- #1
stormgren
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[SOLVED] A block hits a patch of friction
A block of uniform density, length L and height h << L, starts from rest at the top of a hill of height H, slides down. At the bottom there is a flat surface of length greater than L, and then a rough patch with sliding coefficient [tex]\mu[/tex]
I figured out the first part, which is to find the height such that the block comes to a stop the instant the entire block is on the rough surface. The answer is [tex]Hcrit=\frac{L\mu}{2}[/tex] Is this right?
Now I need to find what happens if the hill has a height H < Hcrit.
I think the block still has follows simple harmonic motion, and obviously from conservation of energy it has a speed [tex]\sqrt{2gH}[/tex] at the bottom of the hill, but for some reason I'm having huge trouble finding the distance that the leading edge of the block travels across the surface with friction before it comes to a stop.
I don't know where to go from here. Some hints, please? :)
A block of uniform density, length L and height h << L, starts from rest at the top of a hill of height H, slides down. At the bottom there is a flat surface of length greater than L, and then a rough patch with sliding coefficient [tex]\mu[/tex]
I figured out the first part, which is to find the height such that the block comes to a stop the instant the entire block is on the rough surface. The answer is [tex]Hcrit=\frac{L\mu}{2}[/tex] Is this right?
Now I need to find what happens if the hill has a height H < Hcrit.
I think the block still has follows simple harmonic motion, and obviously from conservation of energy it has a speed [tex]\sqrt{2gH}[/tex] at the bottom of the hill, but for some reason I'm having huge trouble finding the distance that the leading edge of the block travels across the surface with friction before it comes to a stop.
I don't know where to go from here. Some hints, please? :)