 # Power, work and Conservation of Energy discussion Anonymous

### Question Description

Questions that have answers, please let me know if they are right or wrong. If wrong give me the correct answer, if correct just say correct. physics_math_skills__.jpeg physics_diagram_skills_.jpeg physics_diagram_skills_2.jpeg physics_concept_skills_.jpeg

### Unformatted Attachment Preview

School: University of Maryland  Please find attached the solutions in word and PDF format. Please note both files are exactly same content-wise. Please let me know if you have any doubt.

Work
1. 𝑊𝑜𝑟𝑘 𝑑𝑜𝑛𝑒 𝑜𝑛 𝑡ℎ𝑒 𝑐𝑟𝑎𝑡𝑒 𝑏𝑦 𝑡ℎ𝑒 𝑎𝑝𝑝𝑙𝑖𝑒𝑑 𝑓𝑜𝑟𝑐𝑒 = 𝐹𝑑𝑐𝑜𝑠𝜃
𝐴𝑠 𝑎𝑝𝑝𝑙𝑖𝑒𝑑 𝑓𝑜𝑟𝑐𝑒 𝐹 𝑖𝑠 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 𝑡𝑜 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡, 𝑠𝑜 𝜃 = 0°
𝑠𝑜, 𝑊𝑜𝑟𝑘 𝑑𝑜𝑛𝑒 = 𝐹𝑑𝑐𝑜𝑠0° = 𝑭𝒅
All angels and components are shown in below diagram:

2. 𝐴𝑛𝑔𝑙𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑔𝑟𝑎𝑣𝑖𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 𝑎𝑛𝑑 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 = 90° + 30° = 120°
𝑊𝑜𝑟𝑘 𝑑𝑜𝑛𝑒 𝑜𝑛 𝑡ℎ𝑒 𝑐𝑟𝑎𝑡𝑒 𝑏𝑦 𝑡ℎ𝑒 𝑔𝑟𝑎𝑣𝑖𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 = 𝐹𝑔 𝑑𝑐𝑜𝑠120° = 𝐹𝑔 𝑑(−0.5)
= −𝟎. 𝟓𝑭𝒈 𝒅
𝑠𝑜, 𝑊𝑜𝑟𝑘 𝑑𝑜𝑛𝑒 𝑜𝑛 𝑡ℎ𝑒 𝑐𝑟𝑎𝑡𝑒 𝑏𝑦 𝑡ℎ𝑒 𝑔𝑟𝑎𝑣𝑖𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 = −𝟎. 𝟓𝒎𝒈𝒅
3. 𝐴𝑛𝑔𝑙𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑛𝑜𝑟𝑚𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 𝑎𝑛𝑑 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 = 90°
𝑊𝑜𝑟𝑘 𝑑𝑜𝑛𝑒 𝑜𝑛 𝑡ℎ𝑒 𝑐𝑟𝑎𝑡𝑒 𝑏𝑦 𝑡ℎ𝑒 𝑛𝑜𝑟𝑚𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 = 𝐹𝑛 𝑑𝑐𝑜𝑠90° = 𝐹𝑛 𝑑(0)
𝑠𝑜, 𝑊𝑜𝑟𝑘 𝑑𝑜𝑛𝑒 𝑜𝑛 𝑡ℎ𝑒 𝑐𝑟𝑎𝑡𝑒 𝑏𝑦 𝑡ℎ𝑒 𝑛𝑜𝑟𝑚𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 = 𝟎

4.

𝐴𝑛𝑔𝑙𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 𝑎𝑛𝑑 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 = 180°
𝑊𝑜𝑟𝑘 𝑑𝑜𝑛𝑒 𝑜𝑛 𝑡ℎ𝑒 𝑐𝑟𝑎𝑡𝑒 𝑏𝑦 𝑡ℎ𝑒 𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 = 𝐹𝑘 𝑑𝑐𝑜𝑠180° = −𝐹𝑘 𝑑
𝑠𝑜, 𝑊𝑜𝑟𝑘 𝑑𝑜𝑛𝑒 𝑜𝑛 𝑡ℎ𝑒 𝑐𝑟𝑎𝑡𝑒 𝑏𝑦 𝑡ℎ𝑒 𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 = −𝑭𝒌 𝒅

5. As mass doesn’t move perpendicular to ramp, so total force perpendicular to ramp is zero.
so, 𝑇𝑜𝑡𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 = 𝐹𝑜𝑟𝑐𝑒 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 𝑡𝑜 𝑟𝑎𝑚𝑝 = 𝐹 − 𝐹𝑘 − 𝐹𝑔 𝑠𝑖𝑛30° = 𝑭 − 𝑭𝒌 − 𝟎. 𝟓𝑭𝒈
𝑠𝑜, 𝑇𝑜𝑡𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 = 𝑭 − 𝑭𝒌 − 𝟎. 𝟓𝒎𝒈
6. As
𝑇𝑜𝑡𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 𝑖𝑠 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 𝑡𝑜 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡, 𝑠𝑜 𝑊𝑜𝑟𝑘 𝑑𝑜𝑛𝑒 𝑜𝑛 𝑡ℎ𝑒 𝑐𝑟𝑎𝑡𝑒 𝑏𝑦 𝑡ℎ𝑒 𝑡𝑜𝑡𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 =
( 𝐹 − 𝐹𝑘 − 0.5𝐹𝑔 )𝑑𝑐𝑜𝑠0° = ( 𝐹 − 𝐹𝑘 − 0.5𝐹𝑔 )𝑑 = ( 𝑭 − 𝑭𝒌 − 𝟎. 𝟓𝒎𝒈)𝒅
We can see that, this is equal to the sum of answers obtained in part 1. To part 4.

Energy
Please note, here, we have assumed that the block is at ground, which is considered as zero
gravitational potential energy level, so 𝑃𝐸 = 𝑃𝐸𝑔 + 𝑃𝐸𝑒 = 0 + 𝑃𝐸𝑒 = 𝑃𝐸𝑒
So, Potential Energy is just the potential ener...

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