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Physics question please help!?
you are playing a game at the carnival. you want to launch a puck of mass m up an incline by compressing a spring-loaded plunger with spring constant k. i you compress it the right amount, it reaches the cup at the puck's turning point and the puck falls into a cup at height h. compress too little, and the puck doesnt make it high enough. too much, and the puck overshoots the cup because is projects over the cup. the track is pretty much frictionless…except. uh-oh! Someone has spilled sticky soda on the flat part of the track. the stick patch has a lenght L and coefficient of kinetic friction muk. calculate how much you should compress the spring. express your answer in terms of some or all of k, h, g, L, muk and m. make sure your assumptions are clear
1 Answer
- jeffreyLv 79 years agoFavorite Answer
… the kinetic energy must be zero at the highest point reached s that its
final energy is purely gravitational potential … E = m g h … at the foot of the
incline, its total energy is purely kinetic … E₁ = ½ m v ² … since the incline is
frictionless … ½ m v ² = m g h … during compression of the spring at the
plunger, the total energy is E₀ = ½ k x ² … where … x = compression of the
spring … and because of the energy removed by friction along the sticky flat
track … E₀ = ½ k x ² > E₁ = ½ m v ² … but knowing the work W done by
friction … W = - μ m g L … we have by conservation of energy …
… E₀ + | W | = ½ k x ² + μ m g L = E₁ = ½ m v ² = m g h …
… k x ² + 2 μ m g L = 2 m g h ==> k x ² = 2 m g h ‒ 2 μ m g L
….………………………………………….. = 2 m g { h ‒ μ L }
… x ² = 2 m g { h ‒ μ L } / k = 2 ( m g / k ) { h ‒ μ L } …
… x = √ [ 2 ( m g / k ) { h ‒ μ L } ] …
