How Does Friction Impact Block Velocity in a Multi-Height Path?

AI Thread Summary
Friction significantly affects the block's velocity as it travels through the multi-height path. The initial speed at point A is 7.5 m/s, and the block encounters a friction coefficient of 0.70 over a 12 m section. The total mechanical energy must account for both kinetic and potential energy, with the equation K(@A) + U(@A) = K(@B) + U(@B) and K(@B) = U + K(@C) for subsequent points. The discussions clarify that the initial kinetic energy does not equal the potential energy at point B due to the influence of friction. Understanding the energy conservation principles is crucial for accurately determining the block's speeds at points B and C.
dominus96
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Kinetic Energy with diagram!

Homework Statement



In the figure below, a small block is sent through point A with a speed of 7.5 m/s. Its path is without friction until it reaches the section of length L = 12 m, where the coefficient of kinetic friction is 0.70. The indicated heights are h1 = 6.5 m and h2 = 1.6 m.

(a) What is the speed of the block at point B?
(b) What is the speed of the block at point C?

W0156A-N.jpg


Homework Equations



K=.5(mv^2)
U=mgh
F=ma
Friction force=mu*force normal

The Attempt at a Solution



First off, ignore the friction stuff because I already got those. I just need help with the 2 specific questions I listed. For a I did K=U so I set .5v^2=gh since the masses cancel out. But I got velocity and it was wrong...
 
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Ooo! I did this one a while back.

Ok the reason you missed the first one is because U @ point a does NOT equal K @ point B. U+K @ a does though. Don't forget it's initially moving.
 
So U+K(point A)=K(point B)?
 
what's point d in there for then, lol
 
It's for another part of the problem I already figured out so don't worry about it lol.
 
cooolio
 
indeed. the second question is similar. Energy total @ point b = energy total @ c

Ergo... K(@b)=U+K(@c)
 
Thanks!
 
Sure
 

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