Explanation Given: The atmospheric drag resistance is F D = k υ 2 . The time t is ∞ . Write the expression for the instantaneous acceleration. a = d υ d t (I). Here, acceleration is a and rate of change of velocity with respect to time ( t ) is d υ d t . Draw the free body diagram of the crate with equation of motion as shown in Figure (1). Write the formula to calculate vertical force components for Figure (1). ∑ F y = m a (II). Refer Figure (1). Apply equation of motion in y − axis and resolve the forces along y − axis . ∑ F y = m g − F D (III). Conclusion: Substitute d υ d t for a in Equation (II). ∑ F x = m d υ d t Substitute m d υ d t for ∑ F x and k υ 2 for F D in Equation (III). ∑ F y = m g − k υ 2 d υ d t = m g − k υ 2 m d υ d t = g − k υ 2 m d t = d υ g − k υ 2 m (IV). Integrate the Equation (IV) at the limits 0 to t for t and 0 to υ for υ . d t = d υ g − k υ 2 m ∫ 0 t d t = ∫ 0 υ d υ g − k υ 2 m ∫ 0 t d t = m k ∫ 0 υ ( d υ m g k − υ 2 ) [ t ] 0 t = [ m k ( 1 2 m g k ) ln [ m g k + υ m g k − υ ] ] 0 υ Continue with above steps

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

See similar textbooks

Concept explainers

Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be create…

Videos

Question

Chapter 13.4, Problem 43P

To determine

The velocity when man has fallen when time t is ∞ and is his velocity when he lands on the ground.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.4, Problem 42P

Chapter 13.4, Problem 44P

Students have asked these similar questions

Problem (14): A pump is being used to lift water from an underground tank through a pipe of diameter (d) at discharge (Q). The total head loss until the pump entrance can be calculated as (h₁ = K[V²/2g]), h where (V) is the flow velocity in the pipe. The elevation difference between the pump and tank surface is (h). Given the values of h [cm], d [cm], and K [-], calculate the maximum discharge Q [Lit/s] beyond which cavitation would take place at the pump entrance. Assume Turbulent flow conditions. Givens: h = 120.31 cm d = 14.455 cm K = 8.976 Q Answers: (1) 94.917 lit/s (2) 49.048 lit/s ( 3 ) 80.722 lit/s 68.588 lit/s 4

Problem (13): A pump is being used to lift water from the bottom tank to the top tank in a galvanized iron pipe at a discharge (Q). The length and diameter of the pipe section from the bottom tank to the pump are (L₁) and (d₁), respectively. The length and diameter of the pipe section from the pump to the top tank are (L2) and (d2), respectively. Given the values of Q [L/s], L₁ [m], d₁ [m], L₂ [m], d₂ [m], calculate total head loss due to friction (i.e., major loss) in the pipe (hmajor-loss) in [cm]. Givens: L₁,d₁ Pump L₂,d2 오 0.533 lit/s L1 = 6920.729 m d1 = 1.065 m L2 = 70.946 m d2 0.072 m Answers: (1) 3.069 cm (2) 3.914 cm ( 3 ) 2.519 cm ( 4 ) 1.855 cm TABLE 8.1 Equivalent Roughness for New Pipes Pipe Riveted steel Concrete Wood stave Cast iron Galvanized iron Equivalent Roughness, & Feet Millimeters 0.003-0.03 0.9-9.0 0.001-0.01 0.3-3.0 0.0006-0.003 0.18-0.9 0.00085 0.26 0.0005 0.15 0.045 0.000005 0.0015 0.0 (smooth) 0.0 (smooth) Commercial steel or wrought iron 0.00015 Drawn…

The flow rate is 12.275 Liters/s and the diameter is 6.266 cm.

Chapter 13 Solutions

Engineering Mechanics: Statics & Dynamics (14th Edition)

Ch. 13.4 - The 10-kg block is subjected to the forces shown....Ch. 13.4 - The 10-kg block is subjected to the forces shown....Ch. 13.4 - Determine the initial acceleration of the 10-kg...Ch. 13.4 - Prob. 4PP Ch. 13.4 - Prob. 1FP Ch. 13.4 - If motor M exerts a force of F = (10t2 + 100) N on...Ch. 13.4 - A spring of stiffness k = 500 N/m is mounted...Ch. 13.4 - Prob. 5FP Ch. 13.4 - Block B rests upon a smooth surface. If the...Ch. 13.4 - The 6-lb particle is subjected to the action of...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

The velocity when man has fallen when time t is ∞ and is his velocity when he lands on the ground.

Solution Summary: The author explains how to determine the velocity when man has fallen when time t is infty and his velocity if he lands on the ground.

Concept explainers

Videos

The velocity when man has fallen when time t is ∞ and is his velocity when he lands on the ground.

Want to see the full answer?

Chapter 13 Solutions