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Learn what “work” is! Learn how to calculate work See who can do the most work! Learn about power. Learn Hooke’s Law.

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Energy - the ability of a body or system of bodies to perform work. A body is given energy when a force does work on it.

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In physics, work has a special meaning, different to “normal” English.

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A force does work on a body (and changes its energy) when it causes a displacement. If a force causes no displacement, it does no work.

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If a man holds a 50 kg box at arms length for 2 hours as he stands still, how much work does he do on the box? Nada Zip Zilch NONE ZERO

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There is no work done by a force if it causes no displacement. Forces perpendicular to displacement, such as the normal force, can do no work. Likewise, centripetal forces never do work.

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Work is the dot product of force and displacement. Work is a scalar resulting from the interaction of two vectors.

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There are three ways to multiply vectors: Scalar Multiplication Dot Product Cross Product

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Magnitude of vector changes. Direction of vector does not change. a = 10 m·s -1 F = 50 N If m = 5 kg

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Note that the dot product of two vectors gives a scalar. θ

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Geometrically, the dot product is the projection of one vector on a second vector multiplied by the magnitude of the second vector. θ

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θ

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θ F1F1 F2F2 Two forces are acting on the box shown causing it to move across the floor. Which force does more work?

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F

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F s W = F s W = F s cos 0 o W = F s Maximum positive work

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F

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s W = F s W = F s cos Only the component of force aligned with displacement does work. Work is less. F

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F

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Fs W = F s W = F s cos 180 o W = - F s Maximum negative work.

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mgmg F When the load goes up, gravity does negative work and the crane does positive work. When the load goes down, gravity does positive work and the crane does negative work.

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A box is being moved with a velocity v by a force P (parallel to v) along a level floor. The normal force is F N, the frictional force is f k, and the weight of the box is mg. Decide which forces do positive, zero, or negative work.

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v mg P FNFN fkfk s

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J = N·m J = kg·m 2 ·s -2 That’s me! Energy is measured in Joules (J).

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The area under the curve of a graph of force vs displacement gives the work done by the force. F(x) x xaxa xbxb W = F(x) dx xaxa xbxb

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Let’s look at some examples

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A woman pushes a car with a force of 400 N at an angle of 10° to the horizontal for a distance of 15m. How much work has she done?

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W = Fscosθ = 400x15x0.985 W = 5900 J

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A man lifts a mass of 120 kg to a height of 2.5m. How much work did he do?

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Force = weight = 1200N Work = F x d = 1200 x 2.5 Work = 3000 J

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NameMass (kg) Force (N) Distance (m) Work of one lift (J) # of lifts in 1 min Total work (J)

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distance Force required = weight of object = mass (kg) x 10

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NameMass (kg) Force (N) Distance (m) Work of one lift (J) # of lifts in 1 min Total work (J)

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Power is the rate of doing work. Power is the amount of work done per unit time. Power is measured in Watts (1 Watt = 1 J/s)

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For each of the people in your table, can you calculate their power?

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When we stretch or compress a spring, a force arises that attempts to return the spring to its original length.

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A force of 125 N is required to extend a spring by 2.8 cm. What force is required to stretch the same spring by 3.2 cm? Step 1: Solve for k Step 2: Solve for the force

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Last lesson Learn what “work” is! Learn how to calculate work See who can do the most work! Power.

Last lesson Learn what “work” is! Learn how to calculate work See who can do the most work! Power.

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