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n.mastering physics.com/myct/itemView?assignmentproblemID-8131 7914&offsets; next CH 10 HW Problem 10.43 previous l 12 of 17 Inet » Problem 10.43 Part A You have been hired to design a spring-launched roller coaster that will carry two passengers per car. The car goes up a 10-m-high hill, then descends 20 m to the track's lowest point. You've What spring constant should you specity? Express your answer to two significant figures and include the appropriate units ing c k= 2.5x104 maximum of 2.0 m and that a loaded car will have a maximum mass of 450 kg For safety reasons the spring constant should be 15 % larger than the minimum needed for the car to just make it over the top. Correct Part B What is the maximum speed of a 350 kg car if the spring is compressed the full amount? Express your answer to two significant figures and include the appropriate units. aliie Submit My Answers Give Up Incorrect; Try Again: 3 attempts remaining

Explanation / Answer

Given,

h = 10 m ; x = 20 m ; m = 450 kg ;

a)The gravitational PE is:

PE = m g h = 450 x 9.8 x 10 = 44100 J

PE(spring) = 1/2 k x^2

1/2 k x^2 = 44100

k = (2 x 44100/x^2) = sqrt (2 x 44100/2^2) = 22050

15% extra

k = 1.15 x 22050 = 2.54 x 10^4 N/m

Hence, k = 2.54 x 10^4 N/m

when fully compressed, the elastic potential energy stored in the spring

PE = k d^2/2

PEspring = 2.54 x 10^4 x 2^2/2 = 5.08 x 10^4 J

delta h = 20 - 10 = 10 m

PE = m g delta h = 450 x 9.8 x 10 = 44100 J

total energy

TE = 5.04 x 10^4 + 4.41 x 10^4 = 9.49 x 10^4

this is equal to KE

1/2 m v^2 = 9.49 x 10^4

v = sqrt (2 x 9.49 x 10^4/450) = 20.54 m/s

Hence, v = 50.54 m/s

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