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You have just planted a sturdy 2-m-tall palm tree in your front lawn for your mother’s birthday. Your brother kicks a 500 g ball, which hits the top of the tree at a speed of 5 m/s and stays in contact with it for 10 ms. The ball falls to the ground near the base of the tree and the recoil of the tree is minimal. (a) What is the force on the tree? (b) The length of the sturdy section of the root is only 20 cm. Furthermore, the soil around the roots is loose and we can assume that an effective force is applied at the tip of the 20 cm length. What is the effective force exerted by the end of the tip of the root to keep the tree from toppling? Assume the tree will be uprooted rather than bend. (c) What could you have done to ensure that the tree does not uproot easily?
Question by OpenStax is licensed under CC BY 4.0.
Final Answer
  1. $250 \textrm{ N}$
  2. $2500 \textrm{ N}$
  3. Compress the soil so that force is exerted all along the length of the root, not only at its tip. One could also install a guy wire to reinforce the tree.
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OpenStax College Physics Solution, Chapter 9, Problem 38 (Problems & Exercises) (3:20)

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