[PDF] PROBLEM 11.1 Cambiado con la DEMO VERSION de CAD-KAS

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PROPRIETARY MATERIAL. © 2013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed,

reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited

distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual,

you are using it without permission. 5

PROBLEM 11.1

The motion of a particle is defined by the relation 42

10 8 12xt t t=- ++, where x and t are expressed in

inches and seconds, respectively. Determine the position, the velocity, and the acceleration of the particle

when t = 1 s.

SOLUTION

42

10 8 12=- ++xt t t

3

4208==-+dxvttdt

2

12 20== -dvatdt

At

1s,t= 1 10 8 12 11x=- ++ = 11.00 in.=x

4208 8=- +=-v 8.00 in./sv=-

12 20 8=-=-a

2

8.00 in./sa=-

Cambiado con la DEMO VERSION de CAD-KAS PDF-Editor (http://www.cadkas.com). Cambiado con la DEMO VERSION de CAD-KAS PDF-Editor (http://www.cadkas.com). Cambiado con la DEMO VERSION de CAD-KAS PDF-Editor (http://www.cadkas.com). This text only appears in the demo version. This text can be removed with the full version. This text only appears in the demo version. This text can be removed with the full version. This text only appears in the demo version. This text can be removed with the full version. Cambiado con la DEMO VERSION de CAD-KAS PDF-Editor (http://www.cadkas.com). Cambiado con la DEMO VERSION de CAD-KAS PDF-Editor (http://www.cadkas.com). Cambiado con la DEMO VERSION de CAD-KAS PDF-Editor (http://www.cadkas.com). This text only appears in the demo version. This text can be removed with the full version. This text only appears in the demo version. This text can be removed with the full version. This text only appears in the demo version. This text can be removed with the full version.

PROPRIETARY MATERIAL. © 2013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed,

reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited

distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual,

you are using it without permission. 6

PROBLEM 11.2

The motion of a particle is defined by the relation 32

2 9 12 10,=-++xt t t where x and t are expressed in feet

and seconds, respectively. Determine the time, the position, and the acceleration of the particle when v = 0.

SOLUTION

32

2 9 12 10xt t t=-++

Differentiating,

22

618126(32)

6( 2)( 1)==-+= -+

=- -dx vttttdt tt

12 18==-dvatdt

So

0=v at 1s=t and 2s.=t

At 1s,=t 1

2 9 12 10 15=-+ + =x 1.000 st=

1

12 18 6=-=-a

1

15.00 ft=x

2 1

6.00 ft/s=-a

At 2s,=t 32
2

2(2) 9(2) 12(2) 10 14=-++=x 2.00 s=t

2

14.00 ft=x

2 (12)(2) 18 6a=-= 2 2

6.00 ft/s=a

Cambiado con la DEMO VERSION de CAD-KAS PDF-Editor (http://www.cadkas.com). Cambiado con la DEMO VERSION de CAD-KAS PDF-Editor (http://www.cadkas.com). Cambiado con la DEMO VERSION de CAD-KAS PDF-Editor (http://www.cadkas.com). This text only appears in the demo version. This text can be removed with the full version. This text only appears in the demo version. This text can be removed with the full version. This text only appears in the demo version. This text can be removed with the full version. Cambiado con la DEMO VERSION de CAD-KAS PDF-Editor (http://www.cadkas.com). Cambiado con la DEMO VERSION de CAD-KAS PDF-Editor (http://www.cadkas.com). Cambiado con la DEMO VERSION de CAD-KAS PDF-Editor (http://www.cadkas.com). This text only appears in the demo version. This text can be removed with the full version. This text only appears in the demo version. This text can be removed with the full version. This text only appears in the demo version. This text can be removed with the full version.

PROPRIETARY MATERIAL. © 2013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed,

reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited

distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual,

you are using it without permission. 7

PROBLEM 11.3

The vertical motion of mass A is defined by the relation 10 sin 2 15cos2 100,xtt=++ where x and t are expressed in mm and seconds, respectively. Determine (a) the position, velocity and acceleration of A when t = 1 s, (b) the maximum velocity and acceleration of A.

SOLUTION

10sin2 15cos2 100=++xtt

20cos2 30sin2== -dxvttdt

40sin2 60cos2==- -dvattdt

For trigonometric functions set calculator to radians: (a) At 1s.=t 1

10sin2 15cos2 100 102.9x=++=

1

102.9 mmx=

1

20cos2 30sin2 35.6v=-=-

1

35.6 mm/s=-v

1

40sin2 60cos2 11.40=- - =-a

2 1

11.40 mm/sa=-

(b) Maximum velocity occurs when 0.a=

40sin2 60cos2 0tt-- =

60tan2 1.540t=- =-

1

2 tan ( 1.5) 0.9828t

=-=- and 0.9828π-+

Reject the negative value.

2 2.1588t=

1.0794st=

1.0794st= for v

max max

20cos(2.1588) 30sin(2.1588)

36.056v=-

max

36.1 mm/sv=-

Note that we could have also used

22
max

20 30 36.056v=+=

by combining the sine and cosine terms. For a max we can take the derivative and set equal to zero or just combine the sine and cosine terms. 22 2
max

40 60 72.1mm/sa=+=

2 max

72.1 mm/sa=

so Cambiado con la DEMO VERSION de CAD-KAS PDF-Editor (http://www.cadkas.com). Cambiado con la DEMO VERSION de CAD-KAS PDF-Editor (http://www.cadkas.com). Cambiado con la DEMO VERSION de CAD-KAS PDF-Editor (http://www.cadkas.com). This text only appears in the demo version. This text can be removed with the full version. This text only appears in the demo version. This text can be removed with the full version. This text only appears in the demo version. This text can be removed with the full version. Cambiado con la DEMO VERSION de CAD-KAS PDF-Editor (http://www.cadkas.com). Cambiado con la DEMO VERSION de CAD-KAS PDF-Editor (http://www.cadkas.com). Cambiado con la DEMO VERSION de CAD-KAS PDF-Editor (http://www.cadkas.com). This text only appears in the demo version. This text can be removed with the full version. This text only appears in the demo version. This text can be removed with the full version. This text only appears in the demo version. This text can be removed with the full version.

PROPRIETARY MATERIAL. © 2013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed,

reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited

distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual,

you are using it without permission. 8

PROBLEM 11.4

A loaded railroad car is rolling at a constant velocity when it couples with a spring and dashpot bumper system. After the coupling, the motion of the car is defined by the relation 4.8

60 sin16

t xe t = where x and t are expressed in mm and seconds, respectively. Determine the position, the velocity and the acceleration of the railroad car when (a) t = 0, (b) t = 0.3 s.

SOLUTION

4.8

60 sin16

t xe t

4.84.8

4.84.8

60( 4.8) sin16 60(16) cos16

288 sin16 960 cos16

tt tt dxvetetdt ve te t

4.84.8

4.84.8

4.84.8

1382.4 sin16 4608 cos16

4608 cos16 15360 sin16

13977.6 sin16 9216 cos16

tt tt t dvaetetdt etet aetet (a) At 0,t= 0 0x= 0

0 mmx=

0

960 mm/sv=

0

960 mm/sv=

2 0

9216 mm/sa=-

2 0

9220 mm/sa=

(b) At

0.3s,t=

4.8 1.44

0.23692

sin16 sin4.8 0.99616 cos16 cos4.8 0.08750 t ee t t 0.3 (60)(0.23692)( 0.99616) 14.16x=-=- 0.3

14.16 mmx=

0.3 (288)(0.23692)( 0.99616) (960)(0.23692)(0.08750) 87.9v=- - 0.3

87.9 mm/sv=

0.3 (13977.6)(0.23692)( 0.99616) (9216)(0.23692)(0.08750) 3108a=-- 2 0.3

3110 mm/sa=

or 2

3.11 m/s

Cambiado con la DEMO VERSION de CAD-KAS PDF-Editor (http://www.cadkas.com). Cambiado con la DEMO VERSION de CAD-KAS PDF-Editor (http://www.cadkas.com). Cambiado con la DEMO VERSION de CAD-KAS PDF-Editor (http://www.cadkas.com). This text only appears in the demo version. This text can be removed with the full version. This text only appears in the demo version. This text can be removed with the full version. This text only appears in the demo version. This text can be removed with the full version. Cambiado con la DEMO VERSION de CAD-KAS PDF-Editor (http://www.cadkas.com). Cambiado con la DEMO VERSION de CAD-KAS PDF-Editor (http://www.cadkas.com). Cambiado con la DEMO VERSION de CAD-KAS PDF-Editor (http://www.cadkas.com). This text only appears in the demo version. This text can be removed with the full version. This text only appears in the demo version. This text can be removed with the full version. This text only appears in the demo version. This text can be removed with the full version.

PROPRIETARY MATERIAL. © 2013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed,

reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited

distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual,

you are using it without permission. 9

PROBLEM 11.5

The motion of a particle is defined by the relation 43 2

621233,xt t t t=-- ++where x and t are expressed in

meters and seconds, respectively. Determine the time, the position, and the velocity when 0.a=

SOLUTION

We have

43 2

621233xt t t t=-- ++

Then 32

24 6 24 3dxvtttdt== --+

and 2

72 12 24dvattdt== --

When 0:a= 22

72 12 24 12(6 2) 0tt tt--= --=

or (3 2)(2 1) 0tt-+= or

21sand s(Reject)32tt==-

0.667 st=

At

2s:3t=

43 2
2/3

22 2262123333 33x =-- ++

2/3 or 0.259 mx= 32
2/3

22 224 6 24 333 3v =--+

2/3 or 8.56 m/sv=- Cambiado con la DEMO VERSION de CAD-KAS PDF-Editor (http://www.cadkas.com). Cambiado con la DEMO VERSION de CAD-KAS PDF-Editor (http://www.cadkas.com). Cambiado con la DEMO VERSION de CAD-KAS PDF-Editor (http://www.cadkas.com). This text only appears in the demo version. This text can be removed with the full version. This text only appears in the demo version. This text can be removed with the full version. This text only appears in the demo version. This text can be removed with the full version. Cambiado con la DEMO VERSION de CAD-KAS PDF-Editor (http://www.cadkas.com). Cambiado con la DEMO VERSION de CAD-KAS PDF-Editor (http://www.cadkas.com). Cambiado con la DEMO VERSION de CAD-KAS PDF-Editor (http://www.cadkas.com). This text only appears in the demo version. This text can be removed with the full version. This text only appears in the demo version. This text can be removed with the full version. This text only appears in the demo version. This text can be removed with the full version.

PROPRIETARY MATERIAL. © 2013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed,

reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited

distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual,

you are using it without permission. 10

PROBLEM 11.6

The motion of a particle is defined by the relation 32

9248,xt t t=- + - where x and t are expressed in inches

and seconds, respectively. Determine (a) when the velocity is zero, (b) the position and the total distance

traveled when the acceleration is zero.

SOLUTION

We have

32

9248xt t t=- + -

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