Chapter 4 - Forces

By Keiji Oenoki [physics@amersol.edu.pe]

In previous chapters, we studied how objects move. In this chapter, we will study why objects move as they do. We will study Newton's Laws of Motion, which explain the relationship between acceleration and force. We will also use Newton's Laws for problem solving.

1. What is a Force?
2. Newton's First Law of Motion
3. Newton's Second Law of Motion
4. Newton's Third Law of Motion
5. Mass and Weight
6. Friction
7. Chapter 4 Quiz

Section 1. What is a Force?

Force can be defined as a push or a pull. (Technically, force is something that can accelerate objects.) For example, when you throw a baseball, you apply a force to the ball. Force is measured by N (Newton). A force that causes an object with a mass of 1 kg to accelerate at 1 m/s is equivalent to 1 Newton.

Section 2. Newton's First Law of Motion

You will have to learn a new terminology here: net force. Net force is the sum of all forces acting on an object. For example, in a tag of war, when one team is pulling the tag with a force of 100 N and the other with 80 N, the net force would be 20 N at the direction of the first team (100 N - 80 N = 20 N).

QUESTION: If both teams pull the tag with equal force, what would the net force be?
N

When you slide your book on floor it will stop soon. When you slide it on icy surface, it will travel further and then stop. Galileo believed that when you slide a perfectly smooth object on a frictionless floor the object would travel forever.

Isaac Newton developed the idea of Galileo further. He concluded that an object will remain at rest or move with constant velocity when there is no net force acting on it. This is called Newton's First Law of Motion, or Law of Inertia.

Section 3. Newton's Second Law of Motion

Newton's First Law deals with an object with no net force. Newton's Second Law talks about an object that has net force. It states that when the net force acting on an object is not zero, the object will accelerate at the direction of the exerted force. The acceleration is directly proportional to the net force and inversely proportional to the mass. It can be expressed in formula

F = ma

where:

F is the net force in N,
m is the mass of an object in kg and
a is its acceleration in m/s².

From this formula, we can say that force is something that accelerates an object.

QUESTION: How much net force is required to accelerate a 1000 kg car at 5.00 m/s²?
N

QUESTION: If you apply a net force of 1 N on 200 g-book, what is the acceleration of the book?
m/s²

Section 4. Newton's Third Law of Motion

When you kick the wall in your room, you will probably end up hurting your foot. Newton's Third Law of Motion can explain why: when one object applies a force on a second object, the second object applies a force on the first that has an equal magnitude but opposite direction. In other words, when you kick the wall, the wall kicks you back with equal force. As a result you will get hurt. These forces are called action-reaction forces.

Remember when you kick the wall, you exerts force on the wall. When the wall kicks you back, it exerts force on you. Therefore, the net force on the wall is not zero and the net force on your foot is not zero neither.

QUESTION: What is the net force on 200 g ball when it hits a wall with acceleration of 10 m/s²?
N

Section 5. Mass and Weight

Mass and weight are different in physics. For example, your mass doesn't change when you go to the Moon, but your weight does. Mass shows the quantity, and weight shows the size of gravity.

If you know your mass, you can easily find your weight because

W = mg

where:

W is weight in Newton (N),
m is mass in kg, and
g is the acceleration of gravity in m/s².

If your mass is 70 kg on Earth, your weight is
W=(70 kg)(9.8 m/s²) = 686 N.

Weight is measured by Newton (N).

QUESTION: What is the mass of an object that has a weight of 115 N on the Moon? The gravity of the Moon is 1/6 of g (which is 9.8 m/s²).
kg

Section 6. Friction

You will have to learn another vocabulary before you proceed: the normal force. The normal force acts on any object that touches surface (either directly or indirectly). The normal force would be applied on a ball on a table, but not on a ball in the air, for instance. It always acts perpendicularly to the surface. The formula to calculate the normal force is

F_N = - mg

where:

F_N is the normal force in Newton (N),
m is the mass in kg, and
g is the gravitational force in m/s².

For example, the normal force acting on a 70 kg-person would be
F_N = - (70 kg)(-9.8 m/s²) = 686N

QUESTION: What is the normal force acting on the same person on the Moon?
N

Now, we will talk about friction.

When you slide your book on floor, it will come to stop because of the force of friction. Friction is the force that acts between two object in contact because of action-reaction.

Force of friction can be calculated by the formula

where:

F_f is the force of friction in N,
is the coefficient of friction, and
F_N is the normal force in N.

The value of depends on surface you are dealing with. The following table shows some example of .

Surface	Value of
rubber on dry asphalt	~1
rubber on wet asphalt	0.95
steel on steel	0.18
steel on ice	0.010
rubber on ice	0.005

For example, if you throw a 500 g book on floor where = 0.1, the force of friction would be:
F_f = = (0.1)(0.5 * 9.8) = 0.49 N

QUESTION: What is the value of

if the force of friction on a 300 g book was 0.5 N?

Section 7. Chapter 4 Quiz

Try the Chapter 4 Quiz and see how well you can do!

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Colegio Franklin Delano Roosevelt
July, 1997

Comments or Questions to physics@amersol.edu.pe