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- Homework Statement
- I am currently writing a paper on conservation of energy in which I dropped a ball and calculated potential and kinetic energy. The issue I am having is that I have no idea how to incorporate drag force into my equations for P and K energy and also into my uncertainties. I have been looking every where for answers but cannot seem to find them. Please help!

- Relevant Equations
- Ke+Pe=Ke+Pe

Ke= 1/2 mv^2

Pe= mgh

1. Golf ball initial potential energy uncertainty (110-5kg 0.01 m 0.01m/s2)= 110-9J4.31210-5=4.31210-14j

2. Golf ball initial potential energy calculation (4.4 x10-4kg 9.8 m/s2 0.609 m)= 4.31210-54.31210-14j

3.Golf ball final potential energy uncertainty ( 110-5kg 0.0 m0.01 m/s2)= 0.0 J

4. Golf ball final potential energy calculation (4.4 x10-4kg 9.8 m/s2 0.0 m)= 0 0J

5. Initial velocity of golf ball Vi=dt → Vf=0.0m0.0 seconds =0m/s0J

6. Kinetic energy of golf ball initial calculation 1/2(4.4 x10-4kg0 m/s2)= 00 J

8. Final Kinetic energy of golf ball calculation 1/2(4.4 x10-4kg1.353 m/s2)= 4.0210-4 0.120 J

Final velocity of the golf ball uncertainty Vf uncertainty= 0.01m0.609m+0.01 seconds0.45 seconds=0.386 m/s

9. 1/2(4.4 x10-4kg1.353 m/s)= 4.0210-42.4710-5 J

10. Final kinetic energy uncertainty of the golf ball

((110-5kg4.410-4g)2+(20.0386m/s1.353m/s)2= 6.1410-2 x 4.0210-4 J=2.4710-5J

11. Initial Kinetic energy of golf ball calculation 1/2(4.4 x10-4kg0m/s2)=00 J

12. Initial kinetic energy uncertainty of the golf ball (110-5kg4.410-4g)2+(20.0m/s0.0m.s)2= 0.00 x 0.00 J=0.00J

13. Conservation of energy calculation

4.31210-54.31210-14J=4.0210-42.4710-5 J

14. Tennis ball initial potential energy uncertainty (110-5kg 0.01 m 0.01m/s2)= 110-9J3.2810-4J=3.2810-12j

15. Tennis ball initial potential energy calculation (5.5 x10-4kg 9.8 m/s2 0.609 m)=3.28210-33.2810-12J

16.Tennis ball final potential energy uncertainty ( 110-5kg 0.0 m0.01 m/s2)= 0.0 J

17. Tennis ball final potential energy calculation (5.5 x10-4kg 9.8 m/s2 0.0 m)= 0 0J

18. Initial velocity of golf ball Vi=dt → Vf=0.0m0.0 seconds =0m/s0J

Final velocity of golf ball Vi=dt → Vf=0.609m0.47 seconds =1.295 m/s

19. Kinetic energy of golf ball initial calculation 1/2(3.28 x10-4kg0 m/s2)= 00 J

20. Final Kinetic energy of golf ball calculation 1/2(5.5 x10-4kg(1.295 m/s)2)=4.6110-42.7610-5J

21. Final velocity of the tennis ball Vf = 0.609m0.47s=1.296m/s

22. Final velocity of the tennis ball uncertainty Vf uncertainty= 0.01m0.609m+0.01 seconds0.47 seconds=0.037 m/s

23. Final kinetic energy uncertainty of the tennis ball

((110-5kg5.510-4g)2+(20.037m/s1.29m/s)2= 5.9910-2 x 4.6110-4J=2.7610-5J

24. Initial Kinetic energy of tennis ball calculation 1/2(5.5 x10-4kg0m/s2)=00 J

25. Initial kinetic energy uncertainty of the tennis ball (110-5kg5.510-4g)2+(20.0m/s0.0m.s)2= 0.00 x 0.00 J=0.00J

26. Conservation of energy tennis ball drop

3.28210-33.2810-12J = 4.6110-42.7610-5J

2. Golf ball initial potential energy calculation (4.4 x10-4kg 9.8 m/s2 0.609 m)= 4.31210-54.31210-14j

3.Golf ball final potential energy uncertainty ( 110-5kg 0.0 m0.01 m/s2)= 0.0 J

4. Golf ball final potential energy calculation (4.4 x10-4kg 9.8 m/s2 0.0 m)= 0 0J

5. Initial velocity of golf ball Vi=dt → Vf=0.0m0.0 seconds =0m/s0J

6. Kinetic energy of golf ball initial calculation 1/2(4.4 x10-4kg0 m/s2)= 00 J

8. Final Kinetic energy of golf ball calculation 1/2(4.4 x10-4kg1.353 m/s2)= 4.0210-4 0.120 J

Final velocity of the golf ball uncertainty Vf uncertainty= 0.01m0.609m+0.01 seconds0.45 seconds=0.386 m/s

9. 1/2(4.4 x10-4kg1.353 m/s)= 4.0210-42.4710-5 J

10. Final kinetic energy uncertainty of the golf ball

((110-5kg4.410-4g)2+(20.0386m/s1.353m/s)2= 6.1410-2 x 4.0210-4 J=2.4710-5J

11. Initial Kinetic energy of golf ball calculation 1/2(4.4 x10-4kg0m/s2)=00 J

12. Initial kinetic energy uncertainty of the golf ball (110-5kg4.410-4g)2+(20.0m/s0.0m.s)2= 0.00 x 0.00 J=0.00J

13. Conservation of energy calculation

4.31210-54.31210-14J=4.0210-42.4710-5 J

14. Tennis ball initial potential energy uncertainty (110-5kg 0.01 m 0.01m/s2)= 110-9J3.2810-4J=3.2810-12j

15. Tennis ball initial potential energy calculation (5.5 x10-4kg 9.8 m/s2 0.609 m)=3.28210-33.2810-12J

16.Tennis ball final potential energy uncertainty ( 110-5kg 0.0 m0.01 m/s2)= 0.0 J

17. Tennis ball final potential energy calculation (5.5 x10-4kg 9.8 m/s2 0.0 m)= 0 0J

18. Initial velocity of golf ball Vi=dt → Vf=0.0m0.0 seconds =0m/s0J

Final velocity of golf ball Vi=dt → Vf=0.609m0.47 seconds =1.295 m/s

19. Kinetic energy of golf ball initial calculation 1/2(3.28 x10-4kg0 m/s2)= 00 J

20. Final Kinetic energy of golf ball calculation 1/2(5.5 x10-4kg(1.295 m/s)2)=4.6110-42.7610-5J

21. Final velocity of the tennis ball Vf = 0.609m0.47s=1.296m/s

22. Final velocity of the tennis ball uncertainty Vf uncertainty= 0.01m0.609m+0.01 seconds0.47 seconds=0.037 m/s

23. Final kinetic energy uncertainty of the tennis ball

((110-5kg5.510-4g)2+(20.037m/s1.29m/s)2= 5.9910-2 x 4.6110-4J=2.7610-5J

24. Initial Kinetic energy of tennis ball calculation 1/2(5.5 x10-4kg0m/s2)=00 J

25. Initial kinetic energy uncertainty of the tennis ball (110-5kg5.510-4g)2+(20.0m/s0.0m.s)2= 0.00 x 0.00 J=0.00J

26. Conservation of energy tennis ball drop

3.28210-33.2810-12J = 4.6110-42.7610-5J