How to find magnitude of the force?

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An object whose weight is #80N# is balanced in the force of #\vec{F}# as seen on the diagram. Note that the pulley is frictionless. What is the magnitude of #\vec{F}#? (#\sin(37) = 0.6 ; \cos(37) = 0.8#

2 Answers
May 25, 2018

The magnitude of #vecF=50N#

Explanation:

As the forces are in equilibrium and the pulley is frictionless,

Resolving in the vertical direction

#F+Fsin37^@=80#

#F=80/(1+sin37^@) =80/1.6=50N#

May 25, 2018

#vecF = 50 N#

Explanation:

The upward forces in this system is from the 2 parts of the rope: from ceiling to pulley and from #vecF# to pulley. The tension in the rope will be #vecF# throughout its length. The downward force is the 80 N weight. Since the system is to be assumed to be in equilibrium,

#"up forces" + "down force" = 0#

#vecF + sin37*vecF - 80 N = 0#

#vecF * (1 + sin37) = 80 N#

#vecF = (80 N)/(1 + sin37) = (80 N)/1.6 = 50 N#

I hope this helps,
Steve