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### 402-A: Finding Net Force: Finding Net Force in One Dimension

• Topic Cluster: Dynamics
• Topic: Quantitative Dynamics (Newton's Second Law)
• Objective: Given a 1-dimensional quantitative free-body diagram, determine the magnitude and direction of net force acting on an object.
• Content: Net force is calculated from a quantitative free-body diagram of an object.
• Level: 1

#### BACK to Ladder Quantitative Dynamics (Newton's Second Law)

This unit is called quantitative dynamics because we will begin analyzing why objects move the particular way that they do. The key issue is to quantitatively analyze forces.

#### Free-Body Diagrams and Vectors

A free-body diagram is a dot (or simple picture) with arrows emanating from it. The dot represents one object. Each arrow represents one force acting on that object. Here is an example of a quantitative free-body diagram:

This free-body diagram includes two forces:

• A force of 100 Newtons to the right.
• A force of 60 Newtons to the left.

Because force is a vector, each force has both a magnitude and direction. In a quantitative free-body diagram, each force is represented by an arrow and a number. The direction is given by the direction of the arrow, and the magnitude is given by the number next to the arrow. The unit for force is Newtons (N), so each number has this unit.

1. Write the magnitude and the direction of this force:
2. Write the magnitude and the direction of this force:
3. What does the letter "N" stand for in these diagrams?
4. What is the name of a diagram of all of the forces acting on an object, each represented by an arrow?

#### Finding Net Force of Two Forces

To find the net force acting on an object, use the free-body diagrams.

• If two forces (arrows) are in the same direction, ADD.
• If two forces (arrows) are in opposite direction, SUBTRACT. The direction of net force is in the direction that had greater magnitude.
1. Find the net force (Magnitude and direction).
2. Find the net force (Magnitude and direction).
3. Find the net force (Magnitude and direction).
4. Find the net force (Magnitude and direction).

#### Finding Net Force of More than Two Forces

To find the net force from a free body diagram with more than two forces, follow these steps:

• Add all of the forces on the left side.
• Add all of the forces on the right side.
• Subtract the sums of each side.
• The direction of net force is the direction that had more force.
1. Find the net force (Magnitude and direction).
2. Find the net force (Magnitude and direction).
3. Find the net force (Magnitude and direction).

#### Drawing a free-body diagram and finding net force.

Sometimes, a free-body diagram is not given to you in a problem, but you have to draw your own free-body diagram first, then find the net force acting on an object. (In all problems below, please ignore any forces not explicitly stated.)

Also know this: If the net force is zero, then the net force has no direction!

1. Two forces act on an object.
• It is pushed with a force of 50 N to the right.
• Friction resists with a force of 20 N to the left.
1. Draw a free-body diagram showing these two forces.
2. Find the net force (Magnitude and direction).
2. A rocket ship is experiencing three forces.
• An upward thrust of 500 N.
• A weight of 200 N. The direction of weight is always downward.
• An air resistance of 20 N downward.
1. Draw a free-body diagram showing these three forces.
2. Find the net force (Magnitude and direction).
3. A book is lying on a table. There are two forces acting on the book.
• It has a weight of 102 N. The direction of weight is always downward.
• There is an upward normal force of 102 N.
1. Draw a free-body diagram showing these three forces.
2. Find the net force (Magnitude and direction).

#### BACK to Ladder Quantitative Dynamics (Newton's Second Law)

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