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An electric motor spins at 1000 rpm and is slowing down at a rate of 10 t rad/s2 ; where t is measured in seconds. (a) If the mo

REY [17]

Answer:

a) The tangential component of acceleration at the edge of the motor at $t = 1.5\,s$ is -1.075 meters per square second.

b) The electric motor will take approximately 3.963 seconds to decrease its angular velocity by 75 %.

Explanation:

The angular aceleration of the electric motor ( $\alpha$ ), measured in radians per square second, as a function of time ( $t$ ), measured in seconds, is determined by the following formula:

$\alpha = -10\cdot t\,\left[\frac{rad}{s^{2}} \right]$ (1)

The function for the angular velocity of the electric motor ( $\omega$ ), measured in radians per second, is found by integration:

$\omega = \omega_{o} - 5\cdot t^{2}\,\left[\frac{rad}{s} \right]$ (2)

Where $\omega_{o}$ is the initial angular velocity, measured in radians per second.

a) The tangential component of aceleration ( $a_{t}$ ), measured in meters per square second, is defined by the following formula:

$a_{t} = R\cdot \alpha$ (3)

Where $R$ is the radius of the electric motor, measured in meters.

If we know that $R = 7.165\times 10^{-2}\,m$ , $\alpha = 10\cdot t$ and $t = 1.5\,s$ , then the tangential component of the acceleration at the edge of the motor is:

$a_{t} = (7.165\times 10^{-2}\,m)\cdot (-10)\cdot (1.5\,s)$

$a_{t} = -1.075\, \frac{m}{s^{2}}$

The tangential component of acceleration at the edge of the motor at $t = 1.5\,s$ is -1.075 meters per square second.

b) If we know that $\omega_{o} = 104.720\,\frac{rad}{s}$ and $\omega = 26.180\,\frac{rad}{s}$ , then the time needed is:

$26.180\,\frac{rad}{s} = 104.720\,\frac{rad}{s}-5\cdot t^{2}$

$5\cdot t^{2} = 104.720\,\frac{rad}{s}-26.180\,\frac{rad}{s}$

$t^{2} = \frac{104.720\,\frac{rad}{s}-26.180\,\frac{rad}{s} }{5}$

$t = \sqrt{\frac{104.720\,\frac{rad}{s}-26.180\,\frac{rad}{s} }{5} }$

$t \approx 3.963\,s$

The electric motor will take approximately 3.963 seconds to decrease its angular velocity by 75 %.

8 0

3 years ago

The ratio of the number of pigs to the number of horse in a farm is 2 to 3 (2:3), if therected are 24 horses, what is the number

pickupchik [31]

Answer:

16 pigs

Explanation:

Let the horses be H.

Let the pigs be P

Let the total number of animals be x.

Given the following data;

Ratio of P to H = 2:3 = 2 + 3 = 5

Number of horses = 24

To find the number of pigs;

First of all, we would determine the total number of animals x.

From the ratio of horse, H:

3/5 * x = 24

Cross-multiplying, we have;

3x = 120

x = 120/3 = 40

Next, we find the number of pigs;

Pigs = 2/5 * 40

Pigs = 80/5 = 16 pigs

5 0

3 years ago

How can artists suggest volume with light?

Dimas [21]

Answer:

The answer is they utilized light in a few spots to enlighten the subjects and to demonstrate their volume as masses.

Explanation:

That is the reason every one of the particles that move at the speed of light (e.g. photons) have zero rest mass. As a molecule with mass methodologies the speed of light, its vitality increments and winds up unbounded at the speed of light, which is the motivation behind why it can never be quickened to achieve that speed. However, you can state that the photon has relativistic mass on the off chance that you truly need to. In current wording, the mass of a protest is its invariant mass, which is zero for a photon.

5 0

3 years ago

The path of a meteor passing Earth is affected by its gravitational force and falls to Earth's surface. Another meteor of the sa

Lina20 [59]

Answer: The correct answer is option (C).

Explanation:

As it is given in the problem, the path of a meteor passing Earth is affected by its gravitational force and falls to Earth's surface. Another meteor of the same mass falls to Jupiter's surface due to its gravitational force.

According to Newton's law of universal gravitational, every particle attracts every other particles in the universe with the gravitational force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

The Jupiter is the most massive planet in the solar system. It is also the largest planet in the solar system. The gravity of Jupiter on its surface is 2.4 times that of surface gravity of the Earth.

If a person weighs 100 pounds on the Earth then he would weigh 240 pounds on Jupiter.

Therefore, the correct answer is option (C), the meteor falls to Jupiter faster due to its greater gravitational force.

8 0

4 years ago

Read 2 more answers

A square loop of wire is held in a uniform 0.24 T magnetic field directed perpendicular to the plane of the loop. The length of

NNADVOKAT [17]

Answer:

Explanation:

Given that,

Magnetic field of 0.24T

B = 0.24T

Field perpendicular to plane i.e 90°

Rate of decrease of length of side of square is 5.4cm/s

dL/dt = 5.4cm/s = 0.054m/s

Since it is decreasing

Then, dL/dt = -0.054m/s

When L is 14cm, what is the EMF induced?

L = 14cm = 0.14m

EMF is give as

ε = - dΦ/dt

Where flux is given as

Φ = BA

Where A is the area of the square

A = L²

Then, Φ = BL²

Substituting this into the EMF

ε = - dΦ/dt

ε = - d(BL²)/dt

B is constant

ε = - Bd(L²)/dt

ε = -2BL dL/dr

ε = -2 × 0.24 × 0.14 × -0.054

ε = 3.63 × 10^-3 V

ε = 3.63mV

8 0

4 years ago