menu
bartleby
search
close search
Hit Return to see all results

Based on experimental observations, the acceleration of a particle is defined by the relation a = –(0.1 + sin x/b), where a and x are expressed in m/s2 and meters, respectively. Know that b = 0.80 m and that v = 1 m/s when x = 0.Determine the position where the velocity is maximum.

Question

Based on experimental observations, the acceleration of a particle is defined by the relation a = –(0.1 + sin x/b), where a and x are expressed in m/s2 and meters, respectively. Know that b = 0.80 m and that v = 1 m/s when = 0.

Determine the position where the velocity is maximum.

check_circleAnswer
Step 1

The acceleration of the particle is given as the:

0.1+sin
where
b 0.8m
v 1m/s whenx 0
a andx are expressed in m/s2
help_outline

Image Transcriptionclose

0.1+sin where b 0.8m v 1m/s whenx 0 a andx are expressed in m/s2

fullscreen
Step 2

The maximum velocity of the particle will be when acceleration of the particle is zero

As we know:

dv
a
For the position of maximum velocity
dv
dx
v = v,
a 0
ma
0.1+sin
0 =
x
0....
b
0.1 sin
..(1)
help_outline

Image Transcriptionclose

dv a For the position of maximum velocity dv dx v = v, a 0 ma 0.1+sin 0 = x 0.... b 0.1 sin ..(1)

fullscreen
Step 3

Put the value of b in the equat...

b-0.8m
x
0.1+sin 0
0.8
sin1.25x-0.1
1.25x-sin(-0.1)
sin'(-0.1)
x =
1.25
-5.7392 x
x =
180
1.25
x = -0.0801m
help_outline

Image Transcriptionclose

b-0.8m x 0.1+sin 0 0.8 sin1.25x-0.1 1.25x-sin(-0.1) sin'(-0.1) x = 1.25 -5.7392 x x = 180 1.25 x = -0.0801m

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Our solutions are written by experts, many with advanced degrees, and available 24/7

See Solution
Tagged in

Engineering

Mechanical Engineering

Related Mechanical Engineering Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: Technician A says that the front bearing assembly locknuts for RWD vehicles are typically heavily to...

A: A high torque for maintaining the bearing adjustment is required in the FWD vehicles and not the RWD...

question_answer

Q: 2-1. Temperature Response in Cooling a Wire. A small copper wire with a diameter of 0.792 mm and ini...

A: Time can be calculated by,

question_answer

Q: True or False: Objects on a layer that is turned off can still be modified

A: The AutoCAD hides the objects present in a layer that is turned off. The objects are only hidden and...

question_answer

Q: piston, on which rests a weight. . A gas is confined in a 1.25(ft) diameter cylinder by a The mass o...

A: Click to see the answer

question_answer

Q: A steam turbine at steady state is operated at part load by throttling the steam to a lower pressure...

A: Frist we have to draw the line diagram by using assumptions given in the problem 

question_answer

Q: The attached figure shows a gas contained in a vertical piston– cylinder assembly, where D = 10 cm. ...

A: a)Calculate the change in elevation of the piston-shaft.

question_answer

Q: Air enters a compressor operating at steady state at 1.05 bar, 300 K, with a volumetric flow rate of...

A: Given data:

question_answer

Q: A body has a mass of 18 kg falls freely from rest. After falling 235 m, what will its velocity be ju...

A: Given information:mass of the body=18kgAfter falling height =235mThen find the velocity before impac...

question_answer

Q: Two smooth discs A and B have a mass of 0.5 kg. Both discs are moving with velocities shown when the...

A: Given information:And then consider the given diagram 

Sorry about that. What wasn’t helpful?