3/31/2017 10 00 PM o/100 Print calculator Periodic Table Question 5 of 14 Gradeb

Question

3/31/2017 10 00 PM o/100 Print calculator Periodic Table Question 5 of 14 Gradebook Sapling Learning Tom has built a large suingshot, it is not working quite right. He thinks he can model the slingshot like an ideal spring, with a spring constant of 45.0 Nm. When he pulls the back 0.235 a non- stretched position, it just doesn't launch its payload as far as he wants. His physics professor helps with a higher spring constant. By what factor does Tom need to increase the spring constant to hit his potential energy goal? and try a conversation before pulling the back further that musttom pull the without changing the spring constant. How many times further than slingshot back to hit the potential energy goal with the original spring Number in which of the two scenarios does Tom have to pull harder? O Increased Spring Constant O They Are Equal O Increased Pullback Distance Hint O Previous e check Answer 0 Next Exit

Explanation / Answer

k = original spring constant = 45 N/m

n = factor by which the spring constant is increased

k' = new spring constant = nk = 45 n

x = expansion of spring = 0.235 m

U = energy stored in spring = 14.5 J

Energy stored in spring is given as

U = (0.5) k' x2

14.5 = (0.5) (45 n) (0.235)2

n = 11.7

x' = new expansion of spring

k = spring constant = 45

Energy stored in spring is given as

U = (0.5) k x'2

14.5 = (0.5) (45 ) x'2

x' = 0.803 m

n = number of times the expansion increases = x'/x = 0.803/0.235 = 3.42

F = force when spring constant was increased = k' x = (45 x 11.7) (0.235) = 123.73 N

F' = force when expansion was increase = k x' = 45 (3.42 x 0.235) = 36.2 N

so Tom has to pull harder when spring constant is increased

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