How Far Up the Incline Does the Object Travel Before Sliding Back Down?

[vrobins1]

Homework Statement

A spring with k = 40.0 N/m is at the base of a frictionless 30.0° inclined plane. A 0.50 kg object is pressed against the spring, compressing it 0.4 m from its equilibrium position. The object is then released. If the object is not attached to the spring, how far up the incline does it travel before coming to rest and then sliding back down?

Homework Equations

I tried to use the formula (1/2)kx²=mgh

The Attempt at a Solution

I tried (1/2)(40)(.4)²=.5(9.8)h, solving for h.

The first time I worked it out, I got h=.65306. I tried entering .65, .653, .7 3 separate times into my homework website, and they were all incorrect. I tried working the problem out again, and got h=15.68. I tried submitting 15.7 and 16 as answers, and they were both incorrect as well.
If anyone can offer any insight, it would be greatly appreciated. Thanks!

 

[alphysicist]

Hi vrobins1,

You were on the right track when you found the first answer for h. However, they want the distance along the incline. What does h represent, and how is that related to the distance traveled along the incline? Once you answer those questions I think you'll get the right answer.

 

[baba89]

As a scientist, it is important to first check your calculations and make sure they are correct. In this case, your first attempt at solving for h using the formula (1/2)kx^2=mgh was incorrect. The correct equation to use in this scenario is (1/2)kx^2=mghcosθ, where θ is the angle of the inclined plane. In this case, θ = 30°.

Using this equation, we can solve for h as follows:

(1/2)(40)(0.4)^2 = (0.5)(9.8)hcos30°

h = (0.08 x 2)/(0.5 x 9.8 x cos30°)

h = 0.163 m

Therefore, the object will travel 0.163 m up the incline before coming to rest and sliding back down. It is important to note that this calculation assumes ideal conditions, such as a frictionless inclined plane and no air resistance. In reality, the object may not travel exactly 0.163 m due to factors such as friction and air resistance.