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
IgorLugansk [536]
3 years ago
5

Two objects, M = 15.3 ks and m = 8.29 kg are connected with an ideal string and suspended by a pulley (which rotates with no fri

ction) in the shape of a uniform disk with radius R = 7.50 cm and mass Mp = 14.1 kg. The string causes the pulley to rotate without slipping. If the masses are started from rest and allowed to move 2.50 m: What is the final speed (m/s) of mass m? What is the final angular speed (rad/s) of the pulley? How long (s) did it take for the masses to move from rest to the final position? Part (a) can be done by two methods: Forces and torques and energy conservation.
Physics
1 answer:
Scilla [17]3 years ago
5 0

Answer:

(a) 7 m/s

(b) 931 rad/s

(c) 0.716 s

Explanation:

Gravity would be exerting on the 2 masses

G_1 = Mg = 15.3*9.81 = 150.093N

G_2 = mg = 8.29*9.81= 81.32N

Since heavier, mass 1 (M) would be the one pulling down, while mass 2 is being pulled up.

So the net force on mass 1 is

F = G_1 - G_2 = 68.77N

This force would generate torque on the solid pulley

T = FR = 68.77 * 0.0075 = 0.5158 Nm

We can also calculate the pulley moments of inertia, with it being solid

I = 0.5MpR^2 = 0.5*14.1*0.0075^2 = 0.000396563kgm^2

From there we can calculate the angular acceleration of the pulley, which generates the entire system motion

\alpha = \frac{T}{I} = \frac{0.5158}{0.000396563} = 1300.58 rad/s^2

Since the system is moved by a distance of d = 2.5m, the pulley would have turn an angle of

\theta = \frac{d}{R} = \frac{2.5}{0.0075} = 333 rad

(c)The time it takes to get to this distance is

\theta = \frac{\alpha t^2}{2}

t^2 = \frac{2\theta}{\alpha} = \frac{2*333}{1300.58} =0.513

t = \sqrt{0.513} = 0.716s

(b)The final angular speed of the disk is

\omega = \alpha t = 1300.58*0.716 = 931 rad/s

(a) And so the perimeter speed of the pulley, which is also speed of mass 1 when it comes to d = 2.5 m is

v = \omega R = 931*0.0075 \approx 7m/s

You might be interested in
What are the potential out comes of force
AysviL [449]

Answer:

F in the definition of potential energy is the force exerted by the force field, e.g., gravity, spring force, etc. The potential energy U is equal to the work you must do against that force to move an object from the U=0 reference point to the position r.

Explanation:

5 0
2 years ago
Science and Technology are interdependent. Advances in one lead to advances in the other. Give an example of this phenomenon
Pepsi [2]
If more microscopic technology is invented, then more things in the world can be discovered. Likewise, if a new element is discovered, then people can use it in their technology.
7 0
3 years ago
As an intern at an engineering firm, you are asked to measure the moment of inertia of a large wheel for rotation about an axis
klio [65]

Hi there!

We can begin by finding the acceleration of the block.

Use the kinematic equation:

d = v_0t + \frac{1}{2}at^2

The block starts from rest, so:

d = \frac{1}{2}at^2\\\\12 = \frac{1}{2}a(4^2)\\\\\frac{24}{16} = a = 1.5 m/s^2

Now, we can do a summation of forces of the block using Newton's Second Law:

F = ma = m_bg - T

mb = mass of the block

T = tension of string

Solve for tension:

T = m_bg - ma = 8.2(9.8) - 8.2(1.5) = 68.06 N

Now, we can do a summation of torques for the wheel:

\Sigma \tau = rF\\\\\Sigma\tau = rT

Rewrite:

I\alpha = rT

We solved that the linear acceleration is 1.5 m/s², so we can solve for the angular acceleration using the following:

\alpha = a/r\\\\\alpha = 1.5/.42= 3.57 rad/sec^2

Now, plug in the values into the equation:

I(3.57) = (0.42)(68.06)\\\\I = (0.42)(68.06)/(3.57) = \boxed{8.00 kgm^2}

8 0
2 years ago
A sound wave has a frequency of 247 hz and a wavelength of 1.4 m. what is the speed of the sound wave in air?
Pavel [41]
Speed = wavelength * Frequency 
s = 247 /s * 1.4 m
s = 345.8 m/s

In short, Your Answer would be 345.8 m/s

Hope this helps!
7 0
3 years ago
a student measure the mass of an 8 cm^3 block of brown sugar to be 12.9 g. what is the density of the brown sugar?
schepotkina [342]
Density = mass / volume ;
1 Cubic Centimeter = 0,000001 Cubic Meter
8 cm^3 = 0.000008 m^3
12,9 g = 0,0129 kg


The density is 0,0129 kg/ 0,000008 m^3 = <span><u>1612,5 kg/m^3</u> </span>
4 0
3 years ago
Other questions:
  • A car traveling east at 46.8 m/s passes a trooper hiding at the roadside. the driver uniformly reduces his speed to 25.0 m/s in
    11·1 answer
  • Consider a single-slit diffraction pattern for λ=589nm , projected on a screen that is 1.00 m from a slit of width 0.25 mm. How
    15·1 answer
  • 5. Consider two glasses, one filled with water and the other half-full, with the water in the two glasses being at the same temp
    11·1 answer
  • Lighting from the sun travels through space to earths atmosphere.
    9·1 answer
  • Differences Between light year and astronomical unit in two points .
    13·2 answers
  • Margaret swam 100 meters in 5 minutes. What was her swimming speed?
    6·1 answer
  • What is the gravitational potential energy of a ball with a weight of 72 N when it is sitting on a shelf 1.4 m above the floor?
    5·1 answer
  • How is the atomic number of a nucleus changed by alpha decay?
    9·1 answer
  • A 20 kg mass is moving at 10 m/s and collides with a stationary 5 kg mass, transferring all its momentum in the collision, what
    7·1 answer
  • A plane mirror forms an image of an object because it ____________ light from the object.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!