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Reference measurement conversions and formulas:
Pounds to Newtons:
Newtons = pounds x 4. (there are 4.45 N in a Lb)
Kilograms to Newtons:
Newtons = mass ( in kg) x gravity (9.8 m/s 2 on Earth) (This is just Newton’s 2nd^ Law: F=ma !)
Pounds to kilograms: Kilograms =^ Pounds 2.2^ (there are 2.2 Lbs in each Kg)
potential energy
gPE = mass x gravity x height
(Joules) (kg) (9.8 m/s^2 ) (m)
gPE = weight x height
(Joules) (N) (m)
kinetic energy
(kg) (m^ / (^) s)
KE = m ass X v elocity^2
(Joules) 2
momentum p^ =^ m ass x^ v elocity
(kg•m/ s ) (kg) (m^ / s)
The Law of Conservation of Energy and Momentum (LoCoE)
Energy (momentum, too) cannot be created or destroyed but it can be transformed from one form to another (CHEMNRS). Energy and Momentum must be conserved… Every amount must be accounted for in any system!
The Rules of Engagement: SOP-Standard Operating Procedures
- Use your own paper so you can use plenty of space and be neat.
- Always begin your calculations by writing the appropriate formula.
- Algebraically change the formula if that’s required…show this rewritten formula, too.
- Plug all the necessary numbers and UNITS of measurement into the formula.
- Do the calculation. Be very neat. Use plenty of space. Don’t crowd your work!
- Circle your answer with the appropriate units of measurement.
- Shortcuts will not be accepted. All work must be shown.
- A 10 kg object is sitting on a tall shelf at 1m above the floor. What is its gPE at 1 m?
gPE = mgh = (10kg)(9.8 m/ s^2 )(1m) = 98 J
At 2 m?
gPE = mgh = (10kg)(9.8 m/ s^2 )(2m) = 196 J
At 4 m?
gPE = mgh = (10kg)(9.8 m/ s^2 )(4m) = 392 J
At 8 m above the floor?
gPE = mgh = (10kg)(9.8 m/ s^2 )(8m) = 784 J
- A 5 kg cat is in a tree 5 meters above the ground. What is his gPE?
gPE = mgh = (5kg)(9.8 m^ / s^2 )(5m) = 245 J
What is his gPE if he doubles his height?
gPE = mgh = (5kg)(9.8 m^ / s^2 )(10m) = 490 J
- Cliff’s brother, Clyde, is also an accomplished Missouri cliff diver. To what height does Clyde cautiously climb the cliff at Johnson Shut-ins if his initial gPE is 50,000 J and his mass is 80 kg?
gPE = mgh h = gPE = __50,000 J = 63.78 m
mg (80kg) (9.8 m^ / (^) s^2 )
- Cliff and Clyde have another brother named Clive, who is afraid of heights, but wants to become a cliff diver like his clever older brothers. From what height does Clive dive if his mass is 60 kg and his initial gPE is 588 J?
gPE = mgh h = gPE = __588 J = 1.00 m
mg (60kg) (9.8 m^ / (^) s^2 )
- The cliff diving Cleaver clan, Cliff, Clyde and Clive, have a younger brother named Clarence who claims to be able to clamber to a height of 20 m in less than 60 seconds before diving into the water at Johnson Shut-ins. If his initial gPE is 14,700 J, what is his mass?
gPE = mgh m = gPE = __14,700 J = 75 kg
gh (9.8 m^ / (^) s^2 )(20m)
- The cliff diving Cleaver clan’s sister, Claire, who happens to be clairvoyant, cannot cliff dive today because she has a broken clavicle. Instead, she pushes her sister Clarise, who accidently bumps into baby Clementine, who then falls into the water at Johnson Shut-ins, from a height of 5 m. If Clementine’s mass is 10 kg, what is her initial gPE? (Don’t worry! Cousin Cletus was there to catch her.)
gPE = mgh = (10kg)(9.8 m/ s^2 )(5m) = 490 J
- A 50 kg object is traveling northeast with a initial velocity of 2 m^ /s. How much kinetic energy (KE) does the object have?
KE = m v^2
(50 kg)(2 m/s)^2 = (25kg)(4 m^2 / (^) s^2 ) = 100 J 2 2
At 4 m/ (^) s?
KE = m v^2
(50 kg)( 4 m/s)^2 = (25kg)(16 m^2 / (^) s^2 ) = 400 J 2 2
At 8 m/ (^) s?
KE = m v^2
(50 kg)( 8 m/s)^2 = (25kg)(64 m^2 / (^) s^2 ) = 1600 J 2 2
At 16 m/ (^) s?
KE = m v^2
(50 kg)(16 m/s)^2
= (25kg)(256 m^2 /s^2 ) = 6400 J
- What is the KE of a 2700 kg truck if it is traveling westbound on Highway 70 at a velocity of 15 m/ (^) s?
KE = m v^2
(2700 kg)(15 m/s)^2
= (1350kg)(225 m 2 / s^2 )
= 303,750 J
- What is the mass of a projectile traveling at a velocity of 50 m/ (^) s if its initial KE is 250,000 J?
KE = m v
2
m = 2(KE)
2 v
2
= 2 (250,000 J)
m
/s )
2
= 500,000 J
2500 m^2 /s^2
= 200 kg
- A 10 kg bowling ball is dropped from an unknown height but it achieves a velocity of 25 m^ / (^) s just as it contacts the ground below! Find the height from which it was dropped. (find the KE at impact…which equals the total initial gPE
KE = m v^2 = (10 kg)(25 m/ s) 2 = (5kg)(625 m^2 /s^2 ) = 3125 J
2 2
…use the formula for PE to get height)
gPE = mgh h = gPE = __3125 J = 31.89 m
mg (10kg) (9.8 m^ / (^) s^2 )
- Cliff Cleaver, the 70 kg cliff diver, completes a classic backward double tuck before striking the water at a velocity of 10 m/s. What was his KE at the moment of impact?
KE = m v^2 = (70 kg)(10 m/ s) 2 = (35kg)(100 m^2 /s^2 ) = 3500 J
What was his initial gPE?
KE = PE gPE = 3500 J
What was his initial height before diving?
gPE = mgh h = gPE = __3500J = 5.10 m
mg (70kg) (9.8 m^ / (^) s^2 )
- Claire Cleaver’s clavicle is now healed completely and she is back to cliff diving. Fortunately for her, she is claustrophobic, not acrophobic, because her first dive is from 30 meters. If she strikes the water at a velocity of 15 m/ (^) s and has 5625 J of KE at the moment of impact, what is her mass?
KE = m v
2
m = 2(KE)
2 v
2
= 2 (5625 J)
m
/s )
2
= 11,250 J
225 m^2 /s^2
= 50 kg
- A watermelon with a mass of 10,000 g (10kg) is dropped from a window 30 m above ground. At the precise moment of impact, what is the watermelon’s velocity?
KE = gPE = mgh = (10kg)(9.8 m^ / s^2 )(30m) = 2,940 J
KE = m v
2
v = 2(KE)
2 m
v = 2 (2,940 J)
(10 kg )
v =
J
/kg
v = 24.25 m^ / s
- The former Texas Ranger, Nolan Ryan, once pitched a baseball at 109 miles/hour (48.73 m^ / (^) s) during a major league game. If a typical baseball has a mass of 145 g (0.145 kg), what was the KE of Mr. Ryan’s pitched ball?
KE = m v^2 = (.145kg)( 48.73 m/s)^2 = (0.0725kg)(2374.6129 m2/s^2 ) 2 2
= 172.16 J
- A typical 9mm bullet (7.5 g) can travel at a velocity of 381 m^ / (^) s. What is the KE of a 9mm bullet as it travels through the air towards a paper target?
KE = m v^2 = (.0075kg)( 381 m/s)^2 = (0.0 0375 kg)(145,161 m2/s^2 )
2 2
= 544.35 J
- Please explain why the bullet has so much more KE than the baseball, despite its small mass.
Even though it has an extremely small mass, its velocity is significantly greater AND it gets squared by the formula.
- Which has more KE: an eagle flying at 5 m^ / (^) s or a honey bee flying at 5 m/ (^) s? Please explain your answer.
The eagle has more KE than a honey bee because the eagle has more mass.
- While Usain Bolt is running the 100 m dash, he maintains an average velocity of 10.43 m/ (^) s. If his mass is 94 kg, what is his momentum?
P = mv = (94 kg)( 10.43 m^ / (^) s) = 980.42 kg·m^ /s
- Scott Macartney, a former member of the American Olympic Ski team, once crashed while traveling at a velocity of 88 mi^ / (^) hr (39 m^ / (^) s). If his mass was 65 kg, what was his momentum at the moment he crashed?
P = mv = (65 kg)( 39 m^ / (^) s) = 2,535 kg·m/s
- A locomotive weighs 320,000 pounds. It’s traveling at a velocity of 5 m/ (^) s. How fast must a 1000 kg car be traveling to have the same momentum?
P = mv
320000 lbs ( 5 m/s) = 1000 kg ( V 2 )
(145,454.55 kg) ( 5 m/s) = V 2
1000kg
727.27 m^ /s = V (^2)
b. If every Joule of gPE is completely converted to KE at the moment of impact, what is Clyvan’s velocity as he hits the water?
KE = m v
2
v = 2(KE)
2 m
v = 2 (24,990 J)
(85 kg )
v =
J
/kg
v = 24.25 m^ / s
c. What is Clyvan’s total momentum at the moment of impact?
P = mv = (85 kg)(24.25 m^ / s) = 2,061.25 kg • m^ / s
