Net Force: Definition and Calculations

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• 0:01 Forces Are Vectors
• 1:02 Calculating Net Force
• 2:45 Net Force Changes…
• 3:35 Free-Body Diagrams
• 4:55 Lesson Summary

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Lesson Transcript
Instructor: Sarah Friedl

Sarah has two Master's, one in Zoology and one in GIS, a Bachelor's in Biology, and has taught college level Physical Science and Biology.

Because forces are vectors, we can't simply add them up to get a total amount of force on an object. Instead, we calculate the net force, which is important to understand because it tells us about an object's state of motion.

Forces Are Vectors

When you get a paycheck, there are two numbers to look at. First is the gross amount you earn, which is the total amount of money you make. So if you make \$50,000 a year, this would be reflected in the gross earnings of your check.

The second number to take note of is the net amount, which is the amount you actually take home. A net amount is the difference between the gross amount and any deductions. In the case of your paycheck, this may come in the form of taxes, insurance premiums, retirement funds, and any other deductions that come out of your total gross earnings.

The same idea is true for net force. This is the vector sum of all forces acting on an object. As we learned in another lesson, forces are vector quantities because they have both magnitude and direction. We represent vectors with arrows - the size of the arrow shows the relative magnitude of the force, while the direction of the arrow shows in which direction the force is acting.

Calculating Net Force

Because forces have different magnitudes and directions, we can't just add up the forces and get a total amount. What we have to do is find the difference between the forces as we add up the vectors - we have to find the net force.

This is quite similar to adding positive and negative numbers. For example, if there is a force acting on an object and it is 5 Newton (capital letter 'N' for Newton) to the left, we could see this as +5 to the left. If at the same time there is a 5 N force to the right acting on that same object, this would be like subtracting 5 to the right. 5 - 5 = 0, so we have zero net force. The forces cancel each other out.

Forces don't always cancel out, though. For example, if there are two forces acting toward the right, and they are both 5 N, then we have 5 + 5 = 10. This would be 10 N to the right because both forces are acting in the same direction with the same magnitude.

But let's say we have 5 N to the right and 15 N to the left. 15 - 5 = 10, and since the greater magnitude force is acting to the left, that's where our net force is, too. So in this case, the net force is 10 N to the left.

We can do this for vertical forces as well. Say that an object is falling toward the ground, which means that both gravity and air resistance are acting on it. If gravity is pulling down with 600 N and air resistance is pushing up with only 200 N, then 600 - 200 = 400, so we have 400 N downward as our net force.

Net Force Changes State of Motion

Newton's first law says that an object continues in its state of rest or motion unless acted on by an outside unbalanced force. Forces are unbalanced when there is a net force greater than zero. When there is no net force, we say the forces are balanced. This can be true for both moving and stationary objects.

For example, an airplane traveling at constant velocity (so both constant speed and direction) can have balanced forces acting from the front and the back. The plane is moving, but if both forces are the same magnitude, then there is zero net force and the plane will continue traveling along that path until there is a net force. When the net force of an object is zero, we say it is in equilibrium, a state of 'no change.'

Free-Body Diagrams

Net force can be written out mathematically, but we can also create a visual representation of the forces acting on an object. We do this through free-body diagrams, which are force-vector diagrams. You already know that vectors have both magnitude and direction and are represented by arrows. In free-body diagrams, the size of the arrow still indicates the magnitude, and the direction of the arrow tells us which way the force is acting. But now we also have the object, which is represented by a box, and the forces acting on the object come out from its sides.

So if we return to our first example of 5 N of force acting on an object both to the left and the right, our free-body diagram would be a box in the middle with two equal-sized arrows, one pointing left and the other pointing right.

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