YS 211 Summer17-STINNETT I Activities and Due Dates | HW: Potential Energy and E

Question

YS 211 Summer17-STINNETT I Activities and Due Dates | HW: Potential Energy and Energy Conservation 7/17/2017 10:00 PM 28.6/100 -Print calalator-Periodic Table uestion 5 of 14 Ma Sapling Learning Tom has built a large slingshot, but it is not ideal spring, with a spring constant of 65.0 N/m. When he pulls the stretched position, it just doesn't launch its payload as far as he wants, His physics professor "helps" telling him to aim for an elastic potential with a higher spring constant. By what factor does Tom need to increase the spring constant to hit his quite right. He thinks he can model the slingshot like an back 0.515 m from a non- of 19.5 Joules. Tom decides he just needs elastic bands potential energy goal? Number During a followup conversation, Tom's physics professor suggests that he should leave the slingshot alone and try pulling the slingshot back further before must without changing the spring constant. How many times further than Number In which of the two scenarios does Tom have to pull harder? O Increased Pullback Distance O They Are Equal O Increased Spring Constant Previous O Check Answer 0 Next D e

Explanation / Answer

U = targeted elastic potential energy = 19.5 J

x = stretch of the spring = 0.515 m

k' = spring constant required

Using the equation

U = (0.5) k' x2

19.5 = (0.5) k' (0.515)2

k' = 147 N/m

when the sligshot is kept same :

U = targeted elastic potential energy = 19.5 J

x' = stretch of the spring = ?

k = spring constant = 65 N/m

Using the equation

U = (0.5) k x'2

19.5 = (0.5) (65) x'2

x' = 0.775 m

Ratio = x'/x = 0.775/0.515 = 1.5

hence stretch of the spring is 1.5 times

The pulling force is given as

F = kx

in case 1 : F = k' x = 147 x 0.515 = 75.71 N

in case 2 : F = k x' = 65 x 0.0.775 = 50.4 N

clearly , tom has to pull harder in case where spring constant is increased

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