Assistance in Free Body Diagram Question

AI Thread Summary
The discussion revolves around calculating the acceleration of an 82kg couch being pushed with a force of 56N at a 40-degree angle, with a friction coefficient of 0.051. The user initially calculated an acceleration of 0.02m/s² but expressed uncertainty about whether to consider the upward component of the applied force and how to correctly determine the net force. Clarification was sought on whether to combine vertical and horizontal forces for calculating horizontal acceleration, as well as the normal force's role in the overall force balance. The user also questioned if the total vertical forces should equal zero, indicating confusion about the relationship between gravitational force and normal force. Ultimately, the user appears to be working towards a clearer understanding of the Free Body Diagram and the forces involved.
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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