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
Klio2033 [76]
1 year ago
7

FIGURE 2 shows a 1.5 kg block is hung by a light string which is wound around a smooth pulley of radius 20 cm. The moment of ine

rtia of the pulley is 2 kg m².(i) When the mass is released from rest, calculate the angular velocity and number of revolutions of the pulley at t = 4.2 s.

Physics
1 answer:
Sindrei [870]1 year ago
3 0

Answer:

At t = 4.2 s

Angular velocity: 6. 17 rad /s

The number of revolutions: 2.06

Explanation:

First, we consider all the forces acting on the pulley.

There is only one force acting on the pulley, and that is due to the 1.5 kg mass attached to it.

Therefore, the torque on the pulley is

\tau=Fd=mg\cdot R

where m is the mass of the block, g is the acceleration due to gravity, and R is the radius of the pulley.

Now we also know that the torque is related to angular acceleration α by

\tau=I\alpha

therefore, equating this to the above equation gives

mg\cdot R=I\alpha

solving for alpha gives

\alpha=\frac{mgR}{I}

Now putting in m = 1.5 kg, g = 9.8 m/s^2, R = 20 cm = 0.20 m, and I = 2 kg m^2 gives

\alpha=\frac{1.5\cdot9.8\cdot0.20}{2}\boxed{\alpha=1.47s^{-2}}

Now that we have the value of the angular acceleration in hand, we can use the kinematics equations for the rotational motion to find the angular velocity and the number of revolutions at t = 4.2 s.

The first kinematic equation we use is

\theta=\theta_0+\omega_0t+\frac{1}{2}\alpha t^2

since the pulley starts from rest ω0 = 0 and theta = 0; therefore, we have

\theta=\frac{1}{2}\alpha t^2

Therefore, ar t = 4.2 s, the above gives

\theta=\frac{1}{2}(1.47)(4.2)^2

\boxed{\theta=12.97}

So how many revolutions is this?

To find out we just divide by 2 pi:

\#\text{rev}=\frac{\theta}{2\pi}=\frac{12.97}{2\pi}\boxed{\#\text{rev}=2.06}

Or about 2 revolutions.

Now to find the angular velocity at t = 4.2 s, we use another rotational kinematics equation:

\omega^2=w^2_0+2\alpha(\Delta\theta)_{}

Since the pulley starts from rest, ω0 = 0. The change in angle Δθ we calculated above is 12.97. The value of alpha we already know to be 1.47; therefore, the above becomes:

\omega^2=0+2(1.47)(12.97)w^2=38.12\boxed{\omega=6.17.}

Hence, the angular velocity at t = 4.2 w is 6. 17 rad / s

To summerise:

at t = 4.2 s

Angular velocity: 6. 17 rad /s

The number of revolutions: 2.06

You might be interested in
An unknown fluid has a specific gravity of 0.750. What is the volume of 22.5 kg of this fluid?
Andru [333]
<h2>Option C is the correct answer.</h2>

Explanation:

Specific gravity of fluid = 0.750

Density of fluid = Specific gravity of fluid x Density of water

Density of fluid = 0.750 x 1000

Density of fluid = 750 kg/m³

Mass of fluid = 22.5 kg

We have

         Mass = Volume x Density

         22.5 = Volume x 750

         Volume = 0.03 m³ = 30 L

Option C is the correct answer.

5 0
3 years ago
If a gas has a gage pressure of 156 kPa, it is absolute pressure is approximately
Art [367]
In the given question, one important information for getting to the actual solution is not given and that is the atmospheric pressure. To find the approximate absolute pressure, it is needed to add the value of atmospheric pressure with the gage pressure.
Atmospheric pressure = 100 kPa
Then
Absolute pressure = 156 + 100 kPa
                             = 256 KPa.
5 0
3 years ago
Wegener proposed the continental drift hypotheses suggesting that
kipiarov [429]
There was a supercontinent called Pangea
3 0
3 years ago
The horizontal surface on which the block (mass 2.0 kg) slides is frictionless. The speed of the block before it touches the spr
ch4aika [34]

Answer:3.67 m/s

Explanation:

mass of block(m)=2 kg

Velocity of block=6 m/s

spring constant(k)=2 KN/m

Spring compression x=15 cm

Conserving Energy

energy lost by block =Gain in potential energy in spring

\frac{m(v_1^2-v_2^2)}{2}=\frac{kx^2}{2}

2\left [ 6^2-v_2^2\right ]=2\times 10^3\times \left [ 0.15\right ]^2

v_2=3.67 m/s

7 0
3 years ago
James accelerates his skate board uniformly along a straight road from rest to 10 m/s in 4 seconds. What is James Acceleration?
lawyer [7]

Given:

u(initial velocity)=0

v(final velocity)= 10 m/s

t= 4 sec

Now we know that

v= u + at

Where v is the final velocity

u is the initial velocity

a is the acceleration measured in m/s^2

t is the time measured in sec

10=0+ax4

a=10/4

a=2.5 m/s^2

4 0
3 years ago
Other questions:
  • you push your little sister on a swing and in 1.6 minutes you make 52 pushes what is the frequency of your swing? answer in unit
    9·1 answer
  • The motion of an object will not be changed if
    15·2 answers
  • How do a neutron and a proton compare?
    10·1 answer
  • Which biome's yearly rainfall mainly evaporates? A. taiga B. desert C. tropical rainforest D. temperate grassland
    12·2 answers
  • Same object differs in water than in air?
    8·1 answer
  • Click to review the online content. Then answer the question(s) below, using complete sentences. Scroll down to view additional
    10·2 answers
  • a 1.5 kg ball is thrown vertically upward with an initial speed of 15 m/s. if the initial potential energy is taken as zero, fin
    15·1 answer
  • Niobium metal becomes a superconductor when cooled below 9K. Itssuperconductivity is destroyed when the surface magnetic fieldex
    8·1 answer
  • Dipole moment are used to calculate the​
    13·2 answers
  • Select the correct answer.
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!