1. Work Function and gravitational potential and kinetic
Unit 4: Work & Energy
Work Function and gravitational potential and kinetic

2. Work
Work is a transfer of energy from one object to another object by a force
Work is measured in Joules (J)
Work (and therefore energy) is a scalar quantity

3. Work is done on an object by a force
The force comes from some other object: so we say that one object does work on another
W = Fx (as long as d is in the same axis)
W = Fd
W is work (measured in joules)
F is magnitude of the force (newtons)
d = x is the displacement (meters) x F

4. Work (cont.) F W = Fd·cos  d
Work is done only by the component of force parallel to the displacement
GENERAL EQUATION
W = (Fcos)·d
W = Fd·cos F  d

5. SI unit for Work is Joule (J)
1 𝐽=1 𝑁∙𝑚=1 𝑘𝑔𝑚 𝑠 2 𝑚=1 𝑘𝑔 𝑚 2 𝑠 2

6. Example 1
Renatta Gass is out with her friends. Misfortune occurs and Renatta and her friends find themselves getting a workout after their car runs out of fuel. They apply a cumulative force of 1080 N to push the car 218 m to the nearest fuel station. Determine the work done on the car.

7. Answer
2.35 x 105 J

8. Work (cont.)
Work can be positive or negative
If force is in opposite direction from displacement, then work is negative
Friction does negative work on sliding things:
W = Ff d·cos(180)
= Ff d Ff d

9. Example 2
Pete Zaria works on weekends at Barnaby's Pizza Parlor. His primary responsibility is to fill drink orders for customers. He fills a pitcher full of Cola, places it on the counter top and gives the 2.6-kg pitcher a 8.8 N forward push over a distance of 48 cm to send it to a customer at the end of the counter. The coefficient of friction between the pitcher and the counter top is 0.28.
a. Determine the work done by Pete on the pitcher during the 48 cm push. b. Determine the work done by friction upon the pitcher . c. Determine the total work done upon the pitcher .

10. Answer
a. 4.2 J b. -3.4 J c. 0.8 J

11. If there are multiple forces acting on an object, we can find the net work
Wnet = Fnetcos Δx
Work is also defined as the area under the curve of Force vs. Displacement
𝑊= 𝐹∙𝑑𝑥
(W = Area under the curve of an F vs d graph.)

12. Work is not a vector However, Work can be positive or negative
Bobby does positive work lifting box
Bobby does negative work lowering box

13. Gravitational Potential Energy
𝑷𝑬 𝒈 =𝒎𝒈𝒉
𝑊𝑜𝑟𝑘 𝑑𝑜𝑛𝑒 𝑜𝑛 𝑡ℎ𝑒 𝑏𝑜𝑥 𝑏𝑦 𝑡ℎ𝑒 𝑝𝑒𝑟𝑠𝑜𝑛=Δ𝑃𝐸𝑔

14. One of the tallest radio towers is in Fargo, North Dakota
One of the tallest radio towers is in Fargo, North Dakota. The tower is m tall. If a bird lands on top of the tower, so that the gravitational potential energy associated with the bird is J, what is its mass, in kilograms?

15. An astronaut with a mass of 110
An astronaut with a mass of kg visits the moon (which has a different gravitational force than Earth). The astronaut climbs 5.0 m up the ladder into his spacecraft and gains J in GPE. What is the strength of gravity on the moon?

16. Kinetic Energy and Work-Energy Theorem
𝑲𝑬= 𝟏 𝟐 𝒎 𝒗 𝟐
𝑣 𝑓 2 = 𝑣 𝑖 2 +2𝑎∆𝑥
𝑣 𝑓 2 − 𝑣 𝑖 2 =2𝑎∆𝑥
𝑣 𝑓 2 2 − 𝑣 𝑖 2 2 =𝑎∆𝑥
𝑚 𝑣 𝑓 2 2 − 𝑣 𝑖 = 𝑎∆𝑥 𝑚
𝑚𝑣 𝑓 2 2 − 𝑚 𝑣 𝑖 2 2 =𝑚𝑎∆𝑥
𝑚𝑣 𝑓 2 2 − 𝑚 𝑣 𝑖 2 2 =𝐹∆𝑥=W
𝑊(𝑛𝑒𝑡 𝑤𝑜𝑟𝑘 𝑑𝑜𝑛𝑒 𝑜𝑛 𝑡ℎ𝑒 𝑜𝑏𝑗𝑒𝑐𝑡)= ∆𝐾𝐸= 𝐾𝐸 𝑓 − 𝐾𝐸 𝑖

17. Example
A skater of mass 60 kg has an initial velocity of 12 m/s. He slides on ice where the frictional force is 36 N.
How far will the skater slide before he stops?