The value of the friction force

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SUMMARY

The discussion centers on calculating the friction force acting on a box being pushed by a worker at an angle of 35° with a mass of 135 kg and a constant horizontal velocity. The applied force is 2030 N at an angle of 215°. The calculated friction force is determined to be 759.6 N, but the participant is uncertain about its correctness given multiple-choice options. The confusion arises from interpreting the angles and the identities of the worker and the man applying the force.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Knowledge of vector components and trigonometric functions
  • Familiarity with friction force equations, including f = μ · Fs
  • Basic principles of static and kinetic friction
NEXT STEPS
  • Review vector decomposition in physics, particularly for forces at angles
  • Study the relationship between applied force, friction, and motion in horizontal scenarios
  • Learn about the coefficient of friction and its role in calculating friction forces
  • Explore examples of similar physics problems involving friction and forces
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Students in physics, particularly those studying mechanics, as well as educators looking for examples of force analysis in real-world applications.

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Homework Statement


The worker pushes downward and to the left on the box at an angle of 35°. The box has a mass of 135 kg. The box moves horizontally across the floor to the left at a constant velocity. The force applied by the man is 2030 N∠215°. What is the value of the friction force?


Homework Equations


Fgravity · sin35° = Fgravityx
Ffriction + Fgravityx = m · a
f = μ · Fs


The Attempt at a Solution


sin35° =
Fgravity · sin35° = Fgravityx
m · g · sin35° = Fgravityx
(135 kg)(9.81) sin35° = Fgravityx
759.6 N = Fgravityx

Ffriction + (759.6 N) = (135 kg)(0 m/s2)
Ffriction - 759.6 N = 0 N
Ffriction = 759.6 N

I know that this isn't correct, because my study guide is multiple choice. My options are:
a. 1164 N
b. 1324 N
c. 1663 N
d. 2489 N

I'm really not sure what I'm missing or if I am going the wrong way with finding the value of the friction force. My guess is that c. 1663 N is correct, but that is only a guess. I'd like to be able to prove which answer it is. Thank you for any help!
 
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The worker pushes downward and to the left on the box at an angle of 35°
The force applied by the man is 2030 N∠215°

Can you explain what are these two angles? Whether the worker and the man are the same person?
 

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