標題:
system of rigid objects
發問:
2. Two uniform planks AB and BC, each of weight 60N and length 2.6m, are smoothly pin jointed to each other at B. They rest with their ends A and C on a smooth floor and with B vertically above the mid point of AC. To prevent the structure from collapsing, A and C are connected by a rope of length 2m.Calculate... 顯示更多 2. Two uniform planks AB and BC, each of weight 60N and length 2.6m, are smoothly pin jointed to each other at B. They rest with their ends A and C on a smooth floor and with B vertically above the mid point of AC. To prevent the structure from collapsing, A and C are connected by a rope of length 2m. Calculate the tension in the rope. 更新: the answer is 12.5N
For easy explanation, please find the diagram describing the scene of the question below: 圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Phy/Statica.jpg 【此圖乃本人自製圖片，未經本人同意勿擅自連結或使用】 From the diagram, we first calculate those necessary data for usage first as follows: By Pyth Thm, the vertical height of B above the ground = 2.4m cos θ = (2.4/2.6) → θ = 22.6° (corr to 1 d.p.) Perp. distance of A from the line of action of R = 2.6 sin (180° - 2θ) = 1.846 (corr to 3 d.p.) Taking moment about point A, we have: 60(0.5) = R(1.85) (the perpendicular distance of A from the line of action of the plank's weight is 0.5m as seen from the diagram) R = 16.25 N Therefore, in order to keep the plank AB in balance, the tension of the rope must be equal to the horizontal component of R, i.e. T = R cos (90° - θ) (as seen from the diagram) = 16.25 × 0.385 = 6.25 N By symmetry, we can conclude that the conditions for the plank BC will be the same. 2007-01-30 10:53:26 補充： Some corrections:Force at B should be horizontal only.So taking moment about point A:Fb × 2.4 = 60 × 0.5Fb = 12.5NSo in order to keep the plank's horizontal force balanced, T = 12.5NSorry for the confusion.
其他解答:
By calculation B is to be 2.4m above floor level. Then let T be the tension in the rope and R be the reaction at either A or C (i.e. 60N), by taking moment about B, we have: 60 x (2/4) + T x 2.4 = R x (2/2) = 60 Therefore, T = 30/2.4 = 12.5N
system of rigid objects
發問:
2. Two uniform planks AB and BC, each of weight 60N and length 2.6m, are smoothly pin jointed to each other at B. They rest with their ends A and C on a smooth floor and with B vertically above the mid point of AC. To prevent the structure from collapsing, A and C are connected by a rope of length 2m.Calculate... 顯示更多 2. Two uniform planks AB and BC, each of weight 60N and length 2.6m, are smoothly pin jointed to each other at B. They rest with their ends A and C on a smooth floor and with B vertically above the mid point of AC. To prevent the structure from collapsing, A and C are connected by a rope of length 2m. Calculate the tension in the rope. 更新: the answer is 12.5N
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最佳解答:For easy explanation, please find the diagram describing the scene of the question below: 圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Phy/Statica.jpg 【此圖乃本人自製圖片，未經本人同意勿擅自連結或使用】 From the diagram, we first calculate those necessary data for usage first as follows: By Pyth Thm, the vertical height of B above the ground = 2.4m cos θ = (2.4/2.6) → θ = 22.6° (corr to 1 d.p.) Perp. distance of A from the line of action of R = 2.6 sin (180° - 2θ) = 1.846 (corr to 3 d.p.) Taking moment about point A, we have: 60(0.5) = R(1.85) (the perpendicular distance of A from the line of action of the plank's weight is 0.5m as seen from the diagram) R = 16.25 N Therefore, in order to keep the plank AB in balance, the tension of the rope must be equal to the horizontal component of R, i.e. T = R cos (90° - θ) (as seen from the diagram) = 16.25 × 0.385 = 6.25 N By symmetry, we can conclude that the conditions for the plank BC will be the same. 2007-01-30 10:53:26 補充： Some corrections:Force at B should be horizontal only.So taking moment about point A:Fb × 2.4 = 60 × 0.5Fb = 12.5NSo in order to keep the plank's horizontal force balanced, T = 12.5NSorry for the confusion.
其他解答:
By calculation B is to be 2.4m above floor level. Then let T be the tension in the rope and R be the reaction at either A or C (i.e. 60N), by taking moment about B, we have: 60 x (2/4) + T x 2.4 = R x (2/2) = 60 Therefore, T = 30/2.4 = 12.5N
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