Understanding the Relationship Between Force and Acceleration - High School Physics
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Two children standing on a frictionless surface push off of each other with 
of force. If one child has twice the mass of the other child, what is the ratio of the lighter child to the heavier child?
Two children standing on a frictionless surface push off of each other with
First, realize that the force that the lighter child exerts on heavier child is equal and opposite to the force the heavier child exerts on the lighter child, as per Newton's third law.
Using Newton's second law, we can re-write this equation.
The question tells us that 
, making 
the heavier child and 
the lighter child. We can use this in our equation as well.
We are looking for the ratio of 
to 
, so we need to rearrange the equation.
First, the masses cancel out.
Then, divide both sides by 
.
The ratio of 
to 
is 
.
First, realize that the force that the lighter child exerts on heavier child is equal and opposite to the force the heavier child exerts on the lighter child, as per Newton's third law.
Using Newton's second law, we can re-write this equation.
The question tells us that
We are looking for the ratio of
First, the masses cancel out.
Then, divide both sides by
The ratio of
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A 
crate slides along a frictionless surface. If it maintains a constant velocity of 
, what is the net force on the object?
A
Newton's second law states that 
. We know the mass, but we need to calculate the acceleration.
Acceleration is the change in velocity per unit time.
Since the velocity does not change from one moment to the next, then there must be no net acceleration on the object.
Returning to Newton's second law, we can see that if there is no acceleration, then there is no net force.
Newton's second law states that
Acceleration is the change in velocity per unit time.
Since the velocity does not change from one moment to the next, then there must be no net acceleration on the object.
Returning to Newton's second law, we can see that if there is no acceleration, then there is no net force.
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A 
crate slides along the floor with a constant velocity. What is the net force on the crate?
A
The relationship between force and acceleration is 
.
Since the crate has a constant velocity, it has no acceleration.
If there is zero acceleration, that means there is no net force on the object, or 
.
The relationship between force and acceleration is
Since the crate has a constant velocity, it has no acceleration.
If there is zero acceleration, that means there is no net force on the object, or
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The same force is applied to two different objects. One object has a mass of 
, and the other has a mass of 
. Which one has the greater acceleration?
The same force is applied to two different objects. One object has a mass of
The equation for a force is:
We can write this equation in terms of each object:
We know that the force applied to each object will be equal, so we can set these equations equal to each other.
We know that the second object is twice the mass of the first.
We can cancel out the mass from each side, leaving a relationship between the two accelerations.
The acceleration on the first mass is twice the acceleration on the second; thus, the acceleration of the lighter mass is greater.
The equation for a force is:
We can write this equation in terms of each object:
We know that the force applied to each object will be equal, so we can set these equations equal to each other.
We know that the second object is twice the mass of the first.
We can cancel out the mass from each side, leaving a relationship between the two accelerations.
The acceleration on the first mass is twice the acceleration on the second; thus, the acceleration of the lighter mass is greater.
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A car rounds a perfectly circular turn at a constant speed. This causes the acceleration to __________.
A car rounds a perfectly circular turn at a constant speed. This causes the acceleration to __________.
Acceleration results from a change in velocity. Despite the speed remaining constant, velocity is a vector quantity and will change if the car changes direction. In rounding the turn, there is a change in the direction of the velocity, but not in the magnitude. This change in direction causes a non-zero acceleration.
The acceleration will remain equal to the equation for centripetal acceleration:
As long as the magnitude of the velocity and the radius of the turn do not change, the acceleration will remain constant.
Acceleration results from a change in velocity. Despite the speed remaining constant, velocity is a vector quantity and will change if the car changes direction. In rounding the turn, there is a change in the direction of the velocity, but not in the magnitude. This change in direction causes a non-zero acceleration.
The acceleration will remain equal to the equation for centripetal acceleration:
As long as the magnitude of the velocity and the radius of the turn do not change, the acceleration will remain constant.
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A ball begins to roll with a velocity of 
. If no outside forces act upon it, what will be its velocity in 
?
A ball begins to roll with a velocity of
If there are no forces acting upon the object, then there is no acceleration. If there is no acceleration, then the object will move with a constant velocity.
Mathematically, we can look at Newton's second law and the formula for acceleration.
We know that the force is zero.
Since we know that the mass cannot be zero, the acceleration must be zero.
We can now use the formula for acceleration to see the effects on velocity.
We know that the acceleration is zero and that the time is ten seconds.
In order for this to be true, the initial and final velocities must be equal.
If there are no forces acting upon the object, then there is no acceleration. If there is no acceleration, then the object will move with a constant velocity.
Mathematically, we can look at Newton's second law and the formula for acceleration.
We know that the force is zero.
Since we know that the mass cannot be zero, the acceleration must be zero.
We can now use the formula for acceleration to see the effects on velocity.
We know that the acceleration is zero and that the time is ten seconds.
In order for this to be true, the initial and final velocities must be equal.
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Lance pushes a crate of mass 
with 
newtons of force. What is the resultant acceleration?
Lance pushes a crate of mass
The formula for force is Newton's second law:
We are told in the question to use 
for the mass and 
for the force.
Now we can isolate the acceleration.
This also makes sense from a units perspective. Units for force are Newtons, which can be written as:
In our equation, we can see that Newtons are divided by mass:
This would result in the units for acceleration.
The formula for force is Newton's second law:
We are told in the question to use
Now we can isolate the acceleration.
This also makes sense from a units perspective. Units for force are Newtons, which can be written as:
In our equation, we can see that Newtons are divided by mass:
This would result in the units for acceleration.
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Two dogs are pulling on a bone in opposite directions. If the bone does not move, what conclusions can be drawn?
Two dogs are pulling on a bone in opposite directions. If the bone does not move, what conclusions can be drawn?
If the bone does not move, then we know that the resultant acceleration on it is zero. That means that the net force must also equal zero.
In other words, the sum of the two forces acting on the bone must be zero.
Since the forces are pulling in opposite directions, one force must be in the negative direction.
From here, it's simple manipulation to see that the forces are equal.
The forces are equal in size, but going in opposite directions.
If the bone does not move, then we know that the resultant acceleration on it is zero. That means that the net force must also equal zero.
In other words, the sum of the two forces acting on the bone must be zero.
Since the forces are pulling in opposite directions, one force must be in the negative direction.
From here, it's simple manipulation to see that the forces are equal.
The forces are equal in size, but going in opposite directions.
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How much force is required to move a 
filing cabinet 
?
How much force is required to move a
There is insufficient information to solve. Force is the product of mass and acceleration. While we are given the mass, we are not given an acceleration.
If we assume that we are looking for the minimum force required to move the cabinet, then the force would be equal to the force of friction.
Substitute the equations for frictional force and Newton's second law.
Normal force is equal to the force of gravity.
The masses cancel out and we know the acceleration due to gravity is constant.
This equation is unsolvable as we do not know 
, the coefficient of friction between the cabinet and the floor. We cannot find the acceleration of the cabinet, meaning we cannot find the force.
There is insufficient information to solve. Force is the product of mass and acceleration. While we are given the mass, we are not given an acceleration.
If we assume that we are looking for the minimum force required to move the cabinet, then the force would be equal to the force of friction.
Substitute the equations for frictional force and Newton's second law.
Normal force is equal to the force of gravity.
The masses cancel out and we know the acceleration due to gravity is constant.
This equation is unsolvable as we do not know
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An ice skater skates on a frictionless surface with a velocity of 
. If no forces act upon him, what is his velocity after 
?
An ice skater skates on a frictionless surface with a velocity of
If no forces are acting upon the skater and he is on a frictionless surface, then that means he has no net acceleration.
Mathematically, we can see this relationship from Newton's second law:
Presumably the skier has mass, therefore the acceleration must be zero.
If an object moves with a velocity and there is no acceleration, then the velocity remains constant. His velocity after five second will be equal to his initial velocity.
If no forces are acting upon the skater and he is on a frictionless surface, then that means he has no net acceleration.
Mathematically, we can see this relationship from Newton's second law:
Presumably the skier has mass, therefore the acceleration must be zero.
If an object moves with a velocity and there is no acceleration, then the velocity remains constant. His velocity after five second will be equal to his initial velocity.
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An object moves forward with a constant velocity. What additional information do we need to know to determine the force acting upon the object?
An object moves forward with a constant velocity. What additional information do we need to know to determine the force acting upon the object?
Force is given by the product of mass and acceleration. If an object has a constant velocity, then it has no acceleration.
If an object has no acceleration, then it must also have no net force.
No additional information is needed to solve this question.
Force is given by the product of mass and acceleration. If an object has a constant velocity, then it has no acceleration.
If an object has no acceleration, then it must also have no net force.
No additional information is needed to solve this question.
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A 
box slides along the floor with a constant velocity. What is the net force on the box?
A
Since the object is moving with a constant velocity, it has no acceleration. Acceleration is only produced by a change in the velocity.
If acceleration is zero, no force is produced. This conclusion comes from Newton's second law:
Since the acceleration is zero:
Since the object is moving with a constant velocity, it has no acceleration. Acceleration is only produced by a change in the velocity.
If acceleration is zero, no force is produced. This conclusion comes from Newton's second law:
Since the acceleration is zero:
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A constant force acts on an object, causing it to accelerate along a track, when it suddenly breaks in half. What is the ratio of the initial acceleration of the object to the acceleration of one piece after it breaks if the force remains constant after the break?
A constant force acts on an object, causing it to accelerate along a track, when it suddenly breaks in half. What is the ratio of the initial acceleration of the object to the acceleration of one piece after it breaks if the force remains constant after the break?
Newton's second law states that:
We are told that the force on the object remains constant, even after it breaks in half. The mass of the broken piece will be equal to half the mass of the total object.
Using these values, we can set up equations for the initial and final accelerations.
If the force remains constant while the mass is cut in half, the acceleration of the object will double. The ratio of the new acceleration to the old acceleration will be 2:1. If the question asked for the ratio of the old acceleration to the new one, it would be 1:2.
Newton's second law states that:
We are told that the force on the object remains constant, even after it breaks in half. The mass of the broken piece will be equal to half the mass of the total object.
Using these values, we can set up equations for the initial and final accelerations.
If the force remains constant while the mass is cut in half, the acceleration of the object will double. The ratio of the new acceleration to the old acceleration will be 2:1. If the question asked for the ratio of the old acceleration to the new one, it would be 1:2.
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What force is required produce an acceleration of 
on an object of mass 
?
What force is required produce an acceleration of
Newton's second law states that:
We are given the mass of the object and the acceleration. Using these values, we can solve for the necessary force.
Newton's second law states that:
We are given the mass of the object and the acceleration. Using these values, we can solve for the necessary force.
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A car moves with a constant velocity of 
. What is the net force on the car?
A car moves with a constant velocity of
If an object is moving with constant velocity, then its acceleration must be zero.
We can then look at Newton's second law. If the acceleration is zero, then the net force must also be zero.
This means that the gravitational force and normal force cancel out, and the propulsion force of the car cancels out the force of friction. Forces may still be acting in respective directions, but the net sum of these forces is zero.
If an object is moving with constant velocity, then its acceleration must be zero.
We can then look at Newton's second law. If the acceleration is zero, then the net force must also be zero.
This means that the gravitational force and normal force cancel out, and the propulsion force of the car cancels out the force of friction. Forces may still be acting in respective directions, but the net sum of these forces is zero.
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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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