2D Kinematics Problem w/ Coefficient of Friction?

AI Thread Summary
The discussion revolves around solving a physics problem involving a block sliding on a lab bench and encountering a rough patch. The key steps include determining the initial velocity of the block as it becomes a projectile after leaving the bench, using kinematic equations to find time and horizontal distance. The user struggles with calculating the coefficient of friction, needing clarification on the relationship between frictional force and initial velocity. There is a reminder that there is no acceleration in the horizontal direction, which is crucial for solving the problem correctly. The conversation emphasizes the importance of understanding the physics concepts involved to arrive at the solution.
charliexx09
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I'm really lost on how to do this physics problem because I don't really understand all the components of the problem:

A 7.25 kg block is sliding at 5.45m/s on a frictionless lab bench which is 8.6m high. The block hits a 1m "rough patch" before sliding off of the lab bench, and then lands 1.2m from the edge of the bench. What was the coefficient of friction between the block and the rough patch?

If you could show your work or explain how to do this it would be really helpful. Thank you! Also, this is my first post on the forums! :smile:
 
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Ok, this is actually a really nice question! It provides a good mix between projectiles and Newton's laws.

Here's a tip reverse engineer the projectile problem to find the initial velocity of the projectile.
Then work on the part before the rough patch!
 
How should I determine the initial velocity of the projectile if all that is given is is the distance in x & y and the acceleration? This leaves Time, Vi & Vf unknown?
 
Here's a tip, Uy = 0 m/s

U = Viy
 
Okay, here is my process so far:
I know that d= Vi*t + (0.5)(a)(t^2), so
-8.6= -4.9t^2
t= 1.325
Then, I plugged this into the equation for the horizontal
1.2=Vi(1.325) + (-4.9)(1.325)^2
So, Vi=7.398 m/s
This is where I am really stuck seeing as I was always bad at figuring out the coefficient of friction (I've only been doing Physics for a few months!). I know that Force of Fric= u*Fnormal ... is the force of friction here the same as the initial velocity? Thanks for all your help Darth Frodo :)
 
Then, I plugged this into the equation for the horizontal1.2=Vi(1.325) + (-4.9)(1.325)^2

This is wrong I'm afraid, remember there is no acceleration in the x direction.

What the answer at the back of the book?
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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