All categories

3 years ago

Use the Divergence Theorem to calculate the surface integral

1 answer:

3 0

Divergense theorem says flux across the closed surface = ∫∫∫ div F dV

div F = 3y^2+ 3 z^2 
convert to cylindrical 
y = r cos t 
z = r sin t 
x = x 
dx dy dz = r dx dr dt 

∫ [0, 2pi]∫[0,3]∫ [-1,3] 3r^3 dx dr dt 

2pi(3)(81/4)(4) 
486pi

Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions.

You might be interested in

As a dilligent physics student, you carry out physics experiments at every opportunity. At this opportunity, you carry a 1.11-m-

soldier1979 [14.2K]

Answer:

The strength of the magnetic field is 0.0842 mT

Explanation:

Given:

Velocity of rod $v = 3.07$ $\frac{m}{s}$

Length of rod $l = 1.11$ m

Induced emf across the rod $\epsilon = 0.287 \times 10^{-3}$ V

According to the faraday's law

We have a special case for moving rod in magnetic field.

Induced emf in moving rod is given by,

$\epsilon = Blv$

Where $B =$ strength of magnetic field

$B = \frac{\epsilon}{lv}$

$B = \frac{0.287 \times 10^{-3} }{3.07 \times 1.11}$

$B = 0.0842 \times 10^{-3}$ T

$B = 0.0842$ mT

Therefore, the strength of the magnetic field is 0.0842 mT

7 0

3 years ago

In which of these situations, is mechanical energy being conserved? (Neglect, air resistance, friction, and breaking) Check all

lana66690 [7]

1) Mechanical energy is conserved in all the situations listed

2) True

3) The energy that an object has stored due to its position or shape is called potential energy

4) The potential energy of the block is 490 J

5) The potential energy of the elevator is 750,000 J

Explanation:

The mechanical energy of an object is the sum of its kinetic energy (KE) and its potential energy (PE):

$E=KE+PE$

Where

KE is the energy due to the motion of the object

PE is the energy due to the position of the object (it can be either gravitational potential energy or elastic potential energy)

In absence of non-conservative forces, such as friction or air resistance, the mechanical energy is always conserved. Therefore, the mechanical energy is conserved in all the situations listed here:

Child on a swing --> there is a continuous conversion between gravitational potential energy and kinetic energy

Pendulum --> there is a continuous conversion between gravitational potential energy and kinetic energy

Bow and Arrow --> there is a conversion between elastic potential energy of the bow and kinetic energy of the arrow

Roller Coaster --> there is a continuous conversion between gravitational potential energy and kinetic energy

The potential energy of an object is given by

$PE=mgh$

where

m is its mass

g is the acceleration due to gravity

h is the height of the object relative to the ground

While the kinetic energy is given by

$KE=\frac{1}{2}mv^2$

where

v is the speed of the object

As an object falls to the ground, its height h decreases, therefore the potential energy PE decreases as well. However, the speed of the object, v, increases during the fall, and therefore the kinetic energy KE increases. This means that potential energy is converted into kinetic energy.

Potential energy is the energy possessed by an object due to its position. It can be of two types:

Gravitational potential energy: it is the potential energy due to the position of an object in a gravitational field. It is calculated as $mgh$ , as shown in part 2)
Elastic potential energy: it is the potential energy stored in an elastic object when it is stretched or compressed. It is calculated as $\frac{1}{2}kx^2$ , where k is the spring constant of the elastic object and x is the stretching/compression of the object relative to its equilibrium position.

The potential energy stored in an object held above the ground is given by

$PE=mgh$

where

m is the mass of the object

g is the acceleration of gravity

h is the height of the object relative to the ground

For the object in this problem, we have

m = 10 kg

$g=9.8 m/s^2$

h = 5 m

Substituting, we find

$PE=(10)(9.8)(5)=490 J$

As before, the potential energy of the elevator is given by

$PE=mgh$

where m is its mass and h is its height above the ground.

Here we don't have the mass of the elevator. However, we know its weight:

$W=1500 N$

But we also know that the weight of an object is equal to the product between its mass and the acceleration of gravity:

$W=mg$

So we can rewrite the potential energy as

$PE=Wh$

and the height of the elevator is

h = 500 m

Therefore, its potential energy is

$PE=(1500)(500)=750,000 J$

Learn more about potential energy:

brainly.com/question/1198647

brainly.com/question/10770261

#LearnwithBrainly

5 0

3 years ago

35. An object of mass m moving at speed v0 strikes an object of mass 2m which had been at rest. The first object bounces backwar

MAVERICK [17]

Answer:

The collision is not elastic. The system increases his kinetic energy m*v₀² times.

Explanation:

Assuming no external forces acting during the collision, total momentum must be conserved.

Considering the information provided, we can write the momentum conservation equation as follows:

m*v₀ = -m*v₀ + 2*m*vf

Solving for vf, we arrive to this somehow surprising result:

vf = v₀ (in the same direction that m was moving before the collision).

In order to determine if the collision was elastic, or not, we need to calculate the kinetic energy of the system before and after the collision:

K₀ = 1/2*m*v₀²

Kf = 1/2*m*v₀² (due to the object of mass m, as the kinetic energy is always positive) + 1/2 (2m) * v₀²

⇒Kf = 1/2*m*v₀² + 1/2 (2m) * v₀² = 3/2*m*v₀²

ΔK = Kf - K₀ = 3/2*m*v₀² - 1/2*m*v₀² = m*v₀²

As there is a net difference between the final and initial kinetic energies, and the total kinetic energy must be conserved in an elastic collision (by definition) we conclude that the collision is not elastic, and the change in the kinetic energy of the system is equal to m*v₀².

5 0

3 years ago

Each of the objects above is composed of identical thin sticks of uniformly distributed mass 5.51 kg and length 0.737 m. what is

Taya2010 [7]

Based on this particular physics problem, it is given that the mass of the object is 5.51 kg and a length of 0.737 m. Based on calculations, one can conclude that the inertia of each object is

7 0

4 years ago

A bullet is at rest. It travels a distance of 0.34m in a time of 0.0095 seconds. Calculate its acceleration.

tamaranim1 [39]

Answer:

7.5 × 10^3 m/s^2

Explanation:

use the formula that does not have v in it to solve for acceleration.

7 0

4 years ago