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1 month ago

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A displacement vector has a magnitude of 810 m and points at an angle of 18° above the positive x axis. what are the x and y sca

lar components of this vector? x scalar component y scalar component

1 answer:

Keith_Richards [3.2K]1 month ago

5 0

I've shared my work and marked my answers for clarity. I hope it's understandable! Feel free to ask if you have any queries regarding anything that's not clear!:)

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In a demonstration, a 4.00 cm2 square coil with 10 000 turns enters a larger square region with a uniform 1.50 T magnetic field

serg [3582]

Explanation:

It is stated that,

Area of square coil, $A=4\ cm^2=0.0004\ m^2$

Length of one side of the square, L = 0.02 m

Number of coils, N = 10000

Consistent magnetic field, B = 1.5 T

Velocity, v = 100 m/s

An electromotive force is produced in the coil calculated as:

$E=NBLv$

$E=10000\times 1.5\times 0.02\times 100$

E = 30000 V

Breakdown voltage of air, $V=4000\ V/cm=400000\ V/m$

Let d be the distance between the ends of the coil wires that can still produce a spark. Therefore,

Electric field, $E'=\dfrac{V}{d}$

$\dfrac{30000}{d}=400000$

d = 0.075 m

Thus, this forms the final answer.

6 0

18 days ago

You are designing a spacecraft intended to monitor a human expedition to Mars (mass 6.42×1023kg, radius 3.39×106m). This spacecr

Softa [3030]

The height is h = 17 10⁶ meters above the surface of Mars. To determine this, we apply Newton's second law according to the universal law of gravitation, represented by F = m a. The centripetal acceleration a is expressed as v² / r. Applying the gravitational force we have G m M / r² = m v² / r. Given that the speed of the object remains constant, we derive v from d / t, where d is the circumference and t is the orbital period. Substituting gives us d = 2π r and v = 2π r / T. Replacing these values leads to the equation G M / r² = (4π² r² / T) / r, so r³ = G M T² / 4π². Converting time into SI units, T = 24.66 h converts to 88776 seconds. Ultimately, the computed value of r is 2,045 10⁶ m, and after subtracting Mars’ radius of 3.39 10⁶ m, we find the height h to be 17 10⁶ m.

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22 days ago

A spinning wheel is slowed down by a brake, giving it a constant angular acceleration of 25.60 rad/s2. During a 4.20-s time inte

Yuliya22 [3333]

We will use the equations of rotational kinematics,

$\theta =\theta _{0} + \omega_{0} t+ \frac{1}{2}\alpha t^2$ (A)

$\omega^2= \omega^2_{0} +2\alpha\theta$ (B)

Here, $\theta$ and $\theta _{0}$ denote the final and initial angular displacements, respectively, whereas $\omega$ and $\omega_{0}$ represent final and initial angular velocities, and $\alpha$ is the angular acceleration.

We are provided with $\alpha = - 25.60 \ rad/s^2, \theta = 62.4 \ rad$ and $t = 4.20 \ s$ .

By substituting these values into equation (A), we have

$62.4 \ rad = 0 + \omega_{0} 4.20 \ s + \frac{1}{2} (- 25.60 \ rad/s^2) ( 4.20)^2 \\\\ \omega_{0} = \frac{220.5+ 62.4 }{4.20} =67.4 \ rad/s$

Now, using equation (B),

$\omega^2=(67.4 \ rad/s)^2 + 2 (- 25.60 \ rad/s^2)62.4 \ rad \\\\\ \omega = 36.7 \ rad/s$

This indicates that the wheel's angular speed at the 4.20-second mark is 36.7 rad/s.

4 0

1 month ago

Two events are observed in a frame of reference S to occur at the same space point, with the second event occurring after a time

Sav [3153]

Answer:

The distinction between the locations of the two events as perceived in S is calculated to be 4.42 x 10^8 m

Explanation:

The time dilation concept has been utilized to address this question, as detailed in the attachment.

5 0

8 days ago

Five metal samples, with equal masses, are heated to 200oC. Each solid is dropped into a beaker containing 200 ml 15oC water. Wh

ValentinkaMS [3465]

Part 1) Which metal will cool the fastest?
To determine this, we need to consider the heat flow rate formula, which indicates the speed at which a substance can gain or lose heat:
$\frac{\Delta Q}{\Delta t} = -k \frac{A \Delta T}{x}$
where:
$\Delta Q$ denotes the heat exchanged
$\Delta t$ indicates the duration
k represents the thermal conductivity of the material
A is the area over which heat transfer takes place
$\Delta T$ shows the change in temperature
x is the thickness of the substance
It is evident that the heat flow rate $\frac{\Delta Q}{\Delta t}$ is directly related to k, the thermal conductivity. Thus, a higher value of k means that the metal will cool more quickly.
Upon examining the thermal conductivity values for each metal, we observe:
- Aluminium: 237 W/(mK)
- Copper: 401 W/(mK)
- Gold: 314 W/(mK)
- Platinum: 69 W/(mK)
Consequently, copper has the highest heat flow rate, making it the metal that cools the fastest.

Part 2) Which sample of copper demonstrates the greatest increase in temperature
To address this part, we can examine how the heat exchanged Q correlates with temperature increase $\Delta T$ :
$Q=m C_S \Delta T$
where m indicates the mass and Cs represents the specific heat capacity of the material. By rearranging the equation, we derive
$\Delta T= \frac{Q}{m C_s}$
As a result, it becomes clear that the temperature increase is inversely related to the mass m. Thus, the block exhibiting the highest temperature rise will be the one with the least mass, hence the right choice is A) 0.5 kg.

4 0

29 days ago