Answered

Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Ask your questions and receive accurate answers from professionals with extensive experience in various fields on our platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

The terminal velocity of a 3 × 10^-5 raindrop is about 9 m/s. Assuming a drag force Fd = −bv, determine (a) the value of the constant b and (b) the time required for such a drop, starting from rest, to reach 63% of terminal velocity.

Sagot :

mickymike92

Based on the data provided, the value of the constant b is 3.27 × 10^-5 kg/s and the time required to reach 63% of terminal velocity is 0.58 s.

What is terminal velocity?

The terminal velocity of a body is the velocity at which the body falls at constant velocity through a fluid.

For the falling raindrop, let positive direction be downwards and negative direction upwards,

  • mass of the raindrop, m = 3×10-5 kg
  • velocity at time t, is v(t)
  • terminal velocity, v0 = 9 m/s
  • gravitational acceleration, g = 9.81 m/s²

The raindrop experiences a downward gravitational force mg, and an upward drag force -bv.

The total force at a time t is given as

  • F(t) = mg - bv(t)

a)

Terminal velocity is achieved then the total force is 0,

0 = mg - bv0

Therefore

b = mg/v0

Substitutingthe values:

b = (3 × 10^-5 × 9.8)/9

b = 3.27 × 10^-5 kg/s

b) Applying Newton's Second Law

F = ma

where

  • a = v/t
  • F = mg

Therefore,

mg = mv/t t = v/g

however, t is at 63% velocity

thus:

t = 0.63v/g

t = 0.63 × 9 /9.8

t = 0.58 s

Therefore, the value of the constant b is 3.27 × 10^-5 kg/s and the time required to reach 63% of terminal velocity is 0.58 s

Learn more about terminal velocity at: https://brainly.com/question/12903433

Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.