Summary Work, Energy, and Power – Complete Notes with Solved Problems (High School Physics)

Energy, Work, and Power


First: Summary:

Kinetic Energy (𝐾𝐸):
1
𝐾𝐸 = 𝑚𝑣 2
2
Potential Energy (𝑃𝐸):

𝑃𝐸 = 𝑚𝑔ℎ

Mechanical Energy (𝑀𝐸):

𝑀𝐸 = 𝐾𝐸 + 𝑃𝐸

Work (𝑊):

𝑊 = 𝐹 ⅆ 𝑐𝑜𝑠 𝜃 (𝐺𝑒𝑛𝑒𝑟𝑎𝑙 𝑙𝑎𝑤)

𝑊 = 𝛥𝐾𝐸 (𝑆𝑝𝑒𝑐𝑖𝑎𝑙 𝑙𝑎𝑤 𝑜𝑓 𝑡𝑜𝑡𝑎𝑙 𝑚𝑒𝑐ℎ𝑎𝑛𝑖𝑐𝑎𝑙 𝑤𝑜𝑟𝑘)

𝑊 = −𝛥𝑃𝐸 (𝑆𝑝𝑒𝑐𝑖𝑎𝑙 𝑙𝑎𝑤 𝑜𝑓 𝑐𝑜𝑛𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑣𝑒 𝑓𝑜𝑟𝑐𝑒 𝑤𝑜𝑟𝑘)

𝑊 = 𝛥𝑀𝐸 (𝑆𝑝𝑒𝑐𝑖𝑎𝑙 𝑙𝑎𝑤 𝑜𝑓 𝑛𝑜𝑛 − 𝑐𝑜𝑛𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑣𝑒 𝑓𝑜𝑟𝑐𝑒 𝑤𝑜𝑟𝑘)

Power (𝑃):
𝑊
𝑃=
𝛥𝑡




Notes:

① Conservative forces convert kinetic energy into potential energy.

Example: Gravity

② Non-conservative forces convert kinetic energy into different forms of energy, such as heat, sound, and
light.

Example: Friction

③ If a system is conservative, then:

𝑀𝐸 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡

④ For any object moving at a constant speed, the total work done on it is equal to zero.

, Second: Examples:

1. Alex pulls a box of mass (20𝑘𝑔) a distance of (5𝑚) on a smooth horizontal surface using a rope inclined
at an angle of (37°) to the horizontal. Given that the tension force in the rope is (140𝑁), calculate the
following:

a) The work done by Alex on the box.
Ftension
b) The work done by the force of gravity on the box.

c) The Alex's power, noting that he needed three seconds to move the box.
37
d
Given: 𝑚 = 20𝑘𝑔 , ⅆ = 5𝑚 , 𝜃 = 37° , 𝐹𝑡𝑒𝑛𝑠𝑖𝑜𝑛 = 140𝑁 , 𝛥𝑡 = 3𝑠

Required: 𝑊𝑡𝑒𝑛𝑠𝑖𝑜𝑛 , 𝑊𝑔 , 𝑃𝐴𝑙𝑒𝑥

Solution:

a)

𝑊𝑡𝑒𝑛𝑠𝑖𝑜𝑛 = 𝐹𝑡𝑒𝑛𝑠𝑖𝑜𝑛 ⅆ 𝑐𝑜𝑠 𝜃

= 140 × 5 × 𝑐𝑜𝑠 37

= 560𝐽

b) First, we calculate the force of gravity (weight):

𝐹𝑔 = 𝑚𝑔 = 20 × 10 = 200𝑁


d
Now we calculate the work done by the force of gravity:
90
𝑊𝑔 = 𝐹𝑔 ⅆ 𝑐𝑜𝑠 𝜃

= 200 × 5 × 𝑐𝑜𝑠 90 = 0 Fg

► Conclusion: Any force perpendicular to the direction of motion has work done by it equal to zero.



c)
𝑊𝑡𝑒𝑛𝑠𝑖𝑜𝑛
𝑃𝐴𝑙𝑒𝑥 =
𝛥𝑡
560
=
3
= 186.67𝑤𝑎𝑡𝑡