Mass-spring system on an incline

AI Thread Summary
A mass-spring system is analyzed on a frictionless incline with a spring compressed to 15 cm, a mass of 5.4 kg, and a spring constant of 565 N/m. The key equations involved are the potential energy (PE) of the spring and the kinetic energy (KE) of the mass, represented as PE=1/2kx^2 and KE=1/2mv^2. To find the velocity of the mass as it leaves the spring, the conservation of energy principle is applied, equating PE to KE. After determining the initial velocity, the acceleration due to gravity on the incline is used to calculate the maximum height the mass will reach. This approach effectively combines energy conservation with kinematic equations to solve the problem.
easchwen
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Homework Statement


A spring is mounted at an angle of = 38 on a frictionless incline as illustrated in the figure below. The spring is compressed to 15 cm where it is allowed to propel a mass of 5.4 kg up the incline. If the spring constant is 565 N/m, how fast is the mass moving when leaves the spring? To what maximum distance from the starting point will the mass rise up the incline?


Homework Equations


PE=1/2kx^2 and KE=1/2mv^2



The Attempt at a Solution


I honestly don't know. I tried using PE=KE with the formulas above, and then tried adding in the cos(38) to the KE side, but I could not get the correct answer. Help?
 
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easchwen said:

Homework Statement


A spring is mounted at an angle of = 38 on a frictionless incline as illustrated in the figure below. The spring is compressed to 15 cm where it is allowed to propel a mass of 5.4 kg up the incline. If the spring constant is 565 N/m, how fast is the mass moving when leaves the spring? To what maximum distance from the starting point will the mass rise up the incline?


Homework Equations


PE=1/2kx^2 and KE=1/2mv^2



The Attempt at a Solution


I honestly don't know. I tried using PE=KE with the formulas above, and then tried adding in the cos(38) to the KE side, but I could not get the correct answer. Help?


Hi, I am no expert ,but i think you solve for v like you did with PE=KE, and that equla that initial velocity of the mass leaving the spring. After you get that, you use the incline formula for acceleration: ma = -mgsin38, so, a = -gsin38. Then The object reaches a max height so V2 = 0: V2^2 = V1^2 + 2ax, and solve for x!

Hope this helps:)
 
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