1. A 500-kilogram car is driving at 15 meters/second. What's its kinetic energy? How much does the car weigh?

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1 9. Solution Work & Energy Homework - KINETIC ENERGY. A 500-kilogram car i driing at 5 meter/econd. What' it kinetic energy? How much doe the car weigh? m= 500 kg 5 m/ Write Equation: Kinetic Energy = ½ m Plug in Value: K. E. = ½ m = ½ (500 kg) (5 m/) = 56,50 kg m / = 56,50Nm =56,50 J. A low moing car may hae more kinetic energy than a fat moing motorcycle. How i thi poible? Logic the low moing car ha a large ma, which contribute to it Kinetic Energy. The ma of the car can be great enough that it ha a greater Kinetic Energy than the lighter motorcycle. 3. The aircraft carrier Nimitz ha a fully loaded ma of kg. It trael a ditance of 08 kilometer in 3.5 hour. What i the kinetic energy (in Joule) of the Nimitz? We mut firt calculate the elocity of the hip from the definition of elocity. 08km,000m hr 6.5m / t 3.5hr km 3,600 m= kg 6.5 m/ Write Equation: Kinetic Energy = ½ m Plug in Value: K. E. = ½ m = ½ ( kg) (6.5 m/) = Nm = J 4. Let ay the Nimitz i traeling at a elocity of 5 m/ and it accelerate up to a elocity of 6 m/. (Ue the ma from aboe) a. What i the difference in Kinetic Energy of for the two elocitie? b. How much Energy mut be added in the form of work to accelerate the hip from 5 m/ to 6m/? m= kg 5 m/ 6 m/ Logic The work done on the car caue an increae in kinetic energy and therefore an increae in the kinetic energy. Thi mean that W = ΔKE. The change in elocity can be plugged into the Kinetic Energy Formula to calculate thi. W = ΔKE Write Equation: Change in Kinetic Energy = {KE KE }= m m = m

2 Plug in Value: m 7 m m = (8.350 kg ) 6 5 = J 5. What happen to the Kinetic Energy of a moing object if it ma i doubled? Logic here we need to aign ome ariable ince we hae no number. We know that the elocity doe not change, o it will be gien the ame ariable in both State and State. The ma i doubled, o in State m will be twice the ma in State. Lit of Variable: State State m = m m = m = = Write Equation: Kinetic Energy = ½ m A ratio will be et up to compare State and State KE KE / / m m cancel out like term / m / m Thi mean that the energy in tate i twice that of tate or there i twice a much energy for an object twice a maie with the ame elocity. 6. What happen to the Kinetic Energy of an object if it elocity i doubled? Logic here we need to aign ome ariable ince we hae no number. We know that the ma doe not change, o it will be gien the ame ariable in both tate and tate. The elocity i doubled, o in tate m will be twice the ma in tate. Lit of Variable: State State m = m m = m = = Write Equation: Kinetic Energy = ½ m A ratio will be et up to compare State and State / m KE / m 4 KE / m / m

3 cancel out like term / m4 4 / m 7. The dinoaur Tyrannoauru re i thought to hae had a ma of about 7000 kilogram. What i the dinoaur kinetic energy if it walk at 4 kilometer/hour. We mut firt calculate the elocity of the dinoaur by conerting to m/. 4km,000m hr.m / t hr km 3,600 m= 7,000 kg. m/ Write Equation: Kinetic Energy = ½ m Plug in Value: K. E. = ½ m = ½ (7,000 kg) (.m/) = 4,35 Nm = 4,35 J 8. An aerage peron ha a ma of 70 kilogram. How fat mut an aerage peron moe to hae the ame kinetic energy a the T. re? KE = 4,35 Joule m= 70 kg? m/ Write Equation: Kinetic Energy = ½ m Sole for Appropriate Variable: KE m Plug in Value to get : m/ (alue plugged in not hown, you mut how it) 9. A baeball leae a pitcher hand at a peed of 3 m/. The ma of the ball i.45 kg. How much work ha the pitcher done on the ball? Logic here we mut apply the LAW OF CONSERVATION OF ENERGY. The kinetic energy the ball ha when it i moing wa created by the work done on the ball by the pitcher. He had to apply a force oer a ditance to the ball. So if we know the Kinetic Energy of the ball it will be equal to the work done on the ball. Notice alo that we can aume the initial kinetic energy of the ball wa zero. Written out mathematically thi i: So E = W= ½ m E + W = E 0

4 m=.45 kg 3 m/ Plug in Value: K. E. = ½ m = ½ (.45 kg) (3m/) = 74. Nm = 74. J 0. A 4,000 kilogram car i traeling at a elocity of 30 meter/econd. It accelerate to 40 meter per econd. How much work mut the engine do to increae the elocity of the car from 30 meter/econd to 40 meter/econd? m= 4,000 kg 30 m/ 40 m/ Logic The work done on the car caue an increae in kinetic energy and therefore an increae in the kinetic energy. Thi mean that W = ΔKE. The change in elocity can be plugged into the Kinetic Energy Formula to calculate thi. W = ΔKE Write Equation: Kinetic Energy = ½ m Plug in Value: K. E. = ½ m = ½ (4,000 kg) (0m/) = 00,000 Nm = 00,000 J. A PRACTICAL PROBLEM - Let try a quetion imilar to number 3 & 0 with ome real number and compare the Energy required to accelerate a light car and heaier car the ame amount. An aerage car ha a ma of 00 kg (The Phyic Factbook). The car of the mallet ma hae a ma of 990 kilogram while the heaier car hae a ma around 000 kilogram. An aerage gallon of ga ha 5 million joule of Energy and cot about $.30 /gallon. A) How many Joule are required to accelerate each ehicle from 0 mph to 30 mph (3.4 m/) B) By what factor are thee alue different? C) How many gallon of ga doe each require? D) How many $ doe each require? The Kinetic Energy the car hae after accelerating originate in the gaoline. The Kinetic Energy can be calculated eaily: K. E. = ½ m K. E. = ½ m = ½ (990 kg) (3.4 m/) = 88,88 J = ½ (000 kg) (3.4 m/) = 79,560 J The factor between thee i the ratio of the mae. So the fuel conumption i directly related to the ma of the car. Conerion to Gallon 88,88J gallon Conerion to $.007 gallon =.007 gallon 79,560J 5,000,000 gallon =.04 gallon 5,000,000 $.30 =.06 $$.04 gallon $.30 =.03 $$ gallon gallon

5 KINETICE ENERGY QUESTIONS. The pring contant for a particular pring i 0 N/m. How much energy i tored in the pring if it tretched. meter? k= 0 N/m =. meter =? Write Equation: k Plug in Value: k = ½ ( 0 N/m) (.m) =. Joule 3. If a pring i tretched twice a much will it contain twice a much Spring Energy? If not, by what factor doe the Energy increae? Lit of Variable: State State = = Write Equation: k A ratio will be et up to compare State and State / k / k 4 / k / k cancel out like term / / k 4 4 k 4. If you want to increae the elatic potential energy of a pring by a factor of, by what factor mut you increae the tretch of the pring? Lit of Variable: State State = E = E Write Equation: k A ratio will be et up to compare State and State

6 Sole for f / k / k / k / k f f f f f 5. If you want to increae the elatic potential energy of a pring by a factor of 3, by what factor mut you increae the tretch of the pring? By the ame logic preented in # 4, the factor will be 3

7 GRAVITATIONAL POTENTIAL ENERGY QUESTIONS 6. An object with a ma of 0 kilogram i 5 meter aboe the ground. How much GPE doe it hae? m= 0 kg g 0m h = 5 m Write Equation: GPE = mgh Plug in Value: GPE = mgh = ( 0 kg) ( 0m ) ( 5 m) = 500 Joule. A refrigerator (00 kg) i lifted from the 30 th floor to the 34 th floor of a building (each floor i 3 meter). a. What i the increae in GPE of the refrigerator? b. How much work mut be done on the refrigerator to lift it thi far? m= 00 kg g 0m h = m Logic The ditance the object i lifted i h which repreent the change in the height. Write Equation: GPE = mgh Plug in Value: GPE = mgh = ( 00 kg) ( 0m ) ( m) =,000 Joule. How much work mut be done to moe the refrigerator from the 4 th floor to the 8 th floor? Logic Since the change in eleation and ma are the ame, the energy change i alo the ame a the preiou quetion.