A quarry crane is used to lift massive rocks from a quarry pitConsider the simplified model of such a crane shown in the figure(Figure 1) The ends of two poles are anchored to the ground at the same point (point O)From this point, one pole rises vertically and the second pole rises at an angleThe vertical pole has its free end connected to the ground via an unstretchable, massless rope labeled rope 1A second rope, labeled rope 2, connects the free ends of the two polesThe angle between the tilted pole and rope 2 is θBoth poles have length L and can be considered massless for the purposes of this problemHanging from the end of the second pole, via rope 3, is a granite block of mass m.Throughout this problem use g for the magnitude of the acceleration due to gravity.I need to find T1, the tension in rope 1The tension in rope 3 is mg.The tension in rope 2 is 2mgcos(theta).
Loose fill cellulose can be blown into your atticI don't know if I understand the protrusions that you are describing but if you can freely blow the cellulose fiber into this space it should serve as a good insulationYou don't want to poke it in with a stick because you don't want to compress itIf you cannot blow this product directly into the space, you would be better off stuffing it lightly with fiberglass battingJust don't cram it too tightlyIt needs to be loose to be most effective.
If the angle between the tilted pole and rope 2 is Θ, then the angle between the vertical pole and rope 2 is also Θ(You have an isosceles triangle since the two poles have the same length.) Then T2 sinΘ T1 cosφ If T2 2mgcosΘ as you say, then 2mgcosΘ sinΘ T1 cosφ Now, we can use the double angle formula 2cosΘsinΘ sin(2Θ) and reduce to mgsin(2Θ) T1 cosφ T1 mgsin(2Θ) / cosφ If you find this helpful, please select Best Answer!
