An object of mass 16 kg is held in place by an applied force F and a pulley system as shown in the figure.  Find the tension T4.  Hint draw a free body diagram for the top pulley and the bottom pulley?

This is a link to the photo of the pulley system

1 Answer
Morgan
Aug 14, 2017

#vecT_4~~235" N"# upwards

Explanation:

Diagram

Provided by OP

We are given the following information:

We will assume massless ropes and massless, frictionless pulleys.

  • #:. vecT_1=vecT_2=vecT_3#

For the mass, we have the following force diagram:

enter image source here

And so we have:

#sumF=vecT_5-vecF_G=0#

#=>vecT_5=vecF_G#

As #F_G=mg#, we have:

#color(darkblue)(vecT_5=mg)#

#=>=(16"kg")(9.81"m"//"s"^2)#

#=>color(darkblue)(=156.96" N")#

For the small pulley, we have the following force diagram:

enter image source here

And so we have:

#sumF=vecT_2+vecT_3-vecT_5=0#

#=>vecT_5=vecT_2+vecT_3#

And since #vecT_2=vecT_3#:

#=>color(darkblue)(vecT_2=vecT_3=1/2vecT_5=78.48" N")#

Finally, for the large pulley, we have the following force diagram:

enter image source here

And so we have:

#sumF=vecT_4-vecT_1-vecT_2-vecT_3=0#

#=>color(darkblue)(vecT_4=vecT_1+vecT_2+vecT_3)#

#=>vecT_4=3(78.48" N")#

#=>vecT_4=235.44" N"#

#=>color(darkblue)(vecT_4~~235" N")#

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