Explanation The below figure shows the position of hydraulic cylinder of θ = 30 ° . Figure-(1) Write the expression for the distance between point P and A from Δ A P C form Figure-(1). x = P C ¯ tan θ (I) Here, the distance between point P and C is P C ¯ and angle between P C ¯ and C A ¯ θ . Differentiate Equation (I) with respect to t . v A = ω P C ¯ sec 2 θ (II) Here, the velocity of point A is v A , the angular velocity of point A is ω . Differentiate Equation (II) with respect to t . a = α P C ¯ sec 2 θ + ω P C ¯ ( 2 sec θ ) ( ω sec θ tan θ ) = α P C ¯ sec 2 θ + 2 ω 2 P C ¯ sec 2 θ tan θ (III) Here, the acceleration of point A is x ¨ and the angular acceleration of A is θ ¨ . Write the expression for the distance between point D and B . D B ¯ = E C ¯ − D E ¯ tan θ (IV) Here, the distance between point D and E is D E ¯ and the distance between point E and C is E C ¯ Write the expression for the distance between point C and B . C B ¯ = D E ¯ cos θ (V) Here, the distance between point E and D is E D ¯ . Write the expression for the magnitude of velocity of point B . v B = C B ¯ ω (VI) Write the expression for the magnitude of velocity of point D . v D = D E ¯ ω (VII) Here, the length of link D E is D E ¯ . Write the expression for the magnitude of relative velocity of point D with respect to point B . v D / B = v D − v B (VIII) Write the expression for the magnitude of normal acceleration of point B . ( a B ) n = C B ¯ ω 2 (IX) Here, the distance between point B and C is C B ¯ . Write the expression for the magnitude of tangential acceleration of point B . ( a B ) t = C B ¯ α (X) Write the expression for the magnitude of normal acceleration of point D with respect to B . ( a D / B ) n = v D / B 2 D B ¯ (XI) Write the expression for the magnitude to normal acceleration of point D . ( a D ) n = v D 2 D E ¯ (XII) Write the expression for the magnitude of tangential acceleration of point D . ( a D ) t = D E ¯ α D E (XIII) Here, the angular acceleration of D E is α D E . Conclusion: Substitute 0.3 m / s for v A , 30 ° for θ , and 200 mm for P C ¯ in Equation (I). 0.3 m / s = ω ( 200 mm ) sec 2 30 ° ω = 0.3 m / s ( 200 mm × 10 − 3 m 1 mm ) ( 4 3 ) = 1.125 rad / s Substitute 1.125 rad / s for ω , 30 ° for θ , 0 m / s for a , and 200 mm for P C ¯ in Equation (III). 0 m / s = α ( 200 mm ) sec 2 30 ° + 2 ( 1.125 rad / s ) 2 ( 200 mm ) sec 2 30 ° tan 30 ° α = − 2 ( 1.125 rad / s ) 2 ( 1 3 ) = − 1.461 rad / s 2 Substitute 200 mm for E C ¯ , 90 mm for D E ¯ , and 30 ° for θ in Equation (IV). D B ¯ = 200 mm − ( 90 mm ) tan 30 ° = ( 200 mm × 10 − 3 m 1 mm ) − ( 90 mm × 10 − 3 m 1 mm ) ( 0.577 ) = 0.2 m − 0 .052 m = 0.148 m Substitute 90 mm for D E ¯ and 30 ° for θ in Equation (V). C B ¯ = 90 mm cos 30 ° = ( 90 mm × 10 − 3 m 1 mm ) ( 0

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ISBN: 9781118885840

Author: James L. Meriam, L. G. Kraige, J. N. Bolton

Publisher: WILEY

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Chapter 5.8, Problem 202RP

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The angular acceleration αDE of DE at the instant when θ=30°.

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Chapter 5.8, Problem 201RP

Chapter 5.8, Problem 203RP

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Ch. 5.2 - The device shown rotates about the fixed z-axis...Ch. 5.2 - Prob. 12P Ch. 5.2 - The T-shaped body rotates about a horizontal axis...Ch. 5.2 - Prob. 14P Ch. 5.2 - Prob. 15P Ch. 5.2 - Prob. 16P Ch. 5.2 - The bent flat bar rotates about a fixed axis...Ch. 5.2 - At time t = 0, the arm is rotating about the fixed...Ch. 5.2 - A variable torque is applied to a rotating wheel...Ch. 5.2 - Prob. 20P Ch. 5.2 - Prob. 21P Ch. 5.2 - Prob. 22P Ch. 5.2 - Prob. 23P Ch. 5.2 - Prob. 24P Ch. 5.2 - Prob. 25P Ch. 5.2 - During its final spin cycle, a front-loading...Ch. 5.2 - Prob. 27P Ch. 5.2 - Prob. 28P Ch. 5.3 - Slider A moves in the horizontal slot with a...Ch. 5.3 - The fixed hydraulic cylinder C imparts a constant...Ch. 5.3 - Prob. 31P Ch. 5.3 - At the instant under consideration, the hydraulic...Ch. 5.3 - The hydraulic cylinder D is causing the distance...Ch. 5.3 - The Scotch-yoke mechanism converts rotational...Ch. 5.3 - Prob. 35P Ch. 5.3 - The wheel of radius r rolls without slipping, and...Ch. 5.3 - Link OA rotates with a clockwise angular velocity...Ch. 5.3 - Determine the acceleration of the shaft B for θ =...Ch. 5.3 - Prob. 39P Ch. 5.3 - Prob. 40P Ch. 5.3 - Boom OA is being elevated by the rope-and-pulley...Ch. 5.3 - The hydraulic cylinder imparts a constant upward...Ch. 5.3 - Prob. 43P Ch. 5.3 - The rod OB slides through the collar pivoted to...Ch. 5.3 - Prob. 45P Ch. 5.3 - Prob. 46P Ch. 5.3 - Link OA is given a clockwise angular velocity ω =...Ch. 5.3 - Prob. 48P Ch. 5.3 - Derive an expression for the upward velocity v of...Ch. 5.3 - Prob. 50P Ch. 5.3 - Show that the expressions v = rω and at = rα hold...Ch. 5.3 - Prob. 52P Ch. 5.3 - Prob. 53P Ch. 5.3 - Prob. 54P Ch. 5.3 - Prob. 55P Ch. 5.3 - Prob. 56P Ch. 5.3 - Prob. 57P Ch. 5.3 - The punch is operated by a simple harmonic...Ch. 5.4 - The right-angle link AB has a clockwise angular...Ch. 5.4 - The uniform rectangular plate moves on the...Ch. 5.4 - The cart has a velocity of 4 ft/sec to the right....Ch. 5.4 - Prob. 62P Ch. 5.4 - The speed of the center of the earth as it orbits...Ch. 5.4 - Prob. 64P Ch. 5.4 - The circular disk of radius 8 in. is released very...Ch. 5.4 - For a short interval, collars A and B are sliding...Ch. 5.4 - Prob. 67P Ch. 5.4 - The magnitude of the absolute velocity of point A...Ch. 5.4 - Prob. 69P Ch. 5.4 - Prob. 70P Ch. 5.4 - Determine the angular velocity of bar AB just...Ch. 5.4 - For the instant represented, point B crosses the...Ch. 5.4 - Prob. 73P Ch. 5.4 - For a short interval, collars A and B are sliding...Ch. 5.4 - Determine the angular velocity of link BC for the...Ch. 5.4 - The elements of a switching device are shown. 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The angular acceleration α D E of D E at the instant when θ = 30 ° .

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The angular acceleration αDE of DE at the instant when θ=30°.

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Chapter 5 Solutions