Precarious Lunch

A uniform steel beam of length [pic]and mass [pic]is bolted to the side of a building. The beam is supported by a steel cable attached to the end of the beam at an angle [pic], as shown. The wall exerts an unknown force, [pic], on the beam. A workman of mass [pic]sits eating lunch a distance [pic]from the building.[pic] A. Find [pic], the tension in the cable. Remember to account for all the forces in the problem.

Express your answer in terms of [pic], [pic], [pic], [pic], [pic], and [pic], the magnitude of the acceleration due to gravity.
|[pic]|g*(m_1*L/2+m_2*d)/(L*sin(theta)) | | |
|= | | | |

B. Find [pic], the x-component of the …ver más…

Suppose that the actual coefficent of friction is one and a half times as large as the value of [pic]. That is, [pic]. Under these circumstances, what is the magnitude of the force of friction [pic]that the floor applies to the ladder?

Express your answer in terms of [pic], [pic], [pic], [pic], [pic], and [pic]. Remember to pay attention to the relation of force and [pic].
|[pic|(m_1*d+m_2*L/2)*cos(theta)*g/(L*sin(theta)) | | |
|]= | | | |

[pic]
Three-Legged Table
The top view of a table, with weight [pic], is shown in the figure.[pic] The table has lost the leg at ([pic], [pic]), in the upper right corner of the diagram, and is in danger of tipping over. Company is about to arrive, so the host tries to stabilize the table by placing a heavy vase (represented by the green circle) of weight [pic]at ([pic], [pic]). Denote the magnitudes of the upward forces on the table due to the legs at (0, 0), ([pic], 0), and (0, [pic]) as [pic], [pic], and [pic], respectively. A. Find [pic], the magnitude of the upward force on the table due to the leg at ([pic], 0).

Express the force in terms of [pic], [pic], [pic], [pic], [pic], and/or [pic]. Note that not all of these quantities may appear in the answer.
|[pic]=|W_v*X/L_x + W_t/2 | | |
| | | | |

B. Find [pic],