A bridge, constructed of 11 beams of equal length LLL and negligible mass, supports an object of mass MMM as shown. (Figure 1)Real bridges of this sort have steel rockers at the ends (check one out sometime), these assure that the support forces on the bridge are vertical even when it expands or contracts thermally. Throughout this problem, use g for the magnitude of the acceleration due to gravity. Find FP, the vertical force that pier P exerts on the left end of the bridge?. Find FQ, the vertical force that pier Q exerts on the right end of the bridge?. Assuming that the bridge segments are free to pivot at each intersection point, what is the tension T in the horizontal segment directly above the point where the object is attached? (Figure 2)If you find that the horizontal segment directly above the point where the object is attached is being stretched, indicate this with a positive value for T. If the segment is being compressed, indicate this with a negative value for T.
A bridge, constructed of 11 beams of equal length LLL and negligible mass, supports an object of mass MMM as shown. (Figure 1)Real bridges of this sort have steel rockers at the ends (check one out sometime), these assure that the support forces on the bridge are vertical even when it expands or contracts thermally.
Throughout this problem, use g for the magnitude of the acceleration due to gravity.
A bridge, constructed of 11 beams of equal length LLL and negligible mass, supports an object of mass MMM as shown. (Figure 1)Real bridges of this sort have steel rockers at the ends (check one out sometime), these assure that the support forces on the bridge are vertical even when it expands or contracts thermally.
Throughout this problem, use g for the magnitude of the acceleration due to gravity.
A bridge, constructed of 11 beams of equal length LLL and negligible mass, supports an object of mass MMM as shown. (Figure 1)Real bridges of this sort have steel rockers at the ends (check one out sometime), these assure that the support forces on the bridge are vertical even when it expands or contracts thermally.
Throughout this problem, use g for the magnitude of the acceleration due to gravity.
Find FP, the vertical force that pier P exerts on the left end of the bridge?.
Find FQ, the vertical force that pier Q exerts on the right end of the bridge?.
Assuming that the bridge segments are free to pivot at each intersection point, what is the tension T in the horizontal segment directly above the point where the object is attached? (Figure 2)If you find that the horizontal segment directly above the point where the object is attached is being stretched, indicate this with a positive value for T. If the segment is being compressed, indicate this with a negative value for T.
Solution:
Given that,
mass of the object = M
gravitational acceleration = g
We know that,
Torque is given as:
where,
τ = moment of force ( Nm )
F = magnitude of force ( N )
d = perpendicular distance between force and pivot ( m )
Required:
vertical force at pier P =
vertical force at pier Q = = ?
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