Explanation Given information: The velocity and acceleration of the ankle is zero. During a jump, The velocity of the ankle is zero. The angular velocity of the tibia AK is ω = 1.5 rad/s ( Counterclockwise ) . The angular acceleration of the tibia AK is α = 1 rad/s 2 ( Counterclockwise ) . Calculation: Show the unit vectors as follows: i = 1 → j = 1 ↑ k=1 ( Counterclockwise ) Consider the position of the point K with respect to A is denoted by r K / A . Consider the position of the point H with respect to K is denoted by r H / K . Consider the position of the point H with respect to A is denoted by r H / A . Calculate the distances r K / A , r H / K , and r H / A as follows: r K / A = 12 i + 12 j r H / K = − 14 i + 14 j r H / A = r K / A + r K / H = ( 12 i + 12 j ) + ( − 14 i + 14 j ) = − 2 i + 26 j Take the frame of reference moving with the lower leg AK with angular velocity Ω and angular acceleration Ω ′ . Show the angular velocity Ω and Ω ′ as follows: Ω = ( 1.5 rad/s ) k ( Counterclockwise ) Ω ˙ = ( 1 rad/s 2 ) k ( Counterclockwise ) Show the motion of the hip H relative to the frame. The angular velocity and angular acceleration of H is denoted by ω = ω k and α = α k . The angular velocity and angular acceleration measured relative to lower leg AK . Consider the motion of the point H ′ coincides with H . Consider the velocity and acceleration on the point v H ′ are v H ′ and a W ′ . Calculate the value of v H ′ and v H ′ as follows: Substitute ( 1 rad/s 2 ) k for Ω ˙ , ( 1.5 rad/s ) k for Ω and ( − 2 i + 26 j ) for r H / A . v H ′ = Ω × r H / A = ( 1.5 rad/s ) k × ( − 2 i + 26 j ) = − 3 j − 39 i = − 39 i − 3 j a H ′ = Ω ˙ × r H / A − Ω 2 × r H / A = 1 k × ( − 2 i + 26 j ) − ( 1.5 ) 2 × ( − 2 i + 26 j ) = − 2 j − 26 i+4 .5i − 58 .5j = − 21.5 i − 60.5 j Consider the motion of H relative to the frame. Consider the velocity and acceleration on the point H relative to the frame are v H / A K and a H / A K . Calculate the value of v H / A K and a H / A K as follows: Substitute α k for α , ω k for ω and ( − 14 i + 14 j ) for r H / K . v H / A K = ω × r H / K = ω k × ( − 14 i + 14 j ) = − 14 ω j − 14 ω i = − 14 ω i − 14 ω j a H / A K = α × r H / K − ω 2 × r H / K = α k × ( − 14 i + 14 j ) − ω 2 ( − 14 i + 14 j ) = − 14 α j − 14 α i+ 14 ω 2 i − 14 ω 2 j Calculate the velocity of H using the relation: v H = v H ′ + v H / A K Substitute ( − 39 i − 3 j ) for v H ′ and ( − 14 ω i − 14 ω j ) for v W / S E

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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 15.5, Problem 15.171P

To determine

Find the relative angular velocity and relative angular acceleration of KH such that the velocity and acceleration of H both are straight up.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 15.5, Problem 15.170P

Chapter 15.5, Problem 15.172P

Students have asked these similar questions

The system has a pin-connected rod AB, rod BC and disk C. At the instant shown, the disc, with center C, rolls without slipping with an angular acceleration of 6 rad/s counterclockwise. If the velocity of C at this instant is 13 m/s to the left,a. what's the total acceleration of C (m/s^2)b. what's the angular acceleration of rod BC (rad/s^2)c. what's the total acceleration at point B (m/s^2)

Plz attach answer

If crank AB rotates with an angular velocity of wAB angular acceleration a AB = 6 rad/s? at the instant shown, determine: 1.1. The angular velocity of rod BC and the velocity of the slider block 1.2. The angular acceleration of rod BC and the linear acceleration of = 5 rad/s and an 0.5 m 0,3 m B 60° 30° WAB slider Block. 1.3. Locate the instantaneous center (IC) of the rod BC. CAB

Chapter 15 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

Ch. 15.1 - A rectangular plate swings from arms of equal...Ch. 15.1 - Knowing that wheel A rotates with a constant...Ch. 15.1 - Prob. 15.1P Ch. 15.1 - The motion of an oscillating flywheel is defined...Ch. 15.1 - The motion of an oscillating flywheel is defined...Ch. 15.1 - 15.4 The rotor of a gas turbine is rotating at a...Ch. 15.1 - A small grinding wheel is attached to the shaft of...Ch. 15.1 - A connecting rod is supported by a knife-edge at...Ch. 15.1 - Prob. 15.7P Ch. 15.1 - The angular acceleration of an oscillating disk is...

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.

Find the relative angular velocity and relative angular acceleration of KH such that the velocity and acceleration of H both are straight up.

Solution Summary: The author explains the relative angular velocity and relative acceleration of KH, such that they are straight up.

Concept explainers

Videos

Find the relative angular velocity and relative angular acceleration of KH such that the velocity and acceleration of H both are straight up.

Want to see the full answer?

Chapter 15 Solutions