Finding the Net Force on a Box on an Inclined Plane

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SUMMARY

The net force on a box of mass, m, on an inclined plane at an angle, q, is determined by the equation F_net = mg(sin q) - F_friction, where F_friction is calculated as uk * mg(cos q). The box accelerates down the incline due to the gravitational component exceeding the frictional force. The correct formulation for the net force is mg(sin q - uk * cos q). This conclusion is confirmed through the discussion, emphasizing the simplicity of the problem once the forces are correctly identified.

PREREQUISITES
  • Understanding of Newton's Second Law of Motion
  • Knowledge of forces acting on an inclined plane
  • Familiarity with kinetic friction and its coefficient (uk)
  • Basic trigonometry related to angles and force components
NEXT STEPS
  • Study the derivation of forces on inclined planes in physics textbooks
  • Learn about the effects of varying coefficients of friction on motion
  • Explore advanced problems involving multiple forces on inclined surfaces
  • Investigate the applications of Newton's laws in real-world scenarios
USEFUL FOR

Students studying physics, particularly those focusing on mechanics, as well as educators looking for clear examples of force analysis on inclined planes.

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Homework Statement



A box of mass, m, is on a plane inclined at an angle, q, relative to the horizontal. The coefficient of kinetic friction between the box and the incline is uk, and the body is accelerating down the incline. What is the net force on the body?

The Attempt at a Solution



Well, if the box is accelerating down the incline, the mg(sinTheta) vector of the box must be greater than the Ffriction. But I don't know how to go from there.
I'm guessing it's mg (sin q - uk cos q) but I'm not sure. Could anything clarify for me?
 
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No need to guess--you're correct. There are only two forces on the box parallel to the incline: the component of gravity and the kinetic friction.
 
Doc Al said:
No need to guess--you're correct. There are only two forces on the box parallel to the incline: the component of gravity and the kinetic friction.

Yeah, I just realized now how easy this question is. Thanks for confirming.
 

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