Pulling on a rope attached to a box: Newton's Laws and Incline Planes

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SUMMARY

The discussion focuses on applying Newton's Laws to calculate the acceleration of a box being pulled by a force of 130.0 N at an angle of 15.0° above the horizontal. The box has a mass of 25.0 kg and a coefficient of kinetic friction of 0.300. The calculated acceleration on a flat surface is 2.48 m/s². When moving the box up a 10.0° incline, the forces involved include rope tension, weight, normal force, and frictional force, which complicate the calculation of the new acceleration.

PREREQUISITES
  • Understanding of Newton's Laws of Motion
  • Knowledge of force diagrams and vector resolution
  • Familiarity with friction coefficients and their impact on motion
  • Basic algebra for solving equations of motion
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  • Study the effects of inclined planes on forces and motion
  • Learn how to draw and analyze free-body diagrams
  • Explore the relationship between tension, weight, and normal force
  • Investigate advanced applications of Newton's Laws in real-world scenarios
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Students studying physics, particularly those focusing on mechanics and forces, as well as educators looking for practical examples of Newton's Laws in action.

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Homework Statement



A student decides to move a box of books into her dormitory room by pulling on a rope attached to the box. She pulls with a force of 130.0 N at an angle of 15.0° above the horizontal. The box has a mass of 25.0 kg, and the coefficient of kinetic friction between box and floor is 0.300.
(a) Find the acceleration of the box.

(b) The student now starts moving the box up a 10.0° incline, keeping her 130.0 N force directed at 15.0° above the line of the incline. If the coefficient of friction is unchanged, what is the new acceleration of the box?



Homework Equations



F=ma, Assorted equations derived from Newton's Laws



The Attempt at a Solution



I found the answer to part A to be 2.483572006 m/s/s. In part B, I attempted to determine the forces affecting the situation: rope tension, weight, normal force, and frictional force. I think I get lost trying to find these forces.

Thanks!
 
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You will get lost if you don't draw a large diagram. Maybe a couple, as you discard the first when you realize you've marked some things incorrectly. As before, the rope takes some of the "weight", reducing the force the block exerts normal to the incline and thus reducing the force to overcome friction.
 

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