 #1
ET333
 1
 0
 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 (1105kg 0.01 m 0.01m/s2)= 1109J4.312105=4.3121014j
2. Golf ball initial potential energy calculation (4.4 x104kg 9.8 m/s2 0.609 m)= 4.3121054.3121014j
3.Golf ball final potential energy uncertainty ( 1105kg 0.0 m0.01 m/s2)= 0.0 J
4. Golf ball final potential energy calculation (4.4 x104kg 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 x104kg0 m/s2)= 00 J
8. Final Kinetic energy of golf ball calculation 1/2(4.4 x104kg1.353 m/s2)= 4.02104 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 x104kg1.353 m/s)= 4.021042.47105 J
10. Final kinetic energy uncertainty of the golf ball
((1105kg4.4104g)2+(20.0386m/s1.353m/s)2= 6.14102 x 4.02104 J=2.47105J
11. Initial Kinetic energy of golf ball calculation 1/2(4.4 x104kg0m/s2)=00 J
12. Initial kinetic energy uncertainty of the golf ball (1105kg4.4104g)2+(20.0m/s0.0m.s)2= 0.00 x 0.00 J=0.00J
13. Conservation of energy calculation
4.3121054.3121014J=4.021042.47105 J
14. Tennis ball initial potential energy uncertainty (1105kg 0.01 m 0.01m/s2)= 1109J3.28104J=3.281012j
15. Tennis ball initial potential energy calculation (5.5 x104kg 9.8 m/s2 0.609 m)=3.2821033.281012J
16.Tennis ball final potential energy uncertainty ( 1105kg 0.0 m0.01 m/s2)= 0.0 J
17. Tennis ball final potential energy calculation (5.5 x104kg 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 x104kg0 m/s2)= 00 J
20. Final Kinetic energy of golf ball calculation 1/2(5.5 x104kg(1.295 m/s)2)=4.611042.76105J
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
((1105kg5.5104g)2+(20.037m/s1.29m/s)2= 5.99102 x 4.61104J=2.76105J
24. Initial Kinetic energy of tennis ball calculation 1/2(5.5 x104kg0m/s2)=00 J
25. Initial kinetic energy uncertainty of the tennis ball (1105kg5.5104g)2+(20.0m/s0.0m.s)2= 0.00 x 0.00 J=0.00J
26. Conservation of energy tennis ball drop
3.2821033.281012J = 4.611042.76105J
2. Golf ball initial potential energy calculation (4.4 x104kg 9.8 m/s2 0.609 m)= 4.3121054.3121014j
3.Golf ball final potential energy uncertainty ( 1105kg 0.0 m0.01 m/s2)= 0.0 J
4. Golf ball final potential energy calculation (4.4 x104kg 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 x104kg0 m/s2)= 00 J
8. Final Kinetic energy of golf ball calculation 1/2(4.4 x104kg1.353 m/s2)= 4.02104 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 x104kg1.353 m/s)= 4.021042.47105 J
10. Final kinetic energy uncertainty of the golf ball
((1105kg4.4104g)2+(20.0386m/s1.353m/s)2= 6.14102 x 4.02104 J=2.47105J
11. Initial Kinetic energy of golf ball calculation 1/2(4.4 x104kg0m/s2)=00 J
12. Initial kinetic energy uncertainty of the golf ball (1105kg4.4104g)2+(20.0m/s0.0m.s)2= 0.00 x 0.00 J=0.00J
13. Conservation of energy calculation
4.3121054.3121014J=4.021042.47105 J
14. Tennis ball initial potential energy uncertainty (1105kg 0.01 m 0.01m/s2)= 1109J3.28104J=3.281012j
15. Tennis ball initial potential energy calculation (5.5 x104kg 9.8 m/s2 0.609 m)=3.2821033.281012J
16.Tennis ball final potential energy uncertainty ( 1105kg 0.0 m0.01 m/s2)= 0.0 J
17. Tennis ball final potential energy calculation (5.5 x104kg 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 x104kg0 m/s2)= 00 J
20. Final Kinetic energy of golf ball calculation 1/2(5.5 x104kg(1.295 m/s)2)=4.611042.76105J
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
((1105kg5.5104g)2+(20.037m/s1.29m/s)2= 5.99102 x 4.61104J=2.76105J
24. Initial Kinetic energy of tennis ball calculation 1/2(5.5 x104kg0m/s2)=00 J
25. Initial kinetic energy uncertainty of the tennis ball (1105kg5.5104g)2+(20.0m/s0.0m.s)2= 0.00 x 0.00 J=0.00J
26. Conservation of energy tennis ball drop
3.2821033.281012J = 4.611042.76105J