: The truck is to be towed using two ropes. Determine the magnitudes of forces FA and FB acting on each rope in order to develop a resultant force of 950 N directed along the positive x axis. Set θ = 50°.

Answer :

Answer:

Fa=774 N

Fb=346 N

Explanation:

We will solve this problem by equating forces on each axis.

  1. On x-axis let forces in positive x-direction be positive and forces in negative x-direction be negative
  2. On y-axis let forces in positive y-direction be positive and forces in negative y-direction be negative

While towing we know that car is mot moving in y-direction so net force in y-axis must be zero

∑Fy=0

⇒[tex]Fa*sin(50)-Fb*sin(20)=0[/tex]

⇒[tex]Fa*sin(50)=Fb*sin(20)[/tex]

⇒[tex]Fa=2.24Fb[/tex]

Given that resultant force on car is 950N in positive x-direction

∑Fx=950  

⇒[tex]Fa*cos(20)+Fb*cos(50)=950[/tex]

⇒[tex]2.24*Fb*cos(20)+Fb(50)=950[/tex]

⇒[tex]Fb*(2.24*cos(20)+cos(50))=950[/tex]

⇒[tex]Fb=\frac{950}{2.24*cos(20)+cos(50)}[/tex]

⇒[tex]Fb=\frac{950}{2.24*0.94+0.64}[/tex]

⇒ [tex]Fb=\frac{950}{2.75}=345.5[/tex]

⇒[tex]Fa=2.24*Fb[/tex]

      [tex]=2.24*345.5[/tex]

      [tex]=773.93[/tex]

Therefore approximately, Fa=774 N and Fb=346 N

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