Newton's Second Law: Meaning & Calculations

Newton's Second Law: Meaning & Calculations
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  • 0:03 What Is Newton's Second Law?
  • 0:57 Free Body Diagrams
  • 2:32 Calculating Net Force
  • 3:25 Determining Motion
  • 4:17 Graphs
  • 4:57 Lesson Summary
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Lesson Transcript
Instructor: Amanda Robb
In this lesson we'll be learning how to use graphical representations of forces, like free body diagrams and force vs acceleration graphs, to explain Newton's second law. By the end of the lesson, you'll understand these diagrams and how to calculate the net force in two dimensions.

What Is Newton's Second Law?

Picture an object in motion. It could be a skydiver jumping out of an airplane or a rocket zooming out into space. But even smaller objects experience motion, like a mouse skittering across the floor. What's common between all these examples?

They're all in motion, and they're all accelerating, or experiencing a change in velocity. Although velocity can stay constant, most moving objects we experience in the real world accelerate. But, how can we predict how an accelerating mass will move? Scientists use a revelation from hundreds of years ago in the 1600s, known as Newton's second law, to answer this question.

Newton's second law says that mass multiplied by acceleration is equal to the force acting on an object, or:


where F is force, m is mass, and a is acceleration.

Free Body Diagrams

In all the real world examples we mentioned previously, there is more than just one force acting on an object. In order to decide how the object will move, we need to consider how the forces will combine first. To do this, we can use a handy tool called a free body diagram to show which forces are acting on an object.

Objects take all types of forms, and since we're not all artists, we can keep it simple by representing the object as a dot in the diagram. Then, all forces extend out from the dot using arrows. Some forces will push the object forward, such as the applied force (or Fapp) when an object is pushed. Other forces include tension (or FT) when an object is pulled or hung by a string, and force due to friction (or Ff) which opposes the applied force.

Every object has force due to gravity (or Fg) pushing down on it as long as it is on Earth. Objects that are on a surface also have a force that opposes gravity called the normal force (or FN). It extends perpendicular from the surface the object rests on and is the same value as the force due to gravity as long as it is on a flat surface and not an incline.

Let's look at an example: this free body diagram below. A toy car travels across a table with an applied force of 10N. Friction on the table opposes this force with 2N. The car experiences a force due to gravity of 1N.

free body diagram

Since the object is on a flat surface, we can assume that the normal force is equal to the force due to gravity.

Calculating Net Force

Now that we have this free body diagram, what do we do with it? Next, in order to see how motion changes for the object, we must calculate the net force. The net force is the sum of forces extending in one plane of motion. You add forces going forward and subtract forces going backward in the horizontal plane. Forces going up in the vertical plane are added, and forces going down are subtracted. You can't add horizontal forces to vertical forces; we will have two separate quantities for net force on this object.

Let's look at our example.

Since the toy car moves forward with 10N, we will add this force. The frictional force moves backward, so we subtract 2N. Our net force in the horizontal plane is 8N.

In the vertical plane, the forces balance each other, 1N - 1N = 0N. So, there is no net force acting on the object in the vertical plane.

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