1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Delvig [45]
3 years ago
11

Block D of the mechanism is confined to move within the slot of member CB. Link AD is rotating at a constant rate of ωAD = 6 rad

/s measured counterclockwise. Suppose that a = 350 mm , b = 2001)Determine the angular velocity of member CB at the instant shown measured counterclockwise.
2)Determine the angular acceleration of member CB at the instant shown measured counterclockwise.

Engineering
1 answer:
svet-max [94.6K]3 years ago
4 0

Answer:

1) 1.71 rad/s

2) -6.22 rad/s²

Explanation:

Choose point C to be the origin.

Using geometry, we can show that the coordinates of point A are:

(a cos 30°, a sin 30° − b)

Therefore, the coordinates of point D at time t are:

(a cos 30° − b sin(ωt), a sin 30° − b + b cos(ωt))

The angle formed by CB with the x-axis is therefore:

tan θ = (a sin 30° − b + b cos(ωt)) / (a cos 30° − b sin(ωt))

1) Taking the derivative with respect to time, we can find the angular velocity:

sec² θ dθ/dt = [(a cos 30° − b sin(ωt)) (-bω sin(ωt)) − (a sin 30° − b + b cos(ωt)) (-bω cos(ωt))] / (a cos 30° − b sin(ωt))²

sec² θ dθ/dt = -bω [(a cos 30° − b sin(ωt)) sin(ωt) − (a sin 30° − b + b cos(ωt)) cos(ωt)] / (a cos 30° − b sin(ωt))²

sec² θ dθ/dt = -bω [(a cos 30° sin(ωt) − b sin²(ωt)) − (a sin 30° cos(ωt) − b + b cos²(ωt))] / (a cos 30° − b sin(ωt))²

sec² θ dθ/dt = -bω (a cos 30° sin(ωt) − b sin²(ωt) − a sin 30° cos(ωt) + b − b cos²(ωt)) / (a cos 30° − b sin(ωt))²

sec² θ dθ/dt = -bω (a cos 30° sin(ωt) − a sin 30° cos(ωt)) / (a cos 30° − b sin(ωt))²

sec² θ dθ/dt = -abω (cos 30° sin(ωt) − sin 30° cos(ωt)) / (a cos 30° − b sin(ωt))²

We know at the moment shown, a = 350 mm, b = 200 mm, θ = 30°, ω = 6 rad/s, and t = 0 s.

sec² 30° dθ/dt = -(350) (200) (6) (cos 30° sin(0) − sin 30° cos(0)) / (350 cos 30° − 200 sin(0))²

sec² 30° dθ/dt = -(350) (200) (6) (-sin 30°) / (350 cos 30°)²

dθ/dt = (200) (6) (1/2) / 350

dθ/dt = 600 / 350

dθ/dt = 1.71 rad/s

2) Taking the second derivative of θ with respect to time, we can find the angular acceleration.

sec² θ d²θ/dt² + 2 sec² θ tan θ dθ/dt = -abω [(a cos 30° − b sin(ωt))² (ω cos 30° cos(ωt) + ω sin 30° sin(ωt)) − (cos 30° sin(ωt) − sin 30° cos(ωt)) (2 (a cos 30° − b sin(ωt)) (-bω cos(ωt)))] / (a cos 30° − b sin(ωt))⁴

At t = 0:

sec² θ d²θ/dt² + 2 sec² θ tan θ dθ/dt = -abω [(a cos 30°)² (ω cos 30°) − (0 − sin 30°) (2 (a cos 30°) (-bω))] / (a cos 30°)⁴

sec² θ d²θ/dt² + 2 sec² θ tan θ dθ/dt = -abω (a²ω cos³ 30° − 2abω sin 30° cos 30°) / (a⁴ cos⁴ 30°)

sec² θ d²θ/dt² + 2 sec² θ tan θ dθ/dt = -bω (aω cos² 30° − 2bω sin 30°) / (a² cos³ 30°)

d²θ/dt² + 2 tan θ dθ/dt = -bω² (a cos² 30° − b) / (a² cos 30°)

Plugging in values:

d²θ/dt² + 2 tan 30° dθ/dt = -(200) (6)² (350 cos² 30° − 200) / (350² cos 30°)

d²θ/dt² + 2 tan 30° dθ/dt = -7200 (262.5 − 200) / (350² cos 30°)

d²θ/dt² + 2 tan 30° (1.71) = -4.24

d²θ/dt² = -6.22 rad/s²

You might be interested in
In order to fill a tank of 1000 liter volume to a pressure of 10 atm at 298K, an 11.5Kg of the gas is required. How many moles o
lesya [120]

Answer:

The molecular weight will be "28.12 g/mol".

Explanation:

The given values are:

Pressure,

P = 10 atm

  = 10\times 101325 \ Pa

  = 1013250 \ Pa

Temperature,

T = 298 K

Mass,

m = 11.5 Kg

Volume,

V = 1000 r

   = 1 \ m^3

R = 8.3145 J/mol K

Now,

By using the ideal gas law, we get

⇒ PV=nRT

o,

⇒ n=\frac{PV}{RT}

By substituting the values, we get

       =\frac{1013250\times 1}{8.3145\times 298}

       =408.94 \ moles

As we know,

⇒ Moles(n)=\frac{Mass(m)}{Molecular \ weight(MW)}

or,

⇒        MW=\frac{m}{n}

                   =\frac{11.5}{408.94}

                   =0.02812 \ Kg/mol

                   =28.12 \ g/mol

3 0
2 years ago
After a strong storm, a worker does not realize that a power transmission line has fallen on his car and is electrocuted while o
joja [24]

Answer and Explanation:

<u>The correct answer choice is Contacting Overhead Power Lines.</u>

This is because the powerlines are making contact (touching) his car, and the example isn't related to the other answer choices.

<u><em>#teamtrees #PAW (Plant And Water)</em></u>

3 0
2 years ago
a stem and leaf display describes two-digit integers between 20 and 80. for one one of the classes displayed, the row appears as
allochka39001 [22]

Answer:

  52, 50, 54, 54, 56

Explanation:

The "stem" in this scenario is the tens digit of the number. Each "leaf" is the ones digit of a distinct number with the given tens digit.

  5 | 20446 represents the numbers 52, 50, 54, 54, 56

8 0
3 years ago
A pipe 100 mm dia and 1 km long is to carry water from a reservoir to a village of 1000 people consuming 200 l/person/day. The p
natka813 [3]

Answer:

i899999999999999999ijhhh

Explanation:

8 0
3 years ago
Read 2 more answers
DO you of you guys know about Any Anmial rights it is for a resercah project
gizmo_the_mogwai [7]

Explanation:

Sure! I'll give you the definition to start off-

The right of animals to be free from exploitation, domination and abuse by humans. Free-living Animals & Their Environment; To live free, animals need a place to live. Wildlife Law Program; The Wildlife Law Program focuses on the defense of wildlife and their habitats throughout the world.

Here are some examples of companies for Animal Advocates for inspiration.

PETA – People for the Ethical Treatment of Animals

International Fund for Animal Welfare – IFAW

Cincinnati Zoo & Botanical Garden

Here are some of the basic rights of animals.

- No experiments on animals.

- No breeding and killing animals for food or clothes or medicine.

- No use of animals for hard labor.

- No selective breeding for any reason other than the benefit of the animal.

- No hunting.

- No zoos or use of animals in entertainment.

4 0
2 years ago
Other questions:
  • Air flows through a device such that the stagnation pressure is 0.4 MPa, the stagnation temperature is 400°C, and the velocity i
    8·1 answer
  • The news media often report an earthquake's magnitude on the Richter scale. Which of the following items are characteristics of
    14·1 answer
  • The rolling process is governed by the frictional force between the rollers and the workpiece. The frictional force at the entra
    5·1 answer
  • Before accurate distance standards, a cubit was the length of whose forearm?
    5·1 answer
  • Describe what viscoelastic behavior means
    7·1 answer
  • A 40kg steel casting (Cp=0.5kJkg-1K-1) at a temperature of 4500C is quenched in 150kg of oil (Cp=2.5kJkg-1K-1) at 250C. If there
    13·1 answer
  • A battery with an f.e.m. of 12 V and negligible internal resistance is connected to a resistor of 545 How much energy is dissipa
    9·1 answer
  • Is there anyone who can help me with welding?
    7·1 answer
  • Determine the slopes and deflections at points B and C for the beam shown below by the moment-area method. E=constant=70Gpa I=50
    10·1 answer
  • The percentage modulation of AM changes from 50% to 70%. Originally at 50% modulation, carrier power was 70 W. Now, determine th
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!