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Determine from the following diagram a. The spring constant of the bowb. The Elastic Potential Energy storedc. What will be the initial velocity of the arrow once the bow is released?

Determine from the following diagram a. The spring constant of the bowb. The Elastic-example-1
User David Hammen
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1 Answer

16 votes
16 votes

F= 300 N

d = 0.6m

m = 30g = 0.03 kg

• a.

Apply Hooke's law formula:

F = k x

k= F/ x

Where:

k= spring constant

F= force = 300N

x = distance = 0.6 m

k = 300N/0.6m = 500N/m

• b.

PE = 1/2 k (x)^2

PE = 1/2 (500 N/m) (0.6)^2 = 90 J

• c.

KE = 1/2 m v^2

KE = kinetic energy = PE = potential energy

v = √KE/ (1/2*m) = √2KE/m = √ (2* 90 / 0.03 ) = 77.46 m/s

Answers:

a = 500 N/m

b= 90 J

C = 77.46 m/s

User Davidfurber
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