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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 toaccount 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 force exerted by the wall on the beam ([pic]), usingthe axis shown. Remember to pay attention to the direction that the wall exerts the force.

Express your answer in terms of [pic]and other given quantities.
|[pic]=|-T*cos(theta) | | |
| | | | |

C. Find [pic], the y-component of force that the wall exerts on the beam ([pic]), using the axis shown. Remember to pay attention to the direction that the wallexerts the force.

Express your answer in terms of [pic], [pic], [pic], [pic], and [pic].
|[pic]=|-sin(theta)*T+m_1*g+m_2*g | | |
| | | | |

[pic] [ Print ] 
Sliding Dresser
Sam is trying to move a dresser of mass [pic]and dimensions of length [pic]and height [pic]by pushing it with a horizontal force [pic]applied at a height[pic]above the floor. [pic]The coefficient of kinetic friction between the dresser and the floor is [pic]and [pic]is the magnitude of the acceleration due to gravity. The ground exerts upward normal forces of magnitudes [pic]and [pic]at the two ends of the dresser. Note that this problem is two dimensional.
A. If the dresser is sliding with constant velocity, find [pic], the magnitude of theforce that Sam applies.

Express the force in terms of [pic], [pic], and [pic].
|[pic]|mu_k*m*g | | |
|= | | | |

B. Find the magnitude of the normal force [pic]. Assume that the legs are separated by a distance [pic], as shown in the figure.

Express this normal force in terms of [pic], [pic], [pic], [pic], and [pic].
|[pic]= |m*g/2-mu_k*m*g*h/L| | |
| | | | |

C. Find the magnitude of the normal force [pic]. Assume that the legs are separated by a distance [pic], as shown in the figure.

Answer in terms of [pic], [pic], [pic], [pic], and [pic].
|[pic]= |m*g/2+mu_k*m*g*h/L | | |
| | | | |

D. Find [pic], the maximum heightat which Sam can push the dresser without causing it to topple over.

Express your answer for the maximum height in terms [pic]and [pic].
|[pic]= |L/(2*mu_k) | | |
| | | | |

[pic]
A Person Standing on a Leaning Ladder
A uniform ladder with mass [pic]and length [pic]rests against a smooth wall.[pic] A do-it-yourself enthusiast of mass [pic]stands onthe ladder a distance [pic]from the bottom (measured along the ladder). The ladder makes an angle [pic]with the ground. There is no friction between the wall and the ladder, but there is a frictional force of magnitude [pic]between the floor and the ladder. [pic]is the magnitude of the normal force exerted by the wall on the ladder, and [pic]is the magnitude of the normal force exerted by theground on the ladder. Throughout the problem, consider counterclockwise torques to be positive. None of your answers should involve [pic](i.e., simplify your trig functions).
A. What is the minimum coeffecient of static friction [pic]required between the ladder and the ground so that the ladder does not slip?

Express [pic]in terms of [pic], [pic], [pic], [pic], and [pic].
|[pic]=...