Motion Along a Line: Find Force & Acceleration

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To solve the problem of a boy pushing a 5-kg machine, the maximum static friction force that must be overcome is calculated to be approximately 39.77 N. To achieve a constant acceleration of 1.5 m/s², a force of about 31.005 N is required. If the boy pushes with just enough force to initiate movement, the resulting acceleration while in motion is approximately 2.76 m/s². The discussion seeks validation of these calculations and guidance on the steps involved in reaching the answers. Clarification on the methodology and calculations is requested for better understanding.
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Homework Statement



A boy pushes a 5-kg machine along a horizontal floor with a force, P, which makes an angle, theta=30 degree below the horizontal. The coefficients of static and kinetic friction between the machine and the floor are 0.5 and 0.3 respectively. The machine is initially at rest.

a.) find the maximum force of static friction that must be overcome by the applied before the machine moves.
b.) what is the value of the force P needed to move the machine at a constant acceleration of 1.5 m/s^2 along the floor?
c.) suppose he pushes the machine with just enough force to move the machine, and continues to push with the same force after the machine starts moving, calculate the acceleration of the machine while in motion.

Homework Equations


dion't know what i used.

The Attempt at a Solution



just want to know if these answers were right.
2.)a. t= 39.77N
b.) 31.005 N
c.) a=2.76 m/s^2

I don't know if these are right! Please help me to determine whether it's right or not! and show me how you do the steps.

I'm just not sure on where to start on it. Any help on it is appreciated!
 
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