Assistance in Free Body Diagram Question

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SUMMARY

The discussion centers on calculating the acceleration of an 82 kg couch being pushed with a force of 56 N at a 40-degree angle above the horizontal, with a coefficient of friction of 0.051. The user initially calculated an acceleration of 0.02 m/s² but expressed uncertainty regarding the inclusion of vertical force components in the net force calculation. The correct approach involves resolving the applied force into horizontal and vertical components, determining the normal force, and applying Newton's second law to find the net horizontal force affecting acceleration.

PREREQUISITES
  • Understanding of Free Body Diagrams
  • Knowledge of Newton's Laws of Motion
  • Familiarity with force resolution into components
  • Basic grasp of friction coefficients and their impact on motion
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  • Study how to resolve forces into horizontal and vertical components
  • Learn about calculating normal force in inclined scenarios
  • Explore the application of Newton's second law in multi-dimensional problems
  • Investigate the effects of friction on motion and acceleration
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gbaby370
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Hey,

I'm having a bit of trouble with a Free Body Diagram question and I'm not sure if I'm going about it properly.

The question asks;

A 82kg couch is being pushed with a force of 56N at an angle of 40 degrees above the horizontal. If the coefficient of friction between the couch and the floor is 0.051, what is the acceleration of the couch?

My final answer was it accelerated at 0.02m/s^2.

I think I am incorrect because I'm not sure if I need to consider the upwards component of the force applied, and I am not sure when calculating the net force, are you supposed to add up the vertical and horizontal and then apply it to the horizontal acceleration? Or are only the net forces on the horizontal important for the forward acceleration?
 
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I also got a normal force of 803.6N [up]. I wasn't sure if there would be a vertical acceleration involved, so I figured it would be the opposite of the gravitational force.
 
I think I may have figured it out on my own. Please correct me. But the total value of the vertical forces must be 0? So if Fnet= Fg + Fn + Fv, would the normal force be the sum of Fg and Fn?
 

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