IN SI UNITS November 2017 © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. These solutions represent a preliminary version of the Instructors' Solutions Manual (ISM). It is possible and even likely that at this preliminary stage of preparing the ISM there are some omissions and errors in the draft solutions. These will be corrected and this manual will be republished. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. Spring force is given by F(x) = 157 x + 0.2 x3 (1) F = 1000 N With x in mm, 1000 = 157 x* + 0.2 (x*)3 or 0.2 (x*)3 + 157 x*1000 = 0 (2) The roots of the cubic equation (2) can be found from MATLAB as x* = 6.08,3 ± 28.5i Thus x* is given by the real root of Eq (2) and is 6.08 mm. (a) Equivalent linear spring constant of rubber mounting at its static equilibrium position, using Eq. (1.7), is k eq dF dx 0.6 (x *)2 157 x* 0.6(6.08)2 157 179.2 N mm (b) Deflection of rubber mounting corresponding to keq is k F 1000 5.58 mm Keq 179.2 © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. F(x) = 34.6 x + 0.34 x2 + 0.002 x3 The steady-state deflection is 12.7 mm = x* The force extended on the spring is therefore F = 34.6 (12.7) + 0.34 (12.7)2 + 0.002 (12.7)3 = 498.3 N Equivalent linear spring constant at its steady deflection is given by Eq (1.7): k eq dF dx 34.6 0.68 x 0.006 x 2 x x* 34.6 0.68(12.7) 0.68(12.7)2 44.2 N mm © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. k rA2 where r 1.4 for air v 12000 (1.5 106 )(1.4) A2 v A2 5.71 103 v Let diameter of piston = d = 6 cm; A A2 8 106 (0.006)2 2.82 103 m2 4 8 106 v .0014 m 3 3 5.71 10 d 2 l Al 4 2.82 10-3 l 0.0014 m 3 Volume of cylinder l 0.496 m © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. For a helical spring, k Gd4 64nR 3 sinc e D k STEEL (80 109 )(0.05)4 231.5 k N m 8 10 (0.3)3 k ALUM (24 109 )(0.025)4 7.5 k N m (8)(10)(0.25)3 R 2 k Gd4 8nD3 (a) Spring 2 inside spring 1: keq = k1 + k2 = 239 kN/m (b) Spring 2 on top of spring 1: which gives k eq For a helical spring, k k1 k 2 k1 k 2 Gd4 64nR 3 1 1 1 k eq k1 k2 (231.5)(7.5) 7.26 kN m 231.5 7.5 D k1 (80 109 )(0.025)4 14.5 k N m (8)(10)(0.3)3 k2 (24 109 )(0.0125)4 0.468 k N m (8)(10)(0.25)3 (a) keq = k1 + k2 = 14.968 kN/m (b) k eq k1 k 2 k1 k 2 R Gd4 k 2 8nD3 0.453 kN m © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. x2 y sin 30 x1 y cos 30 Equivalence of strain energies: 1 1 1 k eq y2 k2 x 22 k1 x12 2 2 2 1 1 k1 y2 cos2 30 k2 y2 sin2 30 2 2 i.e., k eq k1 k2 A1 E 1 l1 A2 E2 l2 3 1 k1 k 2 4 4 (0.252 0.242 )(207 109 ) 4 318.5 m N m 2.5 (0.182 0.1682 )(207 109 ) 4 357.1 m N m 1.9 Therefore, k eq 3 1 (318.5) (357.1) 328.2 m N m 4 4 Similarly, the equivalent dampting constant can be found as (using equivalence of kinetic energies): c eq 3 1 3 1 c1 c2 (70) (52) 65.5 N s / m 4 4 4 4 Stainless steel: E = 200 × 109 N/m2, G = 86 × 109 N/m2 For each tube: D = 8.25 mm = 0.00825 m d = 8.00 mm = 0.008 m l = 1.3 m © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. Axial stiffness for a single tube ka AE (D2 d2 )E (0.008252 0.0082 )(200 109 ) 490.6 kN / m. l 4 l 4 13 Torsional stiffness for a single tube kT G 32 l (D4 d4 ) (86 104 )(0.008254 0.008 4 ) 3.48 N m / rad. (1.3)32 Total kA for 6 tubes = 6 KA = 6 × 490.6 = 2.94 mN/m Total kT for 6 tubes = 6 KT = 6 × 3.48 = 20.88 N m/rad © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 3 D3 l 2d c 1 ; D=diameter of piston, l = axial length of piston, d = radial clearance 3 D 4d µ = 0.30 Pa ∙ s Let d = 0.02 mm, D = 70 mm, and above equation gives 18 106 0.30 2 0.02 3 l(703 ) 1 3 4(0.02) 70 Therefore, l = 0.229 m = 22 cm © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. x(t) = 0.4 sin 4t + 5.0 cos 4t cm (1) By expressing Eq. (1) as x(t) = A sin(4t + ) = A (sin4t cos + cos4t sin) we obtain A cos = 0.4 (2) A sin = 5.0 (3) Eqs. (2) and (3) yield; tan 5.0 12.5 85.4261 1.4910 rad 0.4 and A 0.4 0.4 5.0181 cos 0.0797 x(t) 5.0181 sin(4t 1.4910)cm Velocity: x 20.0724 cos(4t 1.4910) cm/s Acceleration: x 80.2896 sin(4t 1.4910) cm s 2 Amplitudes of displacement, velocity and acceleration are: x max 5.0181 cm, x max 20.0724 cm s, x max 80.2896 cm s 2 © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. Speed = 100 rpm In a minute, a point will be subjected to the maximum pressure, A = pmax = 690 kPa, 100 × 4 = 400 times. Hence period 60 0.15 s 400 pressure, p(t) A, 0 t 4 p(t) 0, t 4 2 2 A = pmax 0 A 345 kPa a 0 p(t) dt A(t) 0 2 4 0 τ 4 τ 5τ 4 2τ 9τ 4 time, t 2A sin m t A m a m p(t) cos m t dt sin 0 m m 2 0 2 4 2A cos m t A m 1 bm p(t) sin m t dt cos m 0 m 2 0 2 4 Evaluation of am and bm: m=1 m=3 A A 3 a3 sin sin 0 73.2 kPa 3 2 2 2 A A A 3 (cos 1) 73.2 kPa b1 (cos 1) 219.6 kPa b2 (cos 1) 219.6 kPa b3 3 2 2 2 a1 A sin p(t) a0 2 m=2 A 219.6 kPa a2 (a m cos m t bm sin m t) Pa m 1 © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. Speed = 200 rpm In a minute, a point will be subjected to the maximum pressure, A = pmax = 690 kPa, 200 × 6 = 1200 times. Hence 60 0.05 s . 1200 period pressure, p(t) A = pmax A, 0 t 4 p(t) 0, t 4 2 0 A a 0 p(t) dt A(t)04 345 kPa 2 0 2 τ 4 τ 5τ 4 2τ 9τ 4 time, t 4 2A sin m t 2 A m sin a m p(t) cos m t dt 2 m 0 m 0 4 2A cos m t A m 2 bm p(t) sin m t dt cos 1 2 m 0 m 0 Evaluation of am and bm: m=1 a1 A sin A 219.5 kPa 2 A b1 cos 1 219.5 kPa 2 p(t) a0 2 m=2 m=3 A A 3 73.2 kPa sin 0 a3 sin 2 3 2 A A 3 1 73.2 kPa b2 (cos 1) 219.5 kPa b3 cos 3 2 2 a2 (a m cos m t bm sin m t) Pa m 1 © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. Goal: Mass to be maintained at 2.5 kg/min +/0.25 kg/min Parameters to be determined: Angular velocity of crank (), lengths of crank and connecting rod, dimensions of the wedge, dimensions of the orifice in the hopper, dimensions of the actuating rod and dimensions of the lever arrangement. Given: Density of the material in the hopper. Procedure: Select based on available motor. Determine the dimensions of the orifice in the hopper which delivers approximately 2.5 kg/min (assuming continuous flow of material). For trial dimensions of the wedge, determine the increase/decrease in the size (diameter) of the orifice. Choose the final dimensions of the wedge such that the material flow rate delivered by the orifice lies within the specified range. Force to be applied = 900 N, frequency = 50 Hz = 314.16 rad/s Procedure: 1. Select a motor that provides either directly or through a gear system the desired frequency. Assume that it is connected to the cam. 2. Determine the sizes and dimensions of the plate cam and roller. 3. Choose the dimensions of the follower. 4. Select the mass as 90 kg. From the geometry, determine the range of displacements (vertical motion) of the mass. 5. Determine the force exerted due to the falling mass. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. © 2018 Pearson Education Ltd. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.