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
Maksim231197 [3]
2 years ago
12

Calculate (a) the torque, (b) the energy, and (c) the average power required to accelerate Earth in 4.0 days from rest to its pr

esent angular speed about its axis. Take the rotational inertia of Earth to be 9.71 x 10 37 kg m2. (Note: let one day be 24 hours)
Physics
1 answer:
natima [27]2 years ago
5 0
<h2>Answer:</h2>

Torque = <em>2.05 x 10²⁸ Nm</em>

Energy = <em>3.54 x 10³³ J</em>

Average power = <em>1.02 x 10²⁸ W</em>

<h2>Explanation:</h2>

(a) Torque (τ) is the rotational effect of a given force.  

It is given by

τ = I x α          -------------(i)

Where;

I = rotational inertia of the object

α = angular acceleration of the object.

In this case, the object is the Earth. Therefore,

I = 9.71 x 10³⁷ kg m²

α = ω / t

Where;

ω = angular velocity of earth = 2π rad / day

<em>Since </em>

<em>1 day = 24 hours and 1 hour = 3600seconds</em>

<em>1 day = 24 x 3600 seconds = 86400seconds</em>

<em>=> ω = 2π rad / 86400seconds</em>

<em>=> ω = 7.29 × 10⁻⁵ rad/s</em>

<em />

t = 4 days = 4 x 24 x 3600 seconds = 345600 seconds

=> α = ω / t

=> α = 7.29 × 10⁻⁵ / 345600

=> α = (7.29 × 10⁻⁵) / (3.456 x 10⁵)

=> α = (7.29 × 10⁻⁵⁻⁵) / (3.456)

=> α = (7.29 × 10⁻¹⁰) / (3.456)

=> α = 2.11 × 10⁻¹⁰ rad/s²

Now substitute the values of I and α into equation (i)

τ = 9.71 x 10³⁷ x 2.11 × 10⁻¹⁰

τ = 9.71 x 10²⁷ x 2.11

τ = 20.5 x 10²⁷ Nm

τ = 2.05 x 10²⁸ Nm

(ii) The energy (rotational energy) E is given by;

E = \frac{1}{2} x I x ω

E = \frac{1}{2} x 9.71 x 10³⁷ x 7.29 × 10⁻⁵

E = 35.4 x 10³² J

E = 3.54 x 10³³ J

(iii) The average power P, is given by;

P = E / t

P = 3.54 x 10³³ / 345600

P = 1.02 x 10²⁸ W

You might be interested in
You walk to school every day. It is 0.5 miles. After school you walk to Kroger, which is 1.3 miles. You leave Kroger to go all b
marin [14]
The total distance you haved walked should be 2.6 miles
7 0
2 years ago
What is the acceleration of the the object during the first 4 seconds?
AVprozaik [17]

Answer:

Velocity (m/s) over time (s) graph

Velocity (m/s) over time (s) graph

We could write out our average acceleration as:

a = Δv/ Δta=Δv/Δta, equals, Δ, v, slash, Δ, t

a = (15 m/s - 0 m/s) / 0.2 seconds

a = 15 m/s / 0.2 seconds

a = 75 m/s / second

Explanation:

What this formula is telling us is that if we know the acceleration of an object, and the ... we can plug in our acceleration of 12.5 m/s2 for a, and 4 seconds for t.

Velocity (m/s) over time (s) graph

Velocity (m/s) over time (s) graph

We could write out our average acceleration as:

a = Δv/ Δta=Δv/Δta, equals, Δ, v, slash, Δ, t

a = (15 m/s - 0 m/s) / 0.2 seconds

a = 15 m/s / 0.2 seconds

a = 75 m/s / second

6 0
2 years ago
The electronics supply company where you work has two different resistors, R1 and R2, in its inventory, and you must measure the
elixir [45]

Answer:

R₁ = 23.77 ohms and R₂ = 7.92 ohms

Explanation:

When connected in series, the equivalence resistance, R(eq) is given as

R(eq) = (R₁ + R₂)

When connected in parallel, the equivalence resistance, R(eq) is given as

[1/R(eq)] = [(1/R₁) + (1/R₂)]

R(eq) = (R₁R₂)/(R₁ + R₂)

The parallel and series combination are connected to a battery of emf 39.0 V with negligible internal resistance. And the power supplied is measured.

But power supplied is given as

P = IV = (V/R) V = (V²/R)

When connected in series, the power supplied is given as

P = 48.0 W,

V = 39.0 V,

R = R(eq) = (R₁ + R₂)

48 = (39²/R)

R = (39²/48)

R = 31.6875 ohms

R = (R₁ + R₂) = 31.6875

(R₁ + R₂) = 31.6875 (eqn 1)

When connected in series, the power supplied is given as

P = 256.0 W,

V = 39.0 V,

R = R(eq) = (R₁R₂)/(R₁ + R₂)

256 = (39²/R)

R = (39²/256)

R = 5.9414 ohms

R = R(eq) = (R₁R₂)/(R₁ + R₂) = 5.9414

(R₁R₂)/(R₁ + R₂) = 5.9414

But, recall eqn 1

(R₁ + R₂) = 31.6875

(R₁R₂)/(R₁ + R₂) = 5.9414

Substituting for (R₁ + R₂)

(R₁R₂)/(R₁ + R₂) = (R₁R₂)/31.6875 = 5.9414

(R₁R₂) = 31.6875 × 5.9414 = 188.2683

R₁ = (188.2683/R₂)

(R₁ + R₂) = 31.6875

Substituting for R₁

(188.2683/R₂) + R₂ = 31.6875

multiply through by R₂

188.2683 + R₂² = 31.6875R₂

R₂² - 31.6875R₂ + 188.2683 = 0

Solving the quadratic equation

R₂ = 23.77 ohms or 7.92 ohms

If R₂ = 23.77 ohms, R₁ = 7.92 ohms

If R₂ = 7.92 ohms, R₁ = 23.77 ohms

Since the question explains that R₁ > R₂

R₁ = 23.77 ohms and R₂ = 7.92 ohms

Hope this Helps!!!

3 0
2 years ago
If a weightlifter lifts a 286 kg mass 0.25 meters above his head, how much PEg does the mass have?
vazorg [7]

Answer:

Change in potential energy is 700.7 J.

Explanation:

Given:

Mass of the object is, m=286 kg

Height to which the object is raised above his head, h=0.25 m

Acceleration due to gravity is, g=9.8 m/s²

We know that for a mass m raised to a height h, the change in potential energy is given as:

\Delta PE=mgh, where, \Delta PE\rightarrow \textrm{Change in Potential Energy}

Now, plug in the given values and solve.

\Delta PE=286\times 9.8\times 0.25=700.7\textrm{ J}

Therefore, the change in the potential energy is 700.7 J.

3 0
3 years ago
Read 2 more answers
What is your average speed if you walk 2 kilometers in 20minutes
goldenfox [79]

Answer:

12 km/hr

Explanation:

Speed= Distance/Time

3 0
2 years ago
Read 2 more answers
Other questions:
  • Compute the resistance of a hardened copper rod 2 meters long and 8 mm in diameter if resistivity of the material is 1.756 x 10^
    13·1 answer
  • A system of pulleys is used to raise a load of bricks that weighs 1,700 newtons. The force applied to the pulley is 340 newtons.
    9·2 answers
  • A person standing on the edge of a high cliff throws a rock straight up with an initial velocity, v0v0, of 13.0m/s13.0m/s. on th
    11·1 answer
  • Sound is a type of mechanical wave and must have a medium through which to travel. Sound will move at different speeds when whic
    10·1 answer
  • A weightlifter curls a 30 kg bar, raising it each time a distance of 0.50 m .How many times must he repeat this exercise to burn
    7·1 answer
  • How is reflection of light used in research
    5·1 answer
  • Planets in our solar system do not revolve around the sun in perfect circles. Their orbits are more like ovals. Which term do sc
    6·1 answer
  • An object is thrown straight down with an initial speed of 4 m/s from a window which is 8 m above the ground. Calculate: a) The
    13·1 answer
  • As shown in the diagram, an inflated balloon released from rest moves horizontally with velocity "v". The velocity of the balloo
    14·2 answers
  • A certain circuit is composed of two series resistors. The total resistance is 10 Ohms. One of the resistors is 4 Ohms. The othe
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!