will have a smaller acceleration. The smaller mass will have a larger acceleration.
Suppose that the force acting on both objects is 
The smaller mass will accelerate 6 times faster than the smaller mass.
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A net force 
acts on a mass 
and produces an acceleration 
. What is the new acceleration if the force is doubled and the mass is quadrupled.
A net force 
Newton's second law states that force is a mass times an acceleration.
Assuming that all the original values were equal to 
We can substitute in new values for a doubled force and quadrupled mass to find the new acceleration.
This shows that the new acceleration will be 
of the original value or equal to a/2.
Newton's second law states that force is a mass times an acceleration.
Assuming that all the original values were equal to
We can substitute in new values for a doubled force and quadrupled mass to find the new acceleration.
This shows that the new acceleration will be 
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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.
Compare your answer with the correct one above
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,
Compare your answer with the correct one above
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.
Compare your answer with the correct one above
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.
Compare your answer with the correct one above