contestada

Three chains attached to a metal ring are being pulled by different people. Christiane is exerting a force of 1200N at an angle of 30° to the horizontal and Hayley is exerting a force of 200N at an angle of 210° to the horizontal. What force and in which direction must Benjamin be exerting this force if the ring does not move? Round your answers to one decimal place.

Respuesta :

Answer:1000 N

Step-by-step explanation:

Given

Christiane is exerting a force of 1200 N at an angle of [tex]30^{\circ}[/tex] to the horizontal

Hayley exerting a force of 200 N at an angle of [tex]210^{\circ}[/tex] to the horizontal

Resolving Forces in horizontal and vertical direction

[tex]R_x=1200cos\left ( 30\right )+200cos\left ( 210\right )+Fcos\theta [/tex]

[tex]R_y=1200sin\left ( 30\right )+200sin\left ( 210\right )+Fsin\theta [/tex]

For Ring to remains in equilibrium

[tex]R_x & R_y =0[/tex]

[tex]Fcos\theta =-\left ( 1200cos\left ( 30\right )+200cos\left ( 210\right )\right )[/tex]---1

[tex]Fsin\theta =-\left ( 1200sin\left ( 30\right )+200sin\left ( 210\right )\right )[/tex]---2

Divide (1) & (2)

[tex]tan\left ( \theta \right )=\frac{\left ( 1200sin\left ( 30\right )+200sin\left ( 210\right )\right )}{\left ( 1200cos\left ( 30\right )+200cos\left ( 210\right )\right )}[/tex]

[tex]tan\left ( \theta \right )=\frac{1}{\sqrt{3}}[/tex]

therefore [tex]\theta [/tex]is 30 or 210

but 30 is not possible therefore [tex]\theta [/tex] is 210

and magnitude of force will be

[tex]Fcos210=-\left ( 1200cos\left ( 30\right )+200cos\left ( 210\right )\right )[/tex]

F=1000 N

Otras preguntas