High School Physics : Understanding the Relationship Between Force and Acceleration

Example Questions

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Example Question #1 : Understanding The Relationship Between Force And Acceleration

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?

Explanation:

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 .

Example Question #1 : Understanding The Relationship Between Force And Acceleration

crate slides along the floor with a constant velocity. What is the net force on the crate?

Explanation:

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 .

Example Question #1 : Understanding The Relationship Between Force And Acceleration

crate slides along a frictionless surface. If it maintains a constant velocity of , what is the net force on the object?

Explanation:

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.

Example Question #1 : Understanding The Relationship Between Force And Acceleration

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?

We need to know the value of  to solve

We need to know the value of the force applied to solve

The accelerations are equal

Explanation:

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.

Example Question #5 : Understanding The Relationship Between Force And Acceleration

Lance pushes a crate of mass  with  newtons of force. What is the resultant acceleration?

Explanation:

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.

Example Question #1 : Understanding The Relationship Between Force And Acceleration

A ball begins to roll with a velocity of . If no outside forces act upon it, what will be its velocity in ?

Explanation:

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.

Example Question #11 : Introduction To Forces

Two dogs are pulling on a bone in opposite directions. If the bone does not move, what conclusions can be drawn?

We need to know the acceleration on the bone in order to draw any conclusions

We need to know the weight of the dogs in order to draw any conclusions

The dogs are pulling with equal force, but in opposite directions

We need to know the mass of the bone to draw any conclusions

The two forces are equal in size and going in the same direction

The dogs are pulling with equal force, but in opposite directions

Explanation:

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.

Example Question #1 : Understanding The Relationship Between Force And Acceleration

An ice skater skates on a frictionless surface with a velocity of . If no forces act upon him, what is his velocity after ?

We need to know the skater's mass in order to solve

We need to know the displacement of the skater in order to solve

Explanation:

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.

Example Question #13 : Introduction To Forces

How much force is required to move a  filing cabinet ?

We need to know the coefficient of friction between the cabinet and the floor

We need to know the final velocity of the cabinet

We need to know the coefficient of friction between the cabinet and the floor

Explanation:

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.

Example Question #1 : Understanding The Relationship Between Force And Acceleration

A car rounds a perfectly circular turn at a constant speed. This causes the acceleration to __________.

increase

not be predictable

decrease

become zero

remain constant