To determine The normal force exerted by the cam on the roller. The reaction force exerted by the sides of the slot. Explanation Draw the free-body diagram of the system as shown in Figure (1). Write the equation of circle formed with the center of the circle. ( x − x 0 ) 2 + ( y − y 0 ) 2 = R 0 2 (I) Here, x and y coordinates of center of the circle are x 0 and y 0 respectively and radius of the circle is R 0 . Substitute − 0.1 m for x 0 , 0 m for y 0 and 0 .2 m for R 0 in Equation (I). ( x − ( − 0.1 m ) ) 2 + ( y − 0 m ) 2 = ( 0.2 m ) 2 ( x + 0.1 ) 2 + y 2 = 0.04 Write the equation of circle formed with the center of the circle in polar form. ( r cos θ − x 0 ) 2 + ( r sin θ − y 0 ) 2 = R 0 2 (II) Here, radial distance between the points O and A is r and angle made by the slotted arm with horizontal axis is θ . Substitute − 0.1 m for x 0 , 0 m for y 0 and 0 .2 m for R 0 in Equation (II). ( r cos θ − ( − 0.1 m ) ) 2 + ( r sin θ − 0 m ) 2 = ( 0.2 m ) 2 ( r cos θ + 0.1 ) 2 + ( r sin θ ) 2 = 0.04 r 2 + 0.2 r cos θ − 0.03 = 0 (III) Substitute 45 ° for θ in Equation (III). r 2 + 0.2 r ( cos 45 ° ) − 0.03 = 0 r = 0.1164 m Differentiate Equation (III) with respect to time. d d t ( r 2 + 0.2 r cos θ − 0.03 ) = 0 2 r r ˙ + 0.2 r ˙ cos θ − 0.2 r θ ˙ sin θ = 0 (IV) Here, velocity of the slotted arm is r ˙ and angular velocity of the slotted arm is θ ˙ . Substitute 0 .1164 m for r , 45 ° for θ and 15 rad / s for θ ˙ in Equation (IV). 2 ( 0 .1164 m ) r ˙ + 0.2 r ˙ ( cos 45 ° ) − 0.2 ( 0 .1164 m ) ( 15 rad / s ) ( sin 45 ° ) = 0 r ˙ = 0.660 m / s Differentiate Equation (IV) with respect to time. d d t ( 2 r r ˙ + 0.2 r ˙ cos θ − 0.2 r θ ˙ sin θ ) = 0 2 r ˙ 2 + 2 r r ¨ + 0.2 r ¨ cos θ − 0.2 r ˙ θ ˙ sin θ − 0.2 r ˙ θ ˙ sin θ − 0.2 r θ ¨ sin θ − 0.2 r θ ˙ 2 cos θ } = 0 2 r ˙ 2 + 2 r r ¨ + 0.2 r ¨ cos θ − 0.4 r ˙ θ ˙ sin θ − 0.2 r θ ¨ sin θ − 0.2 r θ ˙ 2 cos θ } = 0 (V) Here, acceleration of the slotted arm is r ¨ and angular acceleration of the slotted arm is θ ¨ . Substitute 0 .1164 m for r , 0.660 m / s for r ˙ , 0 for θ ¨ , 45 ° for θ and 15 rad / s for θ ˙ in Equation (V). 2 ( 0.660 m / s ) 2 + 2 ( 0 .1164 m ) r ¨ + 0

8th Edition

ISBN: 9781118885840

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

Publisher: WILEY

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Chapter 3.5, Problem 94P

To determine

The normal force exerted by the cam on the roller.

The reaction force exerted by the sides of the slot.

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Chapter 3.5, Problem 93P

Chapter 3.5, Problem 95P

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