Question

A pinball machine launch ramp is constructed by placing a spring of force constant k at the bottom of a ramp of length L inclined at 30°. This is the second of three questions that refer to the pinball machine. What is the ball's speed immediately after being launched, given your answer to the first question?

answer was root mgL/k

* sqr root mgL/k

Answer 1

Answer Given, force Constant =k length of ramp L 0 30° H- height 11 Ħ We know from figure Sino = H 20 L sin 30° = HIL / Z H. H = 4/2 는 by Conservation of energy £ K x ² = mgh We know H =/ Į kx²= mg % 2 - mgL K xa ngh к

(W) stored in Potential energy spring = £ K x² This potential energy is converted into Kinetic Again using Conservation of energy ↑ K x ² = 1 mu? energy of ball! 11 Height of ramp = L singoo 4 I singo 2 30 so, K.E. of Ball = pie- of ball. I mv2 = mg L v² = g Ve VgL speed of ball is launched gL after being .