Understanding the Solution to an AP Physics C Exam Problem

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The discussion centers on a specific problem from the 1982 AP Physics C exam regarding the behavior of a block connected to a spring. The key point of confusion was how the maximum speed of the block can occur while the spring is compressed, as it seems counterintuitive due to the opposing force exerted by the spring. It was clarified that the block continues to accelerate under the influence of its weight along the slope until the spring force balances it out. The relationship between the spring force and compression, as described by Hooke's law, plays a crucial role in understanding the dynamics involved. Ultimately, the misunderstanding was resolved, highlighting the importance of considering all forces acting on the block.
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[SOLVED] Help on an AP exam problem

I teach AP physics in high school and encountered this problem, from the 1982 AP Physics C exam. http://keydetpiper.com/Misc/1982C.html" has a link to the original problem (#2) and the official solution.

My question is regarding part c: how is it possible that the maximum speed happens as the spring is compressed? Seems to me that as soon as the spring is compressed it exerts a force on the block, and since that force will be in the opposite direction of the velocity it will create a negative acceleration. Am I missing something?
 
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As the solution states the block will still be subject to its weight acting along the slope and will thus still be accelerating until the force from the spring exactly cancels it. The force from the spring is dependent on how much the spring is compressed (i.e. F = -kx if it obeys Hooke's law).
 
Yeah, ok thanks. Don't know why I couldn't see it before... I was thinking it would start to slow down as soon as the spring starts putting a force on it. I get it now, thanks for your response!
 

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