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Work and Power At an angle

Work and Power At an angle. Pre-AP Extension. Work. So, mathematically, we define work as “exerting a force that causes a displacement”: (Work) = (Force exerted) (Displacement of object) (cos Θ ) or W = F*d*cos Θ W = Work done (J) F = Force exerted on object (N)

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Work and Power At an angle

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  1. Work and PowerAt an angle Pre-AP Extension

  2. Work • So, mathematically, we define work as “exerting a force that causes a displacement”: (Work) = (Force exerted) (Displacement of object) (cos Θ) or W = F*d*cosΘ W = Work done (J) F = Force exerted on object (N) d = Displacement of object (m) Θ = Angle between the force and the displacement

  3. Defining Θ – “the angle” • This is a very specific angle • Not just “any” angle - It is the angle between the force and the displacement • Scenario A: A force acts rightward upon an object as it is displaced rightward. The force vector and the displacement vector are in the same direction, therefore the angle between F and d is 0 degrees Because the force and the displacement point in the same direction, there is nothing between them – NO angle - 0° “between” the vectors F Θ = 0 degrees d

  4. Defining Θ – “the angle” • Scenario B: A force acts upward upon an object as it is displaced rightward. The force vector and the displacement vector are at a right angle to each other, therefore the angle between F and d is 90 degrees F Θ = 90 degrees In order to pivot from F to d, you must rotate 90° d

  5. Defining Θ – “the angle” • Scenario C: A force acts leftward upon an object which is displaced rightward. The force vector and the displacement vector are in the opposite direction, therefore the angle between F and d is 180 degrees Θ = 180 degrees In order to pivot from F to d, you must rotate 180°. This is the angle between the 2 vectors. F d

  6. Defining Θ – “the angle” • Scenario D: A pushing force acts leftward upon an object as it is displaced up a ramp to the left. The force vector and the displacement vector need to be drawn starting from the same location in order to find the angle between them. d d F F 28 ° Θ = 28 degrees In order to pivot from F to d, you must rotate 28°

  7. Defining Θ – “the angle” • Scenario D: A gravitational force acts downward upon an object as it is displaced up a ramp to the left. The force vector and the displacement vector need to be drawn starting from the same location in order to find the angle between them. d d F F 28 ° Θ = 118 degrees In order to pivot from F to d, you must rotate 28° + 90°, so 118°

  8. To Do Work, Forces must CAUSE Displacement • Consider scenario C from the previous slide • The situation is similar to a waiter who carried a tray full of meals with one arm (F=20N) straight across a room (d=10m) at constant speed • W = F*d*cosΘ • W = (20N)(10m)(cos 90°) • W = 0J • The waiter does not do work upon the tray as he carries it across the room

  9. Practice Problem • Jessica Lee goes to the market and applies 200N of force at an angle of 35° above horizontal on the handle of the 600N shopping cart. She pushes the cart halfway down the freezer aisle which is 12 m long and stops to grab a bag of peas. She adds them to the cart which increases the amount of force she must push with by 15 N. She continues to the end of the freezer aisle. • How much work did Jessica Lee do before she got the peas? • 983.0 J • How much work did Jessica Lee do total (in the freezer aisle)? • 2039.7 J

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