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Torque Problems Work the following problems with your lab partners. Each member of the lab group should write out their own version of the solution. If you cannot finish them in this lab period, you should turn them in the next day you have lab. Problem 1 - The Plank Problem A plank is hinged to the ground, and you are under it and holding it up to a height \( h \) at the location where you stand, a horizontal distance \( x \) from the hinge (see the figure). Let the length of the plank be \( L \), and assume that you are holding it up by exerting a force \( \vec{F}_{y, p}^{c} \) that is perpendicular to the plank itself at that point. The weight of the plank is \( m g \). (a) Draw on the figure above all the forces acting on the plank. Make sure they are all applied at the right spot and that they point in the right direction. Don't forget the force at the hinge! Make sure you get the direction of that force at least qualitatively right, and explain why it should point that way. (b) By taking torques about an appropriate point, derive an equation that gives the magnitude of \( \vec{F}_{y, p}^{c} \) as a function of \( m g, h, L \) and \( x \). (Note: you'll need to use trigonometry and the Pythagorean

          Torque Problems
Work the following problems with your lab partners. Each member of the lab group should write out their own version of the solution. If you cannot finish them in this lab period, you should turn them in the next day you have lab.

Problem 1 - The Plank Problem
A plank is hinged to the ground, and you are under it and holding it up to a height \( h \) at the location where you stand, a horizontal distance \( x \) from the hinge (see the figure). Let the length of the plank be \( L \), and assume that you are holding it up by exerting a force \( \vec{F}_{y, p}^{c} \) that is perpendicular to the plank itself at that point. The weight of the plank is \( m g \).
(a) Draw on the figure above all the forces acting on the plank. Make sure they are all applied at the right spot and that they point in the right direction. Don't forget the force at the hinge! Make sure you get the direction of that force at least qualitatively right, and explain why it should point that way.
(b) By taking torques about an appropriate point, derive an equation that gives the magnitude of \( \vec{F}_{y, p}^{c} \) as a function of \( m g, h, L \) and \( x \). (Note: you'll need to use trigonometry and the Pythagorean

Torque Problems
Work the following problems with your lab partners. Each member of the lab group should write out their own version of the solution. If you cannot finish them in this lab period, you should turn them in the next day you have lab.

Problem 1 - The Plank Problem
A plank is hinged to the ground, and you are under it and holding it up to a height h at the location where you stand, a horizontal distance x from the hinge (see the figure). Let the length of the plank be L, and assume that you are holding it up by exerting a force F⃗y, p^c that is perpendicular to the plank itself at that point. The weight of the plank is m g.
(a) Draw on the figure above all the forces acting on the plank. Make sure they are all applied at the right spot and that they point in the right direction. Don't forget the force at the hinge! Make sure you get the direction of that force at least qualitatively right, and explain why it should point that way.
(b) By taking torques about an appropriate point, derive an equation that gives the magnitude of F⃗y, p^c as a function of m g, h, L and x. (Note: you'll need to use trigonometry and the Pythagorean

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