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vovikov84 [41]
3 years ago
13

If rho(x,y) is the density of a wire (mass per unit length), then

Physics
1 answer:
lidiya [134]3 years ago
7 0

Answer:

See description

Explanation:

With the given information we have:

x(t) = 1 + cos(t)\\ y(t)=sin(t)\\ \rho(x,y) = 3x

the interval is [0,\pi ]

now the mass m has the given expression:

m = \int \rho(x,y) dS

we will use the formula for a line integral and let:

dS=\sqrt{x'(t)^2 + y'(t)^2}=\sqrt{cos(t)^2 + sin(t)^2}dt=dt

therefore we have:

m=\int \rho(x,y)dS=\int\limits^\pi_0 {3*x}dS=\int\limits^\pi _0{3*(1+cos(t))dS\\=\int\limits^\pi _0{3*(1+cos(t))dt

we solve the integral:

m=3*\int\limits^\pi _0{(1+cos(t))dt= 3*(t+sin(t))\limits^\pi _0=3*\pi=9.42

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A charged particle having mass 6.64 x 10-27 kg (that of a helium atom) moving at 8.70 x 105 m/s perpendicular to a 1.30-T magnet
Fiesta28 [93]

Answer:

the charge of the particle is 2.47 x 10⁻¹⁹ C

Explanation:

Given;

mass of the particle, m = 6.64 x 10⁻²⁷ kg

velocity of the particle, v = 8.7 x 10⁵ m/s

strength of the magnetic field, B = 1.3 T

radius of the circle, r = 18 mm = 1.8 x 10⁻³ m

The magnetic force experienced by the charge is calculated as;

F = ma = qvB

where;

q is the charge of the particle

a is the acceleration of the charge in the circular path

a = \frac{v^2}{r} \\\\ma = qvB\\\\q = \frac{ma}{vB} \\\\q = \frac{mv^2}{rvB} = \frac{mv}{rB} \\\\q = \frac{(6.64\times 10^{-27} ) \times (8.7\times 10^5)}{(1.8\times 10^{-2}) \times (1.3)} \\\\q = 2.47 \ \times 10^{-19} \ C

Therefore, the charge of the particle is 2.47 x 10⁻¹⁹ C

6 0
3 years ago
What are the SI units of thermal conductivity?​
kotykmax [81]

Answer:

The SI unit of thermal conductivity is watts per meter-kelvin (W/(m⋅K)).

Explanation:

hope this will help u

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2 years ago
I will mark brainliest!! The Moon travels around the Earth each month in an elliptical path, as opposed to a perfect circle.
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Answer:

The magnitude decreases

Explanation:

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2 years ago
Could someone please explain to me Archimede's principle without using the term displace (or at least explaining what it means)?
disa [49]
Does this help?

When an object is immersed in a fluid (in this case water, but may include both liquids and gases) the fluid exerts an upward force on the object which is called buoyancy force or <span>up-thrust.  Archimedes’ Principle states that the buoyant force (upward push or force) applied to an object is equal to the weight of the fluid that the object takes the space of by that object.  Thus when an object is placed in water the rise in the water level is dictated by the mass of that object.</span>

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<span>So for example if you fill a bucket with water and you drop a stone in that bucket, if you measure the weight of the water that overflows from the bucket due to the stone being dropped into the bucket is equivalent to the pushing force that the water has on the stone (as the stone drops to the bottom of the bucket the water is pushing it to stay afloat but the rock is more dense than water and as such its downthrust exceeds water's upthrust).</span>


4 0
3 years ago
Magnetic field 0.02 mfrom a wire is 0.1 T. What is the magnitude of the magnetic field of 0.01 m from the same wire?
Gre4nikov [31]

Answer:

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6 0
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