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Aim: How can we describe resultant force (net force)? Identify some forces. Identify some forces. Identify the unit for force. Identify the unit for force. Explain the difference between mass and weight. Explain the difference between mass and weight. A student has a mass of 75 kg. The student weighs 831 newtons. Determine the acceleration due to gravity. A student has a mass of 75 kg. The student weighs 831 newtons. Determine the acceleration due to gravity.

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Aim: How can we describe resultant force (net force)? List all vectors and units. List all vectors and units.

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How can we describe forces acting on an object? Two or more forces that act on the same object at the same time are called Two or more forces that act on the same object at the same time are called concurrent forces. concurrent forces. Ex: Ex:

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Combining forces Resultant force (net force) Resultant force (net force) Is the single force that is equivalent to the combined effect of these concurrent forces. Is the single force that is equivalent to the combined effect of these concurrent forces. Example 1: Example 1: F 1 =10N F 2 =5N R = 15N F eq = -15N

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The force vector needed to produce equilibrium is the same length as the resultant vector but it is pointing in the opposite direction. (F eq ) The force vector needed to produce equilibrium is the same length as the resultant vector but it is pointing in the opposite direction. (F eq )

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Example: 3 Example: 3 If forces act in opposite directions, the angle between them is 180 degrees, the resultant force is the smallest. If forces act in opposite directions, the angle between them is 180 degrees, the resultant force is the smallest. F 1 = 3N F 2 = 10N F 1 = 3N F 2 = 10N

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Combining forces Head-to-tail method – combine the head of one vector to the tail of the other vector. Head-to-tail method – combine the head of one vector to the tail of the other vector. If two forces act in the same direction, the angle between them is 0 degrees and the resultant force is the sum of their magnitudes (R = F 1 +F 2 ) If two forces act in the same direction, the angle between them is 0 degrees and the resultant force is the sum of their magnitudes (R = F 1 +F 2 ) Ex2: Ex2: F 1 =10N F 2 =3N F 1 =10N F 2 =3N R = 13N

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Sketch the Resultant force and Equilibrium force

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How can we sketch the equilibrium force? The vector sum of the concurrent forces acting on an object is called the net force F net. (Resultant force) The vector sum of the concurrent forces acting on an object is called the net force F net. (Resultant force) If the net force acting on the object is zero, the object is in equilibrium. If the net force acting on the object is zero, the object is in equilibrium. F1 F2 F1 F2 R F eq

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If two concurrent forces act at right angles to each other, the head-to-tail method produces a right triangle. If two concurrent forces act at right angles to each other, the head-to-tail method produces a right triangle. F2 F1 F2 F1 R

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When is resultant force is greater? When is resultant force is greater? When the two forces act in the same direction, 0 degree angle, they produce the largest resultant force. When the two forces act in the same direction, 0 degree angle, they produce the largest resultant force. When the two forces act in opposite directions, 180 degree angle, they produce the smallest resultant force. When the two forces act in opposite directions, 180 degree angle, they produce the smallest resultant force.

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How can we analyze force vectors? 1. Find the resultant force vector. 2. A 10 Newton force and a 4 Newton force act concurrently on a point. As the angle increases from 0° to 180° what happens to the resultant force? 3N7N

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Triangular method of adding concurrent forces. Leave the first force in the same position. Take the second force and slide it to the head of the first force. (Head-to-tail method) Leave the first force in the same position. Take the second force and slide it to the head of the first force. (Head-to-tail method) To find the resultant force: draw a line from the tail of the first force vector to the head of the last vector. To find the resultant force: draw a line from the tail of the first force vector to the head of the last vector. To find the equilibrium force: draw the same size line as the resultant force but 180° from the resultant force. To find the equilibrium force: draw the same size line as the resultant force but 180° from the resultant force. F2F2 F2F2 F1F1 R F1F1

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Examples Draw the resultant force for the following vectors. Draw the resultant force for the following vectors. F1 F2 R P P F1

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Examples Examples F1 F2 F3 F1 F2 F3 R

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Equilibrium force The vector sum of the concurrent forces acting on an object is called the net force F net. (Resultant force) The vector sum of the concurrent forces acting on an object is called the net force F net. (Resultant force) If the net force acting on the object is zero, the object is in equilibrium. If the net force acting on the object is zero, the object is in equilibrium. The force vector needed to produce equilibrium is the same length as the resultant vector but it is pointing in the opposite direction. (F eq ) The force vector needed to produce equilibrium is the same length as the resultant vector but it is pointing in the opposite direction. (F eq ) F1 F2 F1 F2 R F eq

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If two concurrent forces act at right angles to each other, the head-to-tail method produces a right triangle. If two concurrent forces act at right angles to each other, the head-to-tail method produces a right triangle. F2 F1 F2 F1 R

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Let’s calculate the resultant force vector using Pythagorean theorem c 2 = a 2 + b 2 c 2 = a 2 + b 2 Use physics terms: Use physics terms: F 2 = 40N F 1 = 30N R

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Using the same example in the previous slide. What is the angle of the resultant force. (The angle is located next to the tail of the resultant force) Using the same example in the previous slide. What is the angle of the resultant force. (The angle is located next to the tail of the resultant force) Using Soh Cah Toa, find angle theta. (hint: Toa) Using Soh Cah Toa, find angle theta. (hint: Toa) F 2 = 40N F 1 = 30N R = 50N θ

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Aim: How can we analyze force vectors and components? Calculate the resultant force and the angle. Sketch and label the equilibrium force. Calculate the resultant force and the angle. Sketch and label the equilibrium force. 10N 5N

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Example: Find the resultant force and the angle. Example: Find the resultant force and the angle. F 2 = 10N F 1 = 5N R = ? θ R = 11.1N

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Aim: How can we analyze force vectors? 1) Sketch the resultant force and equilibrium force. 2) Calculate the magnitude of the equilibrium force. 7N2N

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1) Which pair of vectors produce the greatest resultant force? 1) Which pair of vectors produce the greatest resultant force? 2) Which pair of vectors produce the least resultant force? 2) Which pair of vectors produce the least resultant force?

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The diagram below represents a force vector A, and resultant vector, R. The diagram below represents a force vector A, and resultant vector, R. Where should we draw vector B? Where should we draw vector B? Recall: The resultant vector goes from start to end. Recall: The resultant vector goes from start to end. A R B

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The diagram below represents a force vector A, and resultant vector, R. The diagram below represents a force vector A, and resultant vector, R. Where should we draw vector B? Where should we draw vector B? A R B

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Force vector components A person is pulling a sled with a 100- newton force at a 30° angle with the horizontal. A person is pulling a sled with a 100- newton force at a 30° angle with the horizontal. 1) Sketch a picture 1) Sketch a picture 2) Calculate the horizontal force. 2) Calculate the horizontal force. 3) Calculate the vertical force. 3) Calculate the vertical force. 4) As the angle decreases, describe the horizontal force and vertical force. 4) As the angle decreases, describe the horizontal force and vertical force.

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