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
Ipatiy [6.2K]
3 years ago
15

A long string is wrapped around a 6.6-cm-diameter cylinder, initially at rest, that is free to rotate on an axle. The string is

then pulled with a constant acceleration of 1.5 m/s2 until 1.3 m of string has been unwound. If the string unwinds without slipping, what is the cylinder's angular speed, in rpm, at this time?
Physics
1 answer:
lys-0071 [83]3 years ago
5 0

Answer:

\omega_f=571.42\ rpm

Explanation:

It is given that,

Diameter of cylinder, d = 6.6 cm

Radius of cylinder, r = 3.3 cm = 0.033 m

Acceleration of the string, a=1.5\ m/s^2

Displacement, d = 1.3 m

The angular acceleration is given by :

\alpha =\dfrac{a}{r}

\alpha =\dfrac{1.5}{0.033}

\alpha =45.46\ rad/s^2

The angular displacement is given by :

\theta=\dfrac{d}{r}

\theta=\dfrac{1.3}{0.033}

\theta=39.39\ rad

Using the third equation of rotational kinematics as :

\omega_f^2-\omega_i^2=2\alpha \theta

Here, \omega_i=0

\omega_f=\sqrt{2\alpha \theta}

\omega_f=\sqrt{2\times 45.46\times 39.39}

\omega_f=59.84\ rad/s

Since, 1 rad/s = 9.54 rpm

So,

\omega_f=571.42\ rpm

So, the angular speed of the cylinder is 571.42 rpm. Hence, this is the required solution.

You might be interested in
10. Convert the following:<br> a. 37.4 mL into ML<br> b. 689 km/hr into m/s<br> c. 34.5 m² into mm²
Snezhnost [94]

A. When we convert 37.4 mL to ML, the result obtained is 3.74×10¯⁸ ML

B. When we convert 689 km/hr to m/s, the result obtained is 191.39 m/s

C. When we convert 34.5 m² to mm², the result obtained is 3.45×10⁷ mm²

<h3>A. How to convert millimeters (mL) to megaliter (ML)</h3>
  • Volume (mL) = 37.4 mL
  • Volume (ML) =?

1 mL = 1×10¯⁹ ML

Therefore,

37.4 mL = 37.4 × 1×10¯⁹

37.4 mL = 3.74×10¯⁸ ML

Thus, 37.4 mLis equivalent to 3.74×10¯⁸ ML

<h3>B. How to convert 689 km/hr to m/s</h3>

Conversion scale

3.6 Km/hr = 1 m/s

Therefore,

689 km/hr = 689 / 3.6

689 km/hr = 191.39 m/s

Thus, 689 km/hr is equivalent to 191.39 m/s

<h3>C. How to convert 34.5 m² to mm²</h3>

Conversion scale

1 m² = 1×10⁶ mm²

Therefore,

34.5 m² = 34.5 × 1×10⁶

34.5 m² = 3.45×10⁷ mm²

Thus, 34.5 m² is equivalent to 3.45×10⁷ mm²

Learn more about conversion:

brainly.com/question/2139943

#SPJ1

6 0
1 year ago
a painting in an art gallery has height h and is hung so that its lower edge is a distance d above the eye of an observer. How f
harkovskaia [24]

Solution:

With reference to Fig. 1

Let 'x' be the distance from the wall

Then for \DeltaDAC:

tan\theta = \frac{d}{x}

⇒ \theta = tan^{-1} \frac{d}{x}

Now for the \DeltaBAC:

tan\theta = \frac{d + h}{x}

⇒ \theta = tan^{-1} \frac{d + h}{x}

Now, differentiating w.r.t x:

\frac{d\theta }{dx} = \frac{d}{dx}[tan^{-1} \frac{d + h}{x} -  tan^{-1} \frac{d}{x}]

For maximum angle, \frac{d\theta }{dx} = 0

Now,

0 = [/tex]\frac{d}{dx}[tan^{-1} \frac{d + h}{x} -  tan^{-1} \frac{d}{x}][/tex]

0 = \frac{-(d + h)}{(d + h)^{2} + x^{2}} -\frac{-d}{x^{2} + d^{2}}

\frac{-(d + h)}{(d + h)^{2} + x^{2}} = \frac{{d}{x^{2} + d^{2}}

After solving the above eqn, we get

x = \sqrt{\frac{d}{d + h}}

The observer should stand at a distance equal to x = \sqrt{\frac{d}{d + h}}

4 0
3 years ago
Barney walks at a velocity of 1.7 meters/second on an inclined plane, which has an angle of 18.5° with the ground. What is the h
Viktor [21]
The velocities and the speed build a triangle, where the 1.7 m/s are the hypotenuse and the x-velocity and y-velocity are the other sides. 

<span>So the x-velocity is: speed*cos(angle) </span>

<span>now plug in </span>
<span>x=1.7 m/s * cos(18.5)=1.597 m/s </span>


3 0
2 years ago
How do stars serve as evidence for the expansion of the universe and the Big Bang theory?​
castortr0y [4]

Answer:

The Doppler red-shift of light observed from distant stars and galaxies gives evidence that the universe is expanding (moving away from a central point). This allows for Big Bang Theory, because after a “bang” occurs all of the matter moves away from the point of origin.

7 0
3 years ago
What is heat?
OLEGan [10]
Well you need to have lots of heat
7 0
3 years ago
Other questions:
  • What is the displacement if Ray runs 30ft north, 30ft west, and then 30ft south.
    14·1 answer
  • The downward acceleration of a falling body on Earth is 9.81m/s2. On the moon the same quantity is 1.62m/s2. An astronaut in a s
    6·1 answer
  • What is the largest Planet known to man?
    11·2 answers
  • Pleaseeee help got this homework tomorrow ; if an object vibrates five times every second it has a frequency of ...?
    5·1 answer
  • The ________ is the maximum value or strength of the signal over time; typically this value is measured in volts.
    10·1 answer
  • The force behind electron movement is called <br>A. voltage B. current C. resistance D. ohm​
    11·1 answer
  • The average, year-after-year conditions of temperature, precipitation, winds, and cloud in an area are known as its
    11·1 answer
  • A locomotive with two carriages drives out of the station. The locomotive has a mass of 3.0 tonnes, and each of the two wagons h
    10·1 answer
  • A track star runs 100 meters in 10 seconds. What is the star's average speed?
    9·2 answers
  • If an object with a mass of 248kg is lifted 76 meters in 18 seconds, how much power is used?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!