標題:

A-Level Physics- Work

發問:

• 每日登入我的知識+@1@
• 8條數!20點
• 根式的運算@1@

• 每日登入我的知識+@1@
• 8條數!20點
• 根式的運算@1@

 

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A uniform rope has a length x and mass m. It is held stationary with 3/4 of the length of the rope lying on a smooth horizontal table surface with the remaining 1/4 hanging freely over the edge. What is the minimum work required to pull the whole rope onto the table surface?A mgx / 4B mgx / 8C mgx /... 顯示更多 A uniform rope has a length x and mass m. It is held stationary with 3/4 of the length of the rope lying on a smooth horizontal table surface with the remaining 1/4 hanging freely over the edge. What is the minimum work required to pull the whole rope onto the table surface? A mgx / 4 B mgx / 8 C mgx / 16 D mgx / 32 更新: Can you work out the calculation steps please?

最佳解答:

Let p be the density of the rope Consider a small element, dm, on the rope hanging freely over the edge. dm = pdy Where dy is the length of the small element. And now, define y be the vertical distance of the small element from the edge. 0<= y <= x/4 To raise the small element up on the edge, the work done = dm gy = pgydy To find the work done to raise the remaining part of the rope, do an integration from y = 0 to y = x/4 int [0,x/4] pgydy = pg(x^2/16)/2 = pgx^2 / 32 But px is the mass of the rope, m So, the work done = mgx/32 The answer is D.

其他解答:

The naswer is option D. Just calculate the increase in potential energy of the rope.