Newton’s Laws of Motion



Objective

As a result of this lesson you will be able to

  1. Describe the concept of forces and explain the significance of having a zero net force.
  2. Apply Newton’s second law to solve one and two-dimensional motion problems involving constant forces.
  3. Determine reaction forces when two objects come in contact
  4. Label all applied and reaction forces placed on an object
  5. Describe why balanced forces cause no acceleration
  6. Create accurate force diagrams
  7. Practice I SEE strategy to problem solve

Prerequisites

  • Vectors
  • Trigonometry
  • Algebra
  • Kinematics

 

Question

A bird is gliding in the air and is gaining altitude at a steady rate. Does the force of gravity or the upward force of the air on the bird have a greater magnitude?

 

Introduction

Newton’s laws of motion explain why things move the way they do. Any time an object interacts with another it is exerting a force. Forces are seen as either pushes or pulls. They can be a rope in tension, a resistance, frictional, gravitational, electrostatic, or even nuclear.
 

Connection

In kinematics we were able to describe the motion of objects in three dimensions. Sometimes being able to describe the motion isn’t enough. We may want to actually create a different type of motion and forces are used to create these changes. A force is what causes motion. We classify the subject of dynamics as the interaction between motion and the forces that cause it. This section on forces adds to the previous section of describing motion by now understanding what is causing it.
 

Role

Applying Newton’s laws is the first step to building our problem solving techniques and analytical skills. Unfortunately it is not always good enough to just describe what is occurring with kinematics equations. Our world is dynamic and always changing so we need to examine why these changes occur or determine what is required to create a change ourselves. One of the major points to understanding forces is to understand how objects interact with each other.
 




The First Law

 

Newton’s first law is all about balanced and unbalanced forces. When the forces are all balanced then there is no force. This means an object will stay at rest until a force acts on it. The key idea here is that rest means zero acceleration. An object can move at a constant velocity and it is considered still at rest. When forces are unbalanced then the resulting force causes a change in velocity because the force applies an acceleration to the object. The first law is also known as the law of inertia because it expresses an objects natural tendency to resist change in motion.

Definition/Equation

A body acted on by no net force moves with constant velocity (which may be zero) and zero acceleration.

 

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Example

What net force is required to maintain a 1000 kg object moving at a constant velocity of magnitude 500 m/s?

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The Second Law

 
Newton’s second law is used to predict what happens when a force does exist on an object. When a force is applied to an object and it is not balanced with another object then there will be a change in velocity and acceleration.

Definition/Equation

If a net external force acts on a body, the body accelerates. The direction of acceleration is the same as the direction of the net force. The mass of the body times the acceleration of the body equals the net force vector.

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Additional interaction

 

Example

An object has two forces applied to it. One of the forces is 10 N pulling toward the right and another is 5 N pulling toward the left. If the object’s mass is 10 kg what is the acceleration of the object?

Solution
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The Third Law

 
Newton’s third law is most commonly heard as, to every action, there is an equal, but opposite, reaction. This means that when object 1 exerts a force on object 2, then object 2 exerts a force back on object 1. The two forces are equal in magnitude and opposite in direction. These two forces are also known as an action/reaction pair.

Definition/Equation

If a body A exerts a force on body B (an “action”), then body B exerts a force on body A (a “reaction”). These two forces have the same magnitude but are opposite in direction. These two forces act on different bodies.

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Additional interaction

 

Example

If you press your hand down on the table with a force of 10 N. What is the force that is exerted by the table on your hand?

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Weight

 
It is important to make the distinction between weight and mass since they are commonly interchanged. Weight is a force and it is the gravitational force exerted on an object. Mass on the other hand is an intrinsic property and it measures the inertia of the object. Mass does not change with location but weight does change depending on its location.

Definition/Equation

The weight of an object is the gravitational force exerted on it by the earth (or other planet).

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Example

A book of mass 5 kg sits on a table. What is the weight of the book that sits on the table?

Solution
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Normal Force

 
Whenever an object touches another object there is a normal force. The normal force is exerted by the surface that the first object comes into contact with. This force is called the normal force because it is always perpendicular to the surface and it is what causes objects to not fall through each other.
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Example

The normal force is the contact force that is exerted on an object that comes into contact with another stable object. This can be seen as a reaction force.
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Example

If you press your hand down on the table with a force of 10 N. What is the force that is exerted by the table on your hand?

Solution
Identify
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Evaluate




Contact Forces (Friction)

 
There are many types of forces but contact forces require the interaction between objects. There are frictional forces, tensile forces, normal force, air resistance forces, spring forces, and applied forces. Just to put it in perspective, there are additional forces that do not require contact such a gravitational or electromagnetic forces. We will be covering applied, normal, tension, and frictional forces. When an object slides against another object it creates friction and there is a force that opposes the motion of the object. The frictional force comes in two forms, kinetic and static. Frictional forces also depend on the normal force to the surface that the object is applying. When the two objects are not moving there is a static frictional force and is larger than when the objects are moving with respect to each other and the kinetic frictional force is lower because is smaller.

Definition/Equation

A definition of contact forces(friction)

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Example

A box of mass 10 kg is being pulled across the floor. The coefficient of kinetic friction between the box and floor is .25. What is the magnitude of the frictional force that is acting on the box?

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Inclined Planes

 
One common type of problem in physics is dealing with objects that are on an incline. This results to adjusting our coordinate system. We will then be required to break out forces into the required components that are chosen for the appropriate coordinate system.

Equation/Definition

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Free-Body Diagrams

 
Free=body Diagrams are used to help identify the relevant forces required to solve problems in mechanics. A free-body diagram is a diagram that shows the forces on an object when it is free of its surroundings. The forces on the object are drawn as vectors and show the magnitudes and direction at which they are being applied. It is important to know that we only want to diagram the forces that act on the body itself and not the forces that the body is exerting on other objects in the system. This means, DO NOT label an action-reaction pair on the same FBD.

Equation/Definition

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Evaluation – Unit Analysis

 
Introduction description of topic or step

Equation/Definition

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Review Questions

  1. If a 2kg object rests on a table what is its weight? What is the force on the same object if it is dropped to the floor?
  2. You take your Porsche out for a drive and drive down a very long straight road. You drive down the road at a constant 150 km/h. You quickly pass a Volkswagen that is going a constant 50 km/h. Which car has the greater net force?
  3. Three blocks are connected together and are hanging. Each block has a weight of 15N. What is the net force of the system?
  4. A 500N man stands on the floor of an elevator as shown. If the man is standing on the scale that measures his weight. What does it read? What does the scale read if the elevator moves up with a= 2m/s? What if it moves down with a = 2 m/s?
  5. If a block sits on top of an inclined plane (a wedge) and there is no friction, what is the acceleration of the block as it slides down the incline? What is the acceleration if there is friction between the block and the incline?
  6. A crate with a mass of 20kg is on the floor. You push it with a force of 100N. What is the acceleration? How far does it travel in 10s? What is its final velocity?
  7. A block is placed on an incline of 30 degrees. A force is then applied to the object to pull it up the incline. The force applied is at an angle of 20 degrees to the incline. How large of a force is required to have the component that is horizontal to the incline equal 30N. What is the vertical component to that same force?
  8. A 3kg dog runs in a straight line. The velocity of the dog is shown in the diagram as a function of time. What is the maximum force the dog exerts? When does the dog have a zero net force in its motion?
  9. A block moves across a table by a force pulling on it. Draw the free body diagram of the block if the table is frictionless and if the table and block create friction.
  10. Two blocks are connected by a very strong rope. The mass of block A is 10 kg and the mass of block B is 30 kg. The blocks are then pulled by the rope upward with a 600N force. Draw a free body diagram for each block. What is the acceleration of the system? What is the tension in the rope between the blocks?
  11. A sphere is stuck in the wedge of a block. The block is being pulled by a force toward the left. What are the reaction forces on the sphere as it moves with the block?

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