Calculating Acceleration on an Inclined Ramp with Kinetic Friction

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SUMMARY

The discussion centers on calculating the acceleration of a package on an 8 m inclined ramp at a 37-degree angle with a coefficient of kinetic friction of 0.30. The user seeks to determine the initial speed required for the package to reach the top of the ramp with zero velocity and the speed at which it will return to the bottom if it slides back down. Key equations involve the forces acting on the package, including gravitational force components and friction, leading to the formulation of acceleration using Newton's second law.

PREREQUISITES
  • Understanding of Newton's second law of motion
  • Knowledge of free body diagrams and force analysis
  • Familiarity with the concepts of kinetic friction and normal force
  • Basic trigonometry for resolving forces on an incline
NEXT STEPS
  • Calculate the initial speed required using energy conservation principles
  • Explore the derivation of acceleration on an inclined plane with friction
  • Learn about the effects of varying coefficients of friction on motion
  • Investigate the dynamics of objects on inclined planes in different scenarios
USEFUL FOR

Physics students, educators, and anyone interested in understanding dynamics involving inclined planes and frictional forces.

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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