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Determining Net Force

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What is Net Force? Net Force is the vector sum of all of the forces on an object. In other words, it’s the “total” of all forces.

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So, can’t we just add them up? Its not that simple. You must use the free-body diagram of the forces to decide what type of math to do to total up the forces.

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Same Direction… Only if the forces are in the same direction can you add. Since Fa and Ft are both upward, we can add them. Fa + Ft = 2 + 4 = 6N Fa = 2N Ft = 4N Fg = 6N

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Opposite direction…. If forces are in the opposite direction, you must subtract them from each other. Since Ft and Fg are opposite, we subtract. Ft – Fg = 4 –6 = -2N. The negative sign indicates a net force that is downward. Ft = 4N Fg = 6N

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Let’s sum up the forces in both directions. Fa + Ft= 9 + 7 = 16N, upward. Fg = 20 N, downward. Fa = 9N Ft = 7N Fg= 20N

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Simplified….. 16N upward and 20N downward. Since these are opposites we subtract. 16 – 20 = -4N downward. Remember the minus sign just tells us that the net force is downward. Once you simplify, draw the new FBD. Fnet = 4N, downward

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What about left and right? The same rules still apply. Same direction = add Opposite direction = subtract

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What happens if you have forces that are horizontal and vertical? Simplify in each plane first using the rules for same and opposite directions. Then, draw the new FBD. You should have one force in each plane. Notice that the vectors are PERPENDICULAR now.

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a c b What happens if you have forces that are horizontal and vertical? Once you have perpendicular vectors, you must continue to simplify. How? See the triangle? The hypotenuse is the Fnet! Now since we have the lengths of both sides we just have to use Pythagoreans Theorem!

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4N 3N Using Pythagorean’s Theorem a 2 + b 2 = c 2 We want to find c (net force) 4 2 + 3 2 = c 2 16 + 9 = c 2 25 = c 2 c = 5N (up and right)

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Finding Fnet in Summary… Simplify in both planes: –Same direction = add –Opposite direction = subtract Draw the simplified FBD then use Pythagoreans theorem IF the new vectors are PERPENDICULAR.

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Classwork/Homework…. Get started on Forces: Worksheet 2. This is due tomorrow!

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