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Work Chapter 5 Section 1

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Definition of Work Work – The product of the magnitudes of the component of a force along the direction of displacement and the displacement.

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**Everyday Work vs. Physics Work**

Everyday Work means doing something that takes physical or mental effort. Physics Work is a force that causes a displacement of an object.

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Examples of Work Hanging an object from a scale and holding it stationary. Work: Yes or No Hanging an object from a scale and lifting it upward at a constant velocity. Hanging an object from a scale and holding it still vertically while walking forward at a constant velocity.

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**Units For Work Work = Force • displacement = Newton • meter = Joule**

Joule – The SI unit for Work ( J ) The Joule is named for the British Physicist James Prescott Joule ( ). Joule made major contributions to the understanding of energy, heat and electricity.

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What is work? Work is done when a constant force is applied to an object which causes the displacement and follows from the equation. W = F • d W – Work F – Force d – Displacement Work is not done on an object unless the object is moved due to the action of a force.

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**How To Tell If Work Is Done**

Work is only done when the force, or a component of the force, is parallel to the displacement. Components of the force perpendicular to the displacement do no work.

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**Equation For Work W = Fd(cosθ)**

Where θ is the angle between the force and the displacement. d θ F

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Example Problem What is the work required to pull a chair 6 meters with a force of 75N at an angle of 35 degrees above the horizontal?

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**Example Problem Answer**

W = Fd(cosθ) = (75N)(6m)cos(35º) = 368.6 Work = J

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The Sign of Work Work is a scalar quantity that can be positive or negative. Positive Work: When the component of the force is in the same direction as the displacement. Negative Work: When the component of the force is in the opposite direction of the displacement.

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**Sign of Work When the work is negative, the object will slow down.**

When the work is positive, the object will speed up.

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**Using the Equation Correctly**

With the work equation if the values of θ are used correctly, the answer will have the correct sign. cosθ is negative for angles greater than 90º and less than 270º. Remember, the angle starts on the horizontal axis and increases in the counter-clockwise direction.

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Example Problem A worker at a factory pushes horizontally on a crate with a force of 563N over a distance of 13.5 meters. The force of gravity pulling down on the crate is 2500N. Assume the coefficient of kinetic friction between the crate and the floor is Solve for the following: a. How much work is done by the worker on the crate? b. How much work is done by the floor on the crate? c. What is the net work on the crate?

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**Example Answer (a) How much work is done by the worker on the crate?**

Work = J

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**Example Answer (b) How much work is done by the floor on the crate?**

Work = -6750J

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**Example Answer (c) What is the net work done on the crate?**

Work = 850.5J

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