Concept explainers
The coefficient of kinetic friction between the package and the inclined plane, so that the package reaches the bottom with no speed.
Answer to Problem 82QAP
The coefficient of kinetic friction between the package and the inclined plane, so that the package reaches the bottom with no speed is 0.382.
Explanation of Solution
Given info:
The mass of the package
Length of the inclined plane
Angle made by the plane to the horizontal
Initial speed of the package
Final speed of the package
Formula used:
A free body diagram of the package is drawn to analyze its motion.
Assume a coordinate system, with the +x directed downwards along the incline and +y directed upwards, perpendicular to the incline. The weight
Resolve the weight
The package is in equilibrium along the y direction.
Therefore,
Therefore, using equation (1),
The force of kinetic friction and the normal force are related according to the following equation:
From equation (2)
Write the force equation along the +x direction.
Use the values of wx and fk from equations (2) and (3) in the expression,
Simplify and write an expression for ax.
Use the following equation of motion with equation (4) to determine the coefficient of kinetic friction.
Calculation:
Use the values of the variables in equation (5) and determine the package s acceleration.
Rewrite equation (4) for
Substitute the value of ax in the above equation along with the values of other variables and calculate the value of
Conclusion:
The coefficient of kinetic friction between the package and the inclined plane, so that the package reaches the bottom with no speed is 0.382.
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