Object going up inclined plane with friction, how far does it go?

AI Thread Summary
A box sliding up a 15-degree incline with an initial speed of 1.50 m/s and a coefficient of kinetic friction of 0.180 is analyzed to determine how far it travels before stopping. The frictional force and gravitational component acting down the incline must be calculated to find the net deceleration. A diagram illustrating the forces is recommended for clarity, emphasizing the need to apply trigonometric functions to account for the incline. The solution indicates that the box travels approximately 0.265 meters before coming to rest. Understanding the forces involved is crucial for solving this type of physics problem.
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Homework Statement


A box is sliding up an incline that makes an angle of 15 degrees with respect to the horizontal. The coefficient of kinetic friction between the box and the surface of the incline is .180. The initial speed of the box at the bottom of the incline is 1.50 m/s. How far does the box travel along the incline before coming to rest?


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The Attempt at a Solution


the book this problem came from referred to an example where they were on a flat surface and they used x=(v2-vo2)/2(-.18*9.8). I have no idea how to incorporate the 15 degree incline into my answer, the solution in the book says .265m if that helps.
 
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Make a diagram of all the forces acting on the object, then consider which are slowing it down in it's ascent up the ramp. You'll need to use trig.
 

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