Question

Notify Me Bookmark

For high-speed motion through the air - such as a skydiver shown in the figure, falling before the parachute is opened - air resistance is close to a power of the instantaneous velocity v(t). Determine a differential equation for the velocity v(t) of a falling body of mass m if air resistance is proportional to the square of the instantaneous velocity. Assume the downward direction is positive. (Use k > 0 for the constant of proportionality, g > 0 for acceleration due to gravity, and v for v(t).) dv/dt

For high-speed motion through the air - such as a skydiver shown in the figure, falling before the parachute is opened - air resistance is close to a power of the instantaneous velocity v(t). Determine a differential equation for the velocity v(t) of a falling body of mass m if air resistance is proportional to the square of the instantaneous velocity. Assume the downward direction is positive. (Use k > 0 for the constant of proportionality, g > 0 for acceleration due to gravity, and v for v(t).) dv/dt

For high-speed motion through the air - such as a skydiver shown in the figure, falling before the parachute is opened - air resistance is close to a power of the instantaneous velocity v(t). Determine a differential equation for the velocity v(t) of a falling body of mass m if air resistance is proportional to the square of the instantaneous velocity. Assume the downward direction is positive. (Use k > 0 for the constant of proportionality, g > 0 for acceleration due to gravity, and v for v(t).) dv/dt

Image text
For high-speed motion through the air - such as a skydiver shown in the figure, falling before the parachute is opened - air resistance is close to a power of the instantaneous velocity v(t). Determine a differential equation for the velocity v(t) of a falling body of mass m if air resistance is proportional to the square of the instantaneous velocity. Assume the downward direction is positive. (Use k > 0 for the constant of proportionality, g > 0 for acceleration due to gravity, and v for v(t).) dv/dt

Detailed Answer

2 0

Please enter your email here. You will get email when this question is answered by our tutor.

Answer
Doubtrix Logo

This Problem has been solved!

You'll get a detailed, step-by-step and expert verified solution.

Join Doubtrix with 7-days free trial

  • Icon Correct & Verified Answers
  • Icon No AI-Generated Answers
  • Icon Video Solution for Difficult Questions
  • Icon Work With Experts to Reach at Correct Answers
Login Sign Up
  • Student Reviews:
  • (2)
  • Correct answers (2)
  • Complete solution (2)
  • Step-by-step solution (2)
  • Fully explained (2)

Similar/Related Questions

In (14) of Section 1.3 we saw that a differential equation describing the velocity v of a falling mass subject to air resistance proportional to the instantaneous velocity is mdv/dt = mg - kv, where k > 0 is a constant of proportionality. The positive direction is downward. (a) Solve the equation subject to the initial condition v(0) = v0: v(t) = (b) Use the solution in part (a) to determine the limiting, or terminal, velocity of the mass. (c) If the distance s, measured from the point where the mass was released above ground, is related to velocity v by ds/dt = v(t), find an explicit expression for s(t) if s(0) = 0. s(t) =
Solution
0 0

A bucket crane consists of a uniform boom of mass M = 201 kg and length L = 59.69 ft that pivots at a point on a truck bed. The boom supports an elevated bucket with a worker inside at the other end of the boom, as shown in the figure. Model the bucket and the worker together as a point mass of weight 203 Ib, located at the end point of the boom. Suppose that when the boom makes an angle of 66.3∘ with the horizontal truck bed, the bucket crane suddenly loses power, causing the bucket and boom to rotate freely toward the ground. Take the rotation axis to be at the point where the boom pivots on the truck bed. Use R = 9.81 m/s2 for the acceleration due to gravity. For unit conversions, assume that 1 m = 3.28 ft and 1 Ib = 4.45 N. Find the magnitude of the angular acceleration a of the system just after the crane loses power. Express your answer Io at least two decimal places. a = rad s2
Solution
0 0

A block of mass M and contact area A slides on a thin film of oil with thickness h as shown in the figure. When released, a mass m exerts tension on the cord, causing the block to accelerate. (a) Neglect friction in the pulley and air resistance, and develop an algebraic expression for the viscous force that acts on the block when it moves at a speed V. (b) Derive a differential equation for the block speed as a function of time, and obtain an expression for the block speed as a function of time. (c) For the values μ = 0.04 Pa−s, m = 2 kg, A = 10 cm2, and h = 0.1 mm, determine the block mass M if it takes 10 s for the block speed to reach 1 m/s.
Solution
0 0