05_InstSolManual_PDF_Part14 - 5-14 Chapter 5 5.29 Set Up...

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5.29. Set Up: Let and The two boxes have the same magnitude of acceleration. For the 30.0 kg box let be downward and for the 50.0 kg box use coordinates parallel and perpendicular to the ramp, with up the ramp. Solve: (a) The free-body diagrams are given in Figure 5.29. Figure 5.29 (b) The downward force on the 30.0 kg box is The force pulling the system in the opposite direction is the component of directed down the ramp, and the 30.0 kg box moves downward. Therefore, the 50.0 kg box moves up the ramp. (c) applied to gives applied to gives Com- bining these two equations to eliminate T gives The 50.0 kg box accelerates up the ramp at and the 30.0 kg box accelerates downward at Reflect: Only the component of the weight of the 50 kg box that is parallel to the ramp acts to oppose the weight of the 30 kg box. Therefore, the 30 kg box pulls the 50 kg box up the ramp even though its weight is less than the weight of the 50 kg box. 5.30. Set Up: Assume the box is initially at rest. The box remains at rest and friction is static if the pull is less than
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