Work

The Flower Carrier, Diego Rivera, 1935

What is work, in the science-sense?

Pull a book off the shelf.

Pull yourself up exercising.

Push a box up a ramp.

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What do all these have in common?

1: A force is applied...

2: ...over a distance.

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Work is done when a constant force is applied in the direction of displacement.

W = F_ǁd

• work is a scalar value
• Unit = N·m = kg·m²/s² = J (joule)

Example

How much work is done if you exert 6.67 N of force to lift a book through a vertical distance of 0.750 m?

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W = F_ǁd

= 6.67N x 0.750m

= 5.00 J

Example

Forces applied at an angle

Only the force applied in the direction of the displacement does work.

W = F_ǁd

If the force is applied at an angle to the moving object only the component in the direction of the motion is doing work.

W = Fdcosθ

θ is the angle of the force from the direction of motion

(math note: this is the dot product of F and d which is why work is scalar)

θ

Example

A small plane tows a glider at constant speed and altitude. If the plane does 2.00x10⁵ J of work to tow the glider 145 m and the tension in the tow rope is 2560 N, what is the angle between the two rope and the horizontal?

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Example

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You want to load a 35 kg box into the back of a van. One way is to lift the box straight up 1.00 m to the back of the van. Alternatively, you can slide the box up a 19.47^o (from ground) ramp with wheels (negligible friction) a distance of 3.00 m. Which method would take more work at constant speed? (work out on board)

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They would require the same work! (342 J)

One requires more force and one requires more distance.

Some important notes about work

1) Work has a sign that corresponds to the direction of the force relative to the motion of the object.

• W > 0 if the force is in the same direction as the motion.
• W< 0 if the force is in the opposite direction as the motion of the object.
• W = 0 if the force is perpendicular to the direction of the motion.

2) The total work done on an object is the sum of the work done by all forces acting on the object

• W_total = ∑W = W₁ + W₂ + W₃ + ...

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Example

Wanda Wren pulls her suitcase at constant velocity through the airport on level ground with a force of 35.0 N at 55.0^o above the horizontal for a distance of 30.0 m.

1. Draw a free body diagram of the suitcase.
2. Calculate the work done by all forces.
3. What is the total work done on the suitcase?

Example

Wanda Wren pulls her suitcase at constant velocity through the airport on level ground with a force of 35.0 N at 55.0^o above the horizontal for a distance of 30.0 m.

1. Draw a free body diagram of the suitcase.
2. Calculate the work done by all forces.
3. What is the total work done on the suitcase?

a)

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b) i) W_N = W_g = 0 J because they are perpendicular to the motion of the suitcase

ii) W_pull = (35N)(30m)(cos 55^o) = 602 J

(+ because same direction as motion)

iii) W_f = (35N)(30m)(cos180^o) = -602 J

(- because opposite direction, 180^o, from motion)

c) W_tot = 0J + 0J + 602 J + -602 J = 0 J