Solns MIE 310 2012 HW 3

# Solns MIE 310 2012 HW 3 - the center of the ball. Hint the...

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Dynamics, MIE 230 Spring, 2012 Problem Set #3 Due: Wednesday, February 15 1. (a) At the instant represented, the slotted arm is rotating a speed of N = 80 rpm and is slowing down at the rate of 280 rpm/s. Also, at the same time the radial distance r to the slider P is 250 mm and is decreasing at the constant rate of 300 mm/s. For this instant determine the acceleration a of P . (b) Suppose that at a different instant of time θ is 4 rad/s, = 16 rad/s 2 and r = 250 mm. What would be the corresponding time derivatives of r if the slider P had zero acceleration at this instant? Answer (part b) : r = -0.5 m/s, r = 4 m/s 2 SOLUTION (a) 1

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(b) 2. Consider the power screw shown. The screw has a lead (advancement per revolution), L , of 1.25 in/rev and a distance, b , to the center of the ball A of 6 in. The screen turns at a constant rate of 4 rev/sec. Calculate the magnitudes of the velocity and acceleration of

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Unformatted text preview: the center of the ball. Hint the velocity of advance of the ball can be found by taking into account the helix angle, , by the equation: cos / v v = where the helix angle may be found from: ( 29 b L 2 / tan = 2 SOLUTION 3. 3 SOLUTION 4. 4 SOLUTION 5. Hint: use spherical coordinates 5 SOLUTION Use this equation: e a e a e a a R R + + = where: 2 2 2 cos R R R a R--= ( 29 sin 2 cos 2 R R dt d R a-= ( 29 cos sin 1 2 2 R R dt d R a + = In this situation L R =-= , Therefore: 6 7 6. SOLUTION 8 7. SOLUTION 8. 9 SOLUTION 10 9. If the velocity x of block A up the incline is increasing at a rate of 0.044 m/s each second, determine the acceleration of B. SOLUTION 11...
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## This note was uploaded on 03/27/2012 for the course MIE 310 taught by Professor Corradopoli during the Spring '08 term at UMass (Amherst).

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Solns MIE 310 2012 HW 3 - the center of the ball. Hint the...

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