All of the forces that act on an object add up to equal_______________

Find the mass of the solid cylinder Dequals{(r,theta,z): 0less than or equalsrless than or equals2, 0less than or equalszless

anygoal [31]

The mass of the cylinder D is obtained by integrating the density function over D:

$\displaystyle\iiint_D\rho(r,\theta\,z)\,\mathrm dV$

With $\rho(r,\theta,z)=1+\frac z2$ , and

$D=\left\{(r,\theta,z)\mid 0\le r\le2,0\le z\le10\right\}$

the mass would be

$\displaystyle\int_0^{2\pi}\int_0^2\int_0^{10}1+\frac z2\,\mathrm dz\,\mathrm dr\,\mathrm d\theta=4\pi\int_0^{10}1+\frac z2\,\mathrm dz$

$4\pi\left(z+\dfrac{z^2}4\right)\bigg|_0^{10}$

$=4\pi\left(10+\dfrac{100}4\right)=\boxed{140\pi}$

6 0

3 years ago

An apple falls out of a tree from a height of 2.3m. what is the impact speed of the apple

Anuta_ua [19.1K]

Answer:6.71 m/s

Explanation:

Given

Apple fall from a height of $h=2.3 m$

We need to find the impact speed of apple which can be given by using

$v^2-u^2=2gh$

where v=final velocity

u=initial velocity

h=Displacement

Assuming initial velocity to be zero

substituting the value we get

$v^2-0=2\times 9.8\times 2.3$

$v=\sqrt{2\times 9.8\times 2.3}$

$v=6.71\ m/s$

5 0

3 years ago

You have a spool of copper wire 4.82 mm in diameter and a power supply. You decide to wrap the wire tightly around a soda can th

GalinKa [24]

To solve the problem it is necessary to have the concepts of the magnetic field in a toroid.

A magnetic field is a vector field that describes the magnetic influence of electric charges in relative motion and magnetized materials.

By definition the magnetic field is given by the equation,

$B=\frac{\mu_0 NI}{2\pi r}$

Where,

$\mu_0$ = Permeability constant

N = Number of loops

I = Current

r = Radius

According to the given data we have that the length is 120mm and the thickness of the copper wire is 4.82mm.

In this way the number of turns N would be

$N=\frac{120mm}{4.82mm}$

$N = 24.89 \approx 25 turns$

On the other hand to find the internal radius, we know that:

$2\pi r_i = 12cm$

$r_i= \frac{12}{2\pi}$

$r_i= 1.91cm$

Therefore the total diameter of the soda would be

$r= r_i+r_o = 1.91+6.5=8.51cm$

Applying the concept related to magnetic field you have to for the internal part:

$B_i=\frac{\mu_0 NI}{2\pi r_i}$

$B_i=\frac{(4\pi*10^{-7}) (25)(230)}{2\pi (1.91*10^{-2})}$

$B_i = 0.060T$

The smallest magnetic field would be on the outside given by,

$B_o=\frac{\mu_0 NI}{2\pi r}$

$B_o=\frac{(4\pi*10^{-7}) (25)(230)}{2\pi 8.51}$

$B_o = 0.0136T$

Therefore the maximum magnetic field is 0.06T.

4 0

4 years ago

How can force-time and force-displacement graphs be used to find the impulse or work done?

balandron [24]

Answer:

A. Area under force-time graph & Area under force-displacement graph

Explanation:

To find the impulse or work done the area under force-time graph and area under force-displacement graph will give us these respective values.

Impulse = Force x time

Work done = Force x displacement

When we plot a graph of force and time, the area under it is the impulse.

When a graph of force and displacement is plotted, the area under is the work done.

7 0

3 years ago

In general, covalent compounds do not conduct electric current in a water solution well because they do not dissociate into ions

Margaret [11]

The answer is a. True. Covalent compounds do not conduct electric or does not have electrical properties when dissolved in water as the free moving electrons shared from its original structure is removed when it was dissolved.

4 0

4 years ago

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All of the forces that act on an object add up to equal________________