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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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Chapter 6 Work and Energy

Chapter 6 Work and Energy

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