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?
1 Answer
Explanation:
Diagram
We are given the following information:
-
#|->m=16"kg"# -
System is in static equilibrium
We will assume massless ropes and massless, frictionless pulleys.
#:. vecT_1=vecT_2=vecT_3#
For the mass, we have the following force diagram:
And so we have:
#sumF=vecT_5-vecF_G=0#
#=>vecT_5=vecF_G#
As
#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:
And so we have:
#sumF=vecT_2+vecT_3-vecT_5=0#
#=>vecT_5=vecT_2+vecT_3#
And since
#=>color(darkblue)(vecT_2=vecT_3=1/2vecT_5=78.48" N")#
Finally, for the large pulley, we have the following force diagram:
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")#
