Calculating Acceleration on an Inclined Ramp with Kinetic Friction

AI Thread Summary
To calculate the acceleration of a package on an inclined ramp with kinetic friction, the forces acting on the package must be analyzed. The relevant equations include the sum of forces parallel to the incline, which accounts for gravitational force and friction. The coefficient of kinetic friction, given as 0.30, is essential for determining the frictional force in relation to the normal force. The discussion emphasizes the need to express friction in terms of the normal force to solve for acceleration effectively. Understanding these dynamics is crucial for determining the initial speed required for the package to reach the top of the ramp and its speed when sliding back down.
ccarlson_07
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I am very confused about this problem. The given info is:
You are standing at the bottom of an 8 m long ramp that is incline 37 degrees to above the horizontal. You grab a package from a conveyer belt and push it up the ramp. The coefficient of kinetic friction is 0.30
The questions:
1. What speed do you need to give the package at the bottom of the ramp so it has zero speed at the top?
2. If the person does not grab the package at the top of the ramp and it slides back down what speed will it return to you?

So far I have drawn a free body diagram w/ x-axis parallel to the incline.
I have sum(F(x))=F-mgsin37-F(f)=ma
sum(F(y))=N-mgcos37=ma
I get F=-1.93*m+1.3*N
How do I solve for acceleration? Where do I go from here?
 
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ccarlson_07 said:
I have sum(F(x))=F-mgsin37-F(f)=ma
What's "F"? There are only two forces acting on the package parallel to the ramp. Hint: Express friction in terms of the normal force.
 
Ah ha! I see, it makes a lot more sense now! Thanks!
 
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