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"→T4≈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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