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**More EnergyPractice Problems**

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2. A 5000 kg coaster is released 20 meters above the ground on a frictionless track. What is the approximate speed at ground level? (point A) 7 m/s 10 m/s 14 m/s 20 m/s none of the above Adapted from Franklin/Beale CU Boulder From rest D KEf+PEf=KE0+PE0 so 1/2 m v2+0=0+mgh v=sqrt(2gh)=20m/s Velocity from PE 2

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**3. What is its approximate speed at 10 meters high (point B )?**

A) 7 m/s B) 10 m/s C) 14 m/s D) 20 m/s E) none of the above Adapted from Franklin/Beale CU Boulder C) 14 m/s KEf+PEf=KE0+PE0 so 1/2 m v2+mghf=0+mgh0 v=sqrt(2g(h0-hf))=14m/s 3

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**4. How fast would the coaster have to be going at the start to reach 21 meters high (point C)?**

A) m/s B) 3.2 m/s C) 4.5 m/s D) 20 m/s Adapted from Franklin/Beale CU Boulder C) 4.5 m/s KEf+PEf=KE0+PE0 0+mghf=1/2 mv02 + mgh0 so v0=sqrt(2g(h-h0))=4.5 m/s There are more questions in the folder called KineticPotential 4

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**5. Calculate velocity at B if h = 0.45 m, g = 10 m/s2 A) 3 m/s **

B) 4.5 m/s C) 7.5 m/s D) 9 m/s A h From Tanner/Dubson CU Boulder still no energy lost A Reference level (h = 0) B Pendulum speed 5

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**CQ1 PE to KE from Dubson/Tanner**

6. A block initially at rest is allowed to slide down a frictionless ramp and attains a speed v at the bottom. To achieve a speed 2v at the bottom, how many times higher must the new ramp be? A) B) 2 C) 3 D) 4 E) none of these. From Tanner/Dubson CU Boulder Answer: D. Using conservation of energy, we can write Ei = Ef. If we place the zero of height at the bottom of the ramp, we have.. mghtop = 1/2 mvbottom2 So, the initial height h is proportional to the final speed-squared, v2 . So to get twice the speed v, we need 4 times the height h. [Since (2v)2 = 4v2] ANSWER: D v CQ1 PE to KE from Dubson/Tanner 6

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6. A block initially at rest is allowed to slide down a frictionless ramp and attains a speed v at the bottom. To achieve a speed 2v at the bottom, how many times higher must the new ramp be? A) B) 2 C) 3 D) 4 E) none of these. mghtop + 0KE + 0work = 0PEg + 1/2 mvbottom2 First ramp: htop vbottom2 ANSWER: D 2nd ramp: h'top (2vbottom)2 = 4 (vbottom2) h'top = 4htop CQ 6 Show work

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**1. What will the speed of the 75kg Skater be at 2 seconds?**

Total =2918 J KE=509 J PE=2408 J PE = 0 at dotted line D This is the default track with the PE line moved up to the track A. 14m/s B. 8.8m/s C. 8.0m/s D. 3.7m/s ANSWER: D 8

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**Comments for question 1: This is the default track with the PE line moved up to the track**

14 is no sqrt 8 uses PE 8.8 uses Total E KE= 1/2mv2 509=1/2*75* v2 9

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**2. At what height is the 60kg Skater at 2 seconds?**

Total =3829 J KE=2429 J PE=1365 J ANSWER: C B I used the Double well roller coaster track with the Skater changed to the girl and I moved the PE line to the bottom of the first well. Then I started from the “Return Skater” position A. 6.5m B. 4.2m C. 2.3m D. 1.9m 10

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**6.5 uses Total E, 4.2 uses KE, 1.9 uses mass of 75,**

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**3. Draw what you think the energy graph look like at 10 seconds.**

I used the double well roller coaster again with a ball at 18 kg for #3 and #4 12

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A B C 3. The energy graph at 10 s: B ANSWER: B 10 13

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**4. What might the ball be doing at 5 seconds?**

Going left to right at the lower dip Going right to left at the lower dip Going left to right at the higher dip Going right to left at the higher dip B PE KE 15

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Answer to 4 16

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