- Please Help Me Solve These Questions 1 (169.38 KiB) Viewed 17 times
Please help me solve these questions.
-
answerhappygod
- Site Admin
- Posts: 899603
- Joined: Mon Aug 02, 2021 8:13 am
Please help me solve these questions.
Please help me solve these questions.
(c) The equation of motion for a particle falling under the influence of gravity and a linear drag force is mÿ = mg - by, where m is the particle mass, g is the acceleration due to gravity, b is the coefficient of linear drag, and the vertical coordinate y is taken to have units of meters. (Note: the y-axis points downwards). (i) Identify whether each of the forces acting is conservative. Give reasons for your identification. (ii) Define the terminal speed Uter and obtain an expression for this in terms of the quantities appearing in the equation of motion. (iii) Show that the equation of motion can be equivalently written as dvy 1 = (Vter - Vy), dt T where we have set 7 = m/b (a constant with units of time). (iv) Using the technique of separation of variables solve the above form of the equation of motion to determine the velocity vy as a function of time. You should use that the particle starts at rest (i.e. vy(t = 0) = 0). (v) What is the velocity of the particle at late times (i.e. for t » T)? Explain why this result makes sense.
(c) The equation of motion for a particle falling under the influence of gravity and a linear drag force is mÿ = mg - by, where m is the particle mass, g is the acceleration due to gravity, b is the coefficient of linear drag, and the vertical coordinate y is taken to have units of meters. (Note: the y-axis points downwards). (i) Identify whether each of the forces acting is conservative. Give reasons for your identification. (ii) Define the terminal speed Uter and obtain an expression for this in terms of the quantities appearing in the equation of motion. (iii) Show that the equation of motion can be equivalently written as dvy 1 = (Vter - Vy), dt T where we have set 7 = m/b (a constant with units of time). (iv) Using the technique of separation of variables solve the above form of the equation of motion to determine the velocity vy as a function of time. You should use that the particle starts at rest (i.e. vy(t = 0) = 0). (v) What is the velocity of the particle at late times (i.e. for t » T)? Explain why this result makes sense.