Explanation Given: The radius and angular velocity is shown in Figure (1). The angular velocity is ω A = 40 ( t 3 + 6 t ) rad/s . Time t is 2 s . From Figure (1). The radius r A is 10 mm . The radius r B is 40 mm . The radius r E is 15 mm . Write the equation of the angular velocity. ω A = 40 ( t 3 + 6 t ) rad/s Here, angular velocity is ω . Write the expression for the angular acceleration of gear A . α A = d ω A d t (I) Here, angular acceleration is α and rate of change of angular velocity with respect to time is ( d ω d t ) . Write the expression for the angular acceleration of gear B . α B = d ω B d t (II) Here, angular acceleration is α and rate of change of angular velocity with respect to time is ( d ω d t ) . Write the velocity expression for the spindle E F . υ E = ω B r E (III) Here, velocity at point C is υ C , angular velocity is ω B and radius is r . Write the expression for tangential acceleration of the spindle E F . ( a t ) E = α B r E (IV) Here, tangential acceleration is a t , is radius of spindle E is r E and acceleration at B is α . Since, gear B is in mesh with gear A . Write the expression for normal acceleration of the spindle E F . ( a n ) E = ω B 2 r E (V) Here, normal acceleration is a n , is radius of spindle E is r E and angular velocity is ω . Conclusion: Substitute 40 ( t 3 + 6 t ) rad/s for ω A in Equation (I). α A = d d t 40 ( t 3 + 6 t ) = 40 ( 3 t 2 + 6 ) rad/s 2 Substitute 40 ( t 3 + 6 t ) rad/s for ω A , 10 mm for r A and 40 mm for r B in Equation (III). ω B = r A r B ω A = 10 40 ( 40 ( t 3 + 6 t ) ) (VI) Substitute 2 s for t in Equation (VI). ω B = 10 40 ( 40 ( t 3 + 6 t ) ) = 10 40 ( 40 ( ( 2 ) 3 + 6 ( 2 ) ) ) = 200 rad/s Substitute 10 40 ( 40 ( t 3 + 6 t ) ) for ω B in Equation (II)

15th Edition

ISBN: 9780137514724

Author: HIBBELER

Publisher: PEARSON

See similar textbooks

Concept explainers

Power Transmission Elements

It is defined as the energy transfer from one location to another location. The energy will start moving from the energy generation source to the energy applied position to obtain the work output. From this method, a large amount of electric energy moves…

Videos

Question

Chapter 16, Problem 34P

To determine

The magnitudes of the velocity and the tangential and normal components

of acceleration of the spindle EF when t is 2 s .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 16, Problem 33P

Chapter 16, Problem 35P

Students have asked these similar questions

The uniform 1,157-mm link AB slides up on frictionless rollers as shown below. At the instant shown, the link AB is vertical and the absolute velocity of point A is 19.9 m/s in the direction shown. Ignore the link thickness and roller diametres. For this configuration, 01=39 degrees and O2=25 degrees as shown. VA 01 A G Calculate the absolute velocity of the centre of mass at G. Give your answer in the form Z = 2 VGx + VGy in m/s where vGx is the horizontal component of the velocity vector (positive to the right) and VGy is the vertical component of the velocity vector (positive upwards). Round your final answer to two decimal places.

Slider 4 is moving downward at a speed of 14 = 2 m/s and with a downward acceleration of a = 0,25 m/s at the moment 0=60°. The slider is connected to a wheel of with a radius of R = 1.5 m with a rod of length L = 3 m. The wheel is rolling without slipping. VA ал C B VA OB R A) Sketch a diagram of the rod showing the location of its Instant Center at the moment shown. What is the distance, r from the instant center to to point A? A/IC' B) Using the rod's instant center, determine the angular speed of rod AB. C) Using a relative acceleration approach, determine the acceleration of point B.

For a short time a motor of the random-orbit sander drives the gear A with an angular velocity of WA = 40(t³ + 6t) rad/s, where t is in seconds. This gear is connected to gear B, which is fixed connected to the shaft CD. The end of this shaft is connected to the eccentric spindle EF and pad P, which causes the pad to orbit around shaft CD at a radius of 15 mm. (Figure 1) Figure 1 of 1 Part A Determine the magnitude of the velocity of the spindle EF when t = 2.3 s after starting from rest. Express your answer to three significant figures and include the appropriate units. UE= Submit Part B Value Submit μÅ + (aE)t. (aE)n = Request Answer Provide Feedback Determine the magnitudes of the tangential and normal components of acceleration of the spindle EF when t = 2.3 s after starting from rest. Express your answers in meters per second squared to three significant figures separated by a comma. AΣ 1 vec + Units Request Answer ? ? m/s²

Chapter 16 Solutions

PEARSON ETEXT ENGINEERING MECH & STATS

Ch. 16 - When the gear rotates 20 revolutions, it achieves...Ch. 16 - The flywheel rotates with an angular velocity of ...Ch. 16 - The flywheel rotates with an angular velocity of (...Ch. 16 - The bucket is hoisted by the rope that wraps...Ch. 16 - A wheel has an angular acceleration of = (0.5 )...Ch. 16 - For a short period of time, the motor turns gear A...Ch. 16 - Prob. 1P Ch. 16 - The angular acceleration of the disk is defined by...Ch. 16 - The disk is originally rotating at 0 = 12 rad/s....Ch. 16 - Prob. 4P

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 magnitudes of the velocity and the tangential and normal components of acceleration of the spindle E F when t is 2 s .

Solution Summary: The author explains the magnitudes of the velocity and the tangential and normal components of acceleration in the spindle EF.

Concept explainers

Videos

The magnitudes of the velocity and the tangential and normal components

of acceleration of the spindle EF when t is 2 s .

Want to see the full answer?

Chapter 16 Solutions

The magnitudes of the velocity and the tangential and normal components of acceleration of the spindle E F when t is 2 s .

Solution Summary: The author explains the magnitudes of the velocity and the tangential and normal components of acceleration in the spindle EF.

Concept explainers

Videos

The magnitudes of the velocity and the tangential and normal components of acceleration of the spindle EF when t is 2 s .

Want to see the full answer?

Chapter 16 Solutions

The magnitudes of the velocity and the tangential and normal components

of acceleration of the spindle EF when t is 2 s .