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 342 Chapter 9 | Statics and Torque 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?
Solution 38PE Step-by-step solution Step 1 of 3 (a) From below mention formula calculate force on the tree, Here, F is impulse on the tree, is momentum of ball and is time spend by the ball in air. Since , Here, is momentum, m ismass of ball and v is speed of ball. Hence, Substitute in above equation, Convert time spend by the ball from ms to s. Substitute 0.50 kg for m, 5.0 m/s for v and 0.010 s for solve for F. Hence, force applied on tree is . Step 2 of 3 (b) Take is force exerted by the end of the tip of the root to keep the tree from toppling, since F is force exerted by the ball at the top of tree take moment at any point of the tree, Here, F is force exerted by the ball at the top of tree and is force exerted by the end of the tip of the root to keep the tree from toppling. Substitute 250 N for F solve for , Hence, force exerted by the end of the tip of the root to keep the tree from toppling is .