Question

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Problem 3: Terminal velocity A hailstone of mass m = 6 x 10-4 kg falls under the effect of gravity. It also experiences a drag force of magnitude FD = nu?, where v is the hailstone's velocity and the coefficient 7 for the particular hailstone under consideration is equal to n= 3 x 10-5 kg/m. (a) Calculate the terminal velocity of the hailstone. (b) If the hailstone falls from a height h = 500 m, starting at rest, calculate the velocity it would have when it reaches the ground in the absence of drag (i.e, if Fp = 0). (c) Assuming that in the presence of drag the hailstone reaches the ground with terminal veloc- ity, calculate the amount of energy that has been lost due to drag.

Answer 1

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Criven: m= 6810 kg nuz n = 3x10 -S legim mg a) Given that when a body achieves a terminal velocity then both the forces balan u Fo= w nur= mg mg 6x16"+9,8 196mis n 3xlos vtz Jigo lumis 161 when there is no drag fru thusins free fall equahon. 62-02 zas S= 5oom > a=g=9.8mis? UCO v = 2t 9.8t soo ų? I 9800) 2 g&co bra 98.gg m/s 12

C ) arbored loss - K. E un free fall - IC. Ein due to drag force с Imuz 5 Imut? T m[uzue? з д+ m L38 ою - 196] 1 2. + Exis"C96оч] ។ 8o2 x6xo 1 Energy loss 2. 8812 Jook