Conservation of Energy Block Problem

[GorgonSed]

Homework Statement

A 3.20 kg block starts at rest and slides a distance d down a frictionless 30.0° incline, where it runs into a spring (Fig. 8-6). The block slides an additional 20.5 cm before it is brought to rest momentarily by compressing the spring, whose spring constant k is 438 N/m.

(a) What is the value of d? (I solved this, 0.38196 Meters)

(b) What is the distance between the point of first contact and the point where the block's speed is greatest? (This is the issue)

The Attempt at a Solution

(b) What is the distance between the point of first contact and the point where the block's speed is greatest?
I thought that the point where the block had the greatest speed was actually right at the point described in the question, so I tried 0, but it was incorrect. I don't even know where to start, Help Please!

 

[dynamicsolo]

(b) What is the distance between the point of first contact and the point where the block's speed is greatest?
I thought that the point where the block had the greatest speed was actually right at the point described in the question, so I tried 0, but it was incorrect. I don't even know where to start, Help Please!

Yeah, at first glance, it seems like it ought to be the case that the greatest speed of the block is attained just as it hits the spring. But don't forget that the block is still descending as it compresses the spring. What does the function for velocity look like during this phase of the block's journey?

 

[Chi Meson]

I thought so to at first, but then...

look at the distance the block moves while compressing the spring. For at least a few centimeters the net force is still down-slope, so the block will still accelerate for a while after first contacting the spring. You need to find a point where the net force is zero.

Edit: Ye beat me to the punch there.

 

[GorgonSed]

Thanks guys I got it. It did keep accelerating, I forgot to consider that. If you want to know, the answer was 3.57991 cm

 

[Chi Meson]

Thanks guys I got it. It did keep accelerating, I forgot to consider that. If you want to know, the answer was 3.57991 cm

I got that too, but please, sig figs please, it's 3.58 cm.

 

[dynamicsolo]

Thanks guys I got it. It did keep accelerating, I forgot to consider that. If you want to know, the answer was 3.57991 cm

I'll comment here that spring-on-an-incline problems are an introductory physics exam favorite. The instructor gets to throw kinetic energy and two flavors of potential energy into the same problem. And the most frequent mistake students make on this sort of problem (among those who know what should be kept track of in the analysis) is forgetting that extra bit of gravitational potential energy released from the block(-Earth system) as the spring is compressed. (That's a ProTip! -- which I overlook myself from time to time...)