Lecture_18_web_2007

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Unformatted text preview: Quiet please ladies and gentlemen The lecture is about to begin n M A box of mass M = 10 kg slides down a friction-less wedge with angle of incline θ = 30°. At the base of the wedge the box collides with a spring which compresses 10cm before the box stops moving, if the total distance the box slides is d = 2m . Q. What is the spring constant? Given: • M = 10kg • θ = 30° • d = 2m • x = 10cm Find: • k = ? θ ( 29 ( 29 g S g S i f KE PE PE KE PE PE + + = + + P E mgh = K E = 2 1 2 PS E kx = Initial state Final state K E = PS E = P E = 2 1 2 mgh kx = 2 2 mgh k x = ( 29 sin h d θ = ( 29 2 2 sin mgd k x θ = ( 29 ( 29 2 2 10 9.8 2sin 30 19600 0.1 N k m × × × ° = = h 2 d m = x Conservative systems with springs 2 y m F mg n R υ = + = ∑ A roller-coaster slides down from rest at A on a frictionless track. The radius of the curved path is R. Q. What is the minimum height h required, so that it does not does not fall at point B? h R Conservation of energy: problem solving ( 29 ( 29 B A KE PE KE PE + = + A PE mgh = 2 1 2 KE m υ = A: B: KE = 2 PE mg R = 2 1 2 2 m mg R mgh υ + = 2 m mg R υ = 2 gR υ = 1 2 2 gR g R gh + = 5 2 h R = B mg n +ve n = Friction • If you pull a sled to the top of a hill and there is friction between the sled and the ground, and you expend the...
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