5.1: Normal Force and Friction Force
Objectives
The student will:
 Understand how to solve problems involving the normal force.
 Understand how to solve problems involving friction.
Vocabulary
 friction: A force that opposes two objects sliding against each other. Friction acts in a direction along the flat surface of an object.
 normal force: The force exerted by the ground or other object that prevents other objects from going through it.
 vector components
Introduction
Just as velocity and acceleration are vectors that can point in any direction, force is a vector that has both a magnitude and a direction.
The Normal Force
As discussed in onedimensional forces, a
normal force
is the force exerted by the ground or other object that prevents other objects from going through it. In the
Figure
below
, a block that rests upon the ground is pulled in a diagonal direction up and to the right. Just as velocity and acceleration can be
The applied force,
Check Your Understanding
In the
Figure
above
, the weight,
1. What normal force,
Answer:
We know that gravity and the normal force act only in the
Therefore,
llustrative Examples
1a. A 25.0 kg block experiences an applied force
Answer:
The first thing to do is to resolve the applied force into its
Next, since we were given the mass of the block, we need to find its weight:
The question concerns the forces in the
1b. What is the horizontal acceleration of the block in 1a?
Answer:
This question concerns the forces in the
Check Your Understanding
Had the applied force been directed as shown in this diagram, what effect do you think it would have had on the normal force? See diagram below.
(a) The normal force is greater than the weight of the block.
(b) The normal force is less than the weight of the block.
(c) The normal force equals the weight of the block.
Answer:
The answer is A. See if you can convince yourself that the normal force in this situation would be 295 N if the values of the given quantities were the same as in the previous question, but with the direction of
Friction
Friction is a force that opposes two objects sliding against each other, and is a contact force like the normal force. While the normal force acts perpendicular to the flat surface, friction acts in a direction along the flat surface of an object.
We generally speak of two kinds of friction: kinetic friction and static friction. We will begin our discussion of friction with kinetic friction.
Kinetic Friction
“Kinetic” means
moving
. Kinetic friction means friction between two objects sliding against each other, such as: (1) sliding a book across a desktop and (2) your foot slipping on an icy pavement. The force from kinetic friction is abbreviated
We know a force must exist on the book because it eventually stops moving. Newton’s Second Law implies there must be some force acting on the book to slow it down and eventually bring it to rest. We call this force kinetic friction. Friction arises because no matter how smooth the surface of the book or the surface it is in contact with may look or feel, microscopically the two surfaces are rough. The smallest unevenness of the surfaces acts to impede the motion of the book. In fact, a force must be applied to the book just to overcome this “roughness” before it can be set into motion. The force that acts on the book before it is set into motion is called the static friction force, which we will discuss after dealing with kinetic friction.
Kinetic friction follows three basic rules:
 The frictional force is independent of the relative velocity between the two surfaces for conventional speeds.
 The frictional force is independent of contact surface area. If you slide a book lying flat or turn it on edge, the force of friction is the same.

The frictional force,
fk , is directly proportional to the normal force the two objects press against each other with,FN , and also directly proportional to the roughness or stickiness of the surface, called its coefficient of friction. We write this asfk=μkFN , whereμk is the coefficient of friction. The symbol,μ , is the Greek letter mu and pronounced “myoo” in English. The rougher or stickier the contact between two surfaces, the larger the value ofμk . A frictionless surface would haveμk=0 .
As you well know, it’s easier to push an object from one point to another than to carry it from one point to another. We usually just accept this observation as obvious. But why is this so?
This observation leads to the conclusion that the force of kinetic friction is usually less than the weight of the object to be moved. If not, why push when you could more easily lift?
The coefficients of friction,
The SetUp:
Weight (N)  Spring reading = friction force (N) 

20  10 
40  20 
60  30 
If we graph kinetic friction force vs. weight, we would find a straight line with a slope of 0.5. The slope of this graph represents the coefficient of friction,
Figure below shows two experiments measuring the coefficient of kinetic friction for brick and wood on polished oak.
Check Your Understanding
1. What are the units of
Answer:
Since
2. It is typically stated that
Answer: The force needed to slide the object is the same as the force needed to lift the object.
Since
Illustrative Example 1
In
Figure
above
, a force
(a) Draw the Free Body Diagram (FBD) for the problem.
(b) Determine the friction force between the block and the surface.
(c) Determine the normal force on the block.
(d) Determine the coefficient of kinetic friction,
Answers:
(a) See Figure above . Notice how the friction force is represented in FBDs. It is drawn as an “interface” vector.
(b) Since the block moves at constant velocity
Therefore
(c) We assume the block has no vertical motion, therefore,
(d) Since
Static Friction
The original meaning of “static” is “not moving”. Static friction,
For a given pair of surfaces, the coefficient of static friction
Consider Figure below .
The man in the figure is trying to slide a heavy couch. He exerts a force
The coefficient of static friction,
Illustrative Example 2
The couch in Figure above just begins to move when a force of 175 N is applied to it.
(a) What is the maximum static friction force,
(b) What is the coefficient of static friction,
Answers:
(a) Since the maximum force applied before the couch moves is 175 N, this must be the maximum static friction:
(b)
Notice that the coefficient of static friction,
Kinetic and static friction oppose motion. Friction acts to oppose the motion caused by an applied force, thus opposing the relative motion between two surfaces.
If you attempt to accelerate your car and there is insufficient static friction between the tires and the road (for example, if you’re on ice), the tires would spin and the car would gain no additional speed. Kinetic friction would oppose the motion of the tires, even on ice, and you’d “burn rubber.” However, during those moments when your tires made contact with the asphalt, static friction would oppose the applied force your tires put upon the road and send the car forward. At the area of contact between the tire and the road, the tire pushes back on the pavement and the pavement pushes on the tire in the forward direction (Newton’s Third Law in action!). The force of static friction is responsible for pushing the car forward. The force of static friction opposes the motion of the tire relative to the road, but has the same direction as the velocity of the car.
Check Your Understanding
1. How does the magnitude of the force of friction change as the angle of
Answer : As the angle increases, the normal force decreases so the friction force must also decrease. If the normal force goes to zero, so does the friction force.
2. If the man in the Figure below were taller and he applied the force of the same magnitude to the weight, how would the normal force on the weight change?
Answer : The taller he is, the more vertical the force, so the normal force would decrease.
3. A student pushes a calculator along a table with a horizontal force of 1 N, but the calculator remains motionless ( Figure below ).
(a) What is the magnitude of the static friction force on the calculator?
(b) Can the static friction force ever be smaller or larger than 1 N?
http://phet.colorado.edu/en/simulation/forcesandmotion
Answers :
2a. Since the calculator remains stationary, the force of static friction and the force that the student exerts must be equal and opposite.
2b. The static force can easily be smaller. Any force less than 1 N that the student exerts upon the calculator will be equal and opposite to the static friction force. The static friction can take on an infinite number of values below the threshold force that sets the calculator in motion.
The static friction force may possibly be larger than 1 N if the student applies a bit more force and the calculator remains motionless. The force at which the calculator just begins to move is the maximum force that static friction can provide.
Image Attributions
Description
Learning Objectives
Difficulty Level:
At GradeSubjects:
Date Created:
Jan 18, 2013Last Modified:
Jun 18, 2015Vocabulary
If you would like to associate files with this Modality, please make a copy first.