Solve the following numerical problems​

a)New position vector in vector form= r = 0.233404 î + 2.94056j m

b) Lies in second quadrant at 161.391°

c)Velocity =4.8675 m/s

d)It is moving in a direction making 161.391° with positive x-direction.

e)Acceleration will be centripetal acceleration (8.031 m/s²).

Given:

Mass of the object m = 3.95 kg

ω=1.65 rad/s

Radius of the circle = 2.95 m

a)

new position vector in vector form

=R cos1.65 î  + R sin 1.65 j

= 2.95 cos1.65 î  +2.95 sin1.65 j

= 2.95 x 0.07912 î + 2.95 x 0.9968 j

r = 0.233404 î + 2.94056j

b)

Angular Displacement = θ₀ = 9.10 rad

9.10 radian = 180/π× 9/10 degree

= 521.391°

=521.391°- 360°

=161.391°

This will lie in second quadrant.

Angle made with positive x-axis

=161.391°

c)

Velocity

v = ω R

= 1.65 x 2.95

=4.8675 m/s

d)

It is moving in a direction making 161.391° with positive x-direction.

e)

Acceleration will be centripetal acceleration.

= v²/R

=(4.8675)² / 2.95

=23.6925562 / 2.95

=8.031 m/s²

f) Position, Velocity and Acceleration graph:

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a) New position vector is r = 0.233404 î + 2.94056j m

b) Lies in second quadrant at 161.391°

c) Velocity =4.8675 m/s

d) It is moving in a direction making 161.391° with positive x-direction.

e) Acceleration will be centripetal acceleration (8.031 m/s²).

Given:

Mass of the object m = 3.95 kg

ω=1.65 rad/s

The radius of the circle = 2.95 m

a) new position vector in vector form

 r =R cos1.65 î  + R sin 1.65 j

 r = 2.95 cos1.65 î  +2.95 sin1.65 j

 r = 2.95 x 0.07912 î + 2.95 x 0.9968 j

 r = 0.233404 î + 2.94056j

b) Angular Displacement = θ₀ = 9.10 rad

9.10 radian = 180/π× 9/10 degree

 = 521.391°

 = 521.391°- 360°

 =161.391°

This will lie in the second quadrant.

Angle made with the positive x-axis =161.391°

c) Velocity

   v = ω R

   v = 1.65 x 2.95

   v = 4.8675 m/s

d) It is moving in a direction making 161.391° with positive x-direction.

e) Acceleration will be centripetal acceleration.= v²/R

   =(4.8675)² / 2.95

   =23.6925562 / 2.95

   =8.031 m/s²

f) Position, Velocity, and Acceleration graph:

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The solution for the acceleration of gravity is given as

This is further explained below.

Generally,

Mass of earth [tex]$M=5.97 \times 10^{24} \mathrm{~kg}$[/tex]

Radius of earth [tex]$R=6371 \mathrm{~km}$[/tex]

Gravitational const. [tex]$G=6.67 \times 10^{-11} \mathrm{Nm}^{2} \mathrm{~kg}^{-2}$[/tex]

height [tex]$h_{1}=7900 \mathrm{~m}=7.9 \mathrm{~km}$$$[/tex]

[tex]R+h_{1}=6371+7.9 &\\\\R+h_{1}=6378.9 \mathrm{~km} \\\\&R+h_{1}=6378.9 \times 10^{3} \mathrm{~m}\end{aligned}[/tex]

In conclusion, acceleration due to gravity at this point will be

[tex]g_{1}=\frac{G M}{\left(\bar{R}+\overline{h_{1}}\right)^{2}}$\\\\$g_{1}=\frac{6.67 \times 10^{-11} \times 5.97 \times 10^{24}}{\left(6378.9 \times 10^{3}\right)^{2}}$\\\\$g_{1}=9.789 \mathrm{~m} / \mathrm{s}^{2}$[/tex]

for [tex]$h_{2}=7900 \mathrm{~km}$[/tex]

[tex]R+h_{2}=6371+7900\\\\R+h_{2}=14271 \mathrm{~km}\\\\$g_{2}=\frac{6.67 \times 10^{-11} \times 5.97 \times 10^{24}}{\left(14271 \times 10^{3}\right)^{2}}$\\\\$g_2=1.955 \mathrm{~m} / \mathrm{s}^{2}$[/tex]

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The buoyant force acting on the cylinder is, [tex]Fb = \rho Ahg[/tex]. Here A is the cross-sectional area of the cylinder, h is the height of the cylinder, ρ is the density of the cylinder, and g is the acceleration due to gravity.

This buoyant force is also equal to the volume of the fluid displaced. [tex]Fb = \sigma h(A-x)g[/tex]. Here σ is the density of the fluid.

Equate the above two equations and solve for x.

[tex]\rho Ahg = \sigma A(h-x)g\\\rho h = \sigma h - \sigma x\\x = \frac{(\sigma - \rho)h}{\sigma}[/tex]

So, the distance x depends on the density of the fluid, density of the cylinder and the height of the cylinder.

1. The density of the cylinder is same and distance x is independent of the diameter of the cylinder. Therefor, there will be no change in the distance x. Hence, the correct answer is No change.

2. Now the height is changing keeping the density same. As the distance x is directly proportional to the height, the distance x will increase.

3. The density of the added liquid is greater than of the water and it does not mix with the water. So, the liquid will settle down and there will be no change in the distance x.

4. The density of the added liquid is less than that of the water and it does not mix with the water. So, the liquid will not settle down and the distance x will change. The change in distance x can be determined as follow:

[tex]\rho Agh = \sigma' Axg + \sigma A(h-x)g\\\rho h=\sigma' x + \sigma h - \sigma x\\x=(\frac{\sigma - \rho}{\sigma - \sigma'})h[/tex]

Here, σ' is the density of the added liquid.

From the above relation it is clear, that on adding the liquid of the density less than that of water, the denominator term become small ando so the value of x will increase.  

5. On removing some of the water inside the glass, the height of the water column will decrease, but the value of x does not depend on the height of the water column. So, there will be no change in the distance x.

6. The density of the new cylinder is smaller than that of the earlier one. So, the numerator term will increase. Therefore, the value of x will increase.

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The double-slit experiment shows that both matter and light can exhibit properties of conventionally defined waves and particles.

The double-slit experiment  is a part of a class of "double path" experiments in which a wave is split into two separate waves that later combine to form a single wave (the wave is typically composed of many photons and is better known as a wave front, which should not be confused with the wave properties of the individual photon).

Isaac Newton's corpuscular theory of light, which had previously prevailed as the accepted explanation of light transmission in the 17th and 18th centuries, was defeated by double-slit experiment , which was conducted in the early 1800s.

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(a) The weight of the drop is 1.54 x 10⁻²⁵ N,

(b) The the charge on the drop, in terms of e is 5 x 10⁻¹²e and

(c) The excess electrons is 5 x 10⁻¹² electron.

The weight of the drop is calculated as follows;

Volume of the drop; V = ⁴/₃πr³

V = ⁴/₃π(1.64 x 10⁻⁶)³ = 1.845 x 10⁻¹⁷ m³

mass = density x volume

mass =  0.851 g/cm³ x  1.845 x 10⁻²³ cm³ = 1.572 x 10⁻²³ g =  1.57 x 10⁻²⁶ kg.

Weight = 1.57 x 10⁻²⁶ kg x 9.8 m/s² = 1.54 x 10⁻²⁵ N.

q = F/E

q = (1.54 x 10⁻²⁵ N)/(1.92 x 10⁵)

q = 8.01 x 10⁻³¹ C

1.6 x 10⁻¹⁹ C = 1e

8.01 x 10⁻³¹ C = ?

= 5 x 10⁻¹²e

1.6 x 10⁻¹⁹ C ------- 1 electron

8.01 x 10⁻³¹ C ------- ?

= 5 x 10⁻¹² electron

Thus, the weight of the drop is 1.54 x 10⁻²⁵ N, the the charge on the drop, in terms of e is 5 x 10⁻¹²e and the excess electrons is 5 x 10⁻¹² electron.

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Endarterectomy is used to reduce the risk of stroke and correct the stenosis in the artery.

The primary blood vessels that supply the brain with blood and oxygen are the carotid arteries.

The narrowing of these arteries is referred to as carotid artery disease. Carotid artery stenosis is another name for it. The main factor causing constriction is atherosclerosis.

This fat deposit reduces the blood flow to the brain which cause a stroke.

Carotid endarterectomy is a surgical treatment to remove plaque, an accumulation of fatty deposits that causes a carotid artery to become narrowed.

Hence, an Endarterectomy is used to reduce the risk of stroke, it will correct stenosis in the artery.

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A. The acceleration of the ball while it is in flight?

magnitude is 0 m/s² (magnitude is zero)

B. The velocity of the ball when it reaches its maximum height is 0 m/s (magnitude is zero)

C. The initial velocity of the ball 8.036 m/s upward

D. The maximum height reached by the ball is 3.29 m

Considering that the ball came to rest after 1.64s, it means the entire acceleration of the flight is zero as the ball was not moving in any form again.

At maximum height, the velocity of the ball is zero as it no longer has magnitude to keep going upwards. Hence the ball begins to ball down.

v = u - gt (since the ball is going against gravity)

0 = u - (9.8 × 0.82)

0 = u - 8.036

Collect like terms

u = 0 + 8.036

u = 8.036 m/s upward

h = ½gt²

h = ½ × 9.8 × 0.82²

h = 3.29 m

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Hi there!

We can use Biot-Savart's Law for a moving particle:
[tex]B= \frac{\mu_0 }{4\pi}\frac{q\vec{v}\times \vec{r}}{r^2 }[/tex]

B = Magnetic field strength (T)
v = velocity of electron (0.130c = 3.9 × 10⁷ m/s)

q = charge of particle (1.6 × 10⁻¹⁹ C)

μ₀ = Permeability of free space (4π × 10⁻⁷ Tm/A)

r = distance from particle (2.10 μm)

There is a cross product between the velocity vector and the radius vector (not a quantity, but specifies a direction). We can write this as:

[tex]B= \frac{\mu_0 }{4\pi}\frac{q\vec{v} \vec{r}sin\theta}{r^2 }[/tex]

Where 'θ' is the angle between the velocity and radius vectors.

a)
To find the angle between the velocity and radius vector, we find the complementary angle:

θ = 90° - 60° = 30°

Plugging 'θ' into the equation along with our other values:

[tex]B= \frac{\mu_0 }{4\pi}\frac{q\vec{v} \vec{r}sin\theta}{r^2 }\\\\B= \frac{(4\pi *10^{-7})}{4\pi}\frac{(1.6*10^{-19})(3.9*10^{7}) \vec{r}sin(30)}{(2.1*10^{-5})^2 }[/tex]

[tex]B = \boxed{7.07 *10^{-10} T}[/tex]

b)
Repeat the same process. The angle between the velocity and radius vector is 150°, and its sine value is the same as that of sin(30°). So, the particle's produced field will be the same as that of part A.

c)

In this instance, the radius vector and the velocity vector are perpendicular so

'θ' = 90°.

[tex]B= \frac{(4\pi *10^{-7})}{4\pi}\frac{(1.6*10^{-19})(3.9*10^{7}) \vec{r}sin(90)}{(2.1*10^{-5})^2 } = \boxed{1.415 * 10^{-9}T}[/tex]

d)
This point is ALONG the velocity vector, so there is no magnetic field produced at this point.

Aka, the radius and velocity vectors are parallel, and since sin(0) = 0, there is no magnetic field at this point.

[tex]\boxed{B = 0 T}[/tex]

Answer:

Object A's momentum is larger

Explanation:

as the formula for momentum goes:

P = M * V

where P is momentum, M is mass, V is velocity.

so where Va (Object A's velocity) is larger than Vb (Object B's velocity) we get:

( i ) Va > Vb

as the masses of both objects are equal, we mark:

( ii) Ma = Mb = M

we multiply both sides of ( i ) by M to get:

( iii ) Va × M > Vb × M

and we finally get:

( iv ) Pa > Pb

Answer: Object A's momentum of larger than compared to that of object B.

Explanation:

The force required to pull the two hemispheres apart 53696.25N and  the minimum number of horses required is 37 .

( Note: 1 millibar=100 N/m2. One atmosphere is 1013 millibar = 1.013×105 N/m2 )

(1)The contact area between the hemispheres is (π x 0.430²) = 0.5805m²

Pressure difference = (940 - 15) = 925millibars.

(925 x 100) = 92,500N/m^2.

(92500 x 0.5805) = 53696.25N. is the force required to part the hemispheres.

(2)[tex]\frac{53696.25N}{1450N}[/tex] = 37 horses for each side .

37 + 37 = 74 horses will be required.

Force is something which can change the motion of an object, stop it or move it, change its shape or size with it. There are two types of forces, contact forces and non-contact forces. Here, it is a contact force at first, then when the horses come it becomes non-contact force.

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The change in temperature is 20 kelvin


What is Temperature?


Temperature can simply be described as how hot or how cold an object is at a particular period in time. The unit of temperature is Kelvin.

The formula for calculating change in temperature is

Final temperature - Initial temperature

Final temperature = 300 kelvin
Initial temperature= 280 kelvin

Change in temperature= 300-280

= 20 kelvin

Thus the change in temperature for this process is 20 kelvin


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Answer:

Explanation:

Answer: True

hope this helps!

A grandfather paradox is a situation where individual travels to the past and then introduces a change which affects or contradicts the present.

A paradox is a situation or statement which involves two contradictions.

A grandfather paradox is a situation which is defined by the ability of an individual to travel to a time in the past usually before the birth of their grandfather and then introduces a change which affects or contradicts the present. For example, killing the grandfather to prevent their birth.

In conclusion, a grandfather paradox is is an event which contradicts the present as a result of a change done to the past.

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Answer:

Yes.

Explanation:

When you move your hand from the cold water to the “warmer” (room temp) water, one hand feels warm.

As you move your hand from the warm water to the “colder” (room temp) water, that hand feels colder.

Although both hands experience the last bowl of water at the same temperature, your brain senses two

separate sensations. So the water feels “warm” or “cold” relative to the water your hand was in previously.

The greater the difference in temperature, the easier it is to sense a difference.

The horizontal force applied is  160 N while the velocity is  2.03 m/s.

The work done by the car is obtained as the product of the force and the distance;

W = F x

F = ?

x = 30.0 m

W = 4,800 J

F = 4,800 J/30.0 m

F = 160 N

But F = ma

a = F/m

a = 160 N/2.30 ✕ 10^3-kg

a= 0.069 m/s

Now;

v^2 = u^2 + 2as

u = 0/ms because the car started from rest

v = √2as

v = √2 * 0.069 * 30

v = 2.03 m/s

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Answer:

Create space

Watch your breath

Watch your thoughts

Be gentle with yourself

Affirm what you want

Explanation:

Answer:

the branch of science that is concerned with nature and properties of matter and energy.

Explanation:

a study of the basis of what does what in science.

The velocity of a 55.0-kg person hitting the ground, is mathematically given as

vt=39.5983m/s

Generally, the equation for is  mathematically given as

mass of squirrel,

[tex]m=550 \mathrm{~g}\\\\Surface area, $A=945 \mathrm{~cm}^{2}=88 \times 10^{-3}$\\\\Height, $h-4 \mathrm{~m}$\\[/tex]

Terminal velocity is given by:

[tex]$v_{i}=\sqrt{\frac{2 m g}{\rho A C}}$[/tex]

where \rho is the density of fluid that is falling and it is given by

[tex]$\rho=\frac{m}{V}$[/tex]

since, volume =area * height

[tex]^{\rho=} \frac{0.55 \mathrm{Kg}}{0.0945 \mathrm{~m}^{2} \times 4.0 \mathrm{~m}}\\\\$\rho=0.1455 \mathrm{Kg} / \mathrm{m}^{3}$[/tex]

A is the surface area of squirrels.

C is the drag coefficient.

The surface area facing the fluid is given by:

[tex]A_{f}=\frac{0.0945 \mathrm{~m}^{2}}{2} \\\\\\ A_{f}=0.04725 \mathrm{~m}^{2}[/tex]

so, terminal velocity is :

[tex]$v_{t}=\sqrt{\frac{2 \times 0.55 \mathrm{Kg} \times 9.8 \mathrm{~m} / \mathrm{s}^{2}}{0.1455 \mathrm{Kg} / \mathrm{m}^{3} \times 0.04725 \mathrm{~m}^{2} \times 1}}$[/tex]

Vt=39.5983

In conclusion, the terminal velocity of the squirrel is 39.5983m/s

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No. of turns in the solenoid is an option (b) 144.

The self-inductance of a long solenoid depends only on its physical properties (such as the number of turns of wire per unit length and the volume), and not on the magnetic field or the current.

Self-inductance of solenoid = 39.1 μH

                                           = 39.1 × [tex]10^-^6[/tex] H

Length of the solenoid = 4.0 cm

Cross-sectional area = 0.60 cm²

Expression for the self-inductance of a coil ;

L = µ₀N²A / [tex]l[/tex]

where,

L = Self- Inductance

N = No. of turns.

A = Cross-sectional area

[tex]l=[/tex] Length of the solenoid

L =( 4π × [tex]10^-^7[/tex] × N² × 0.60 ) / 4.0

39.1× 4.0 / 4π × [tex]10^-^7[/tex] × 0.60 = N²

N² = 2.07 × [tex]10^6[/tex]

N = 144

Therefore, the no. of turns of the solenoid is 144.

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Sound will travel fastest in air at 15°C.

The speed of sound in air, given in the range of 100 degrees Celsius and 0 degree Celsius include;

Air at 100°C 387 m/s

Air at 0°C 331 m/s

From the date above, the speed of sound in air increases with increases in temperature. Thus, Sound will travel fastest in air at 15°C.

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The two aircrafts are skidded for 14.9 s.

To find the answer, we need to know about the Newton's equation of motion.

As per Newton's equation of motion

=> a= -1000/224.2= -4.5 m/s²

=> t= 20/4.5 = 4.4 s

Thus, we can conclude that the two aircrafts are skidded for 4.4 s.

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Answer:

D. Impulse

Explanation: Hope this helps

The minimum necessary height of the IV bag above the position of the needle, if the density of the solution is 1.308kg/L, and the pressure in the vein is 35.7 mmHg is, 2.78m.

To find the answer, we need to know more about the pressure exerted by a liquid column.

                                                [tex]P=[/tex] ρgh

                                           [tex]density=1.308 kg/L\\\\P=35.7 mmHg.\\[/tex]

                                       [tex]h=\frac{P}{density*g} =\frac{35.7}{1.308*9.8}\\\\ h=2.78 m[/tex]

Thus, we can conclude that, the height of the Iv bag is 2.78 m above the position of needle.

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If the solution has a density of 1.308 kg/L and the vein pressure is 35.7 mmHg, the minimum height of the IV bag above the needle position is 2.78 m.

We need to learn more about the pressure that a liquid column exerts in order to determine the solution.

                            [tex]P=[/tex] ρgh

                        [tex]Density=1.308kg/L\\P=35.7mmHg[/tex]

                           [tex]h=\frac{P}{density*g}\\\\ h=2.78m[/tex]

As a result, we may say that the I.V. bag is 2.78 m above the ground.

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Based on the calculations, the ratio of the intensity of Ir to Ip is equal to 50.12.

Mathematically, sound intensity level can be calculated by using this formula:

[tex]\beta = 10 log(\frac{I}{I_{ref}} )[/tex]

Where:

I is the intensity of the sound.

Making I the subject of formula, we have:

I = Io × [tex]10^{\frac{\beta }{10} }[/tex]

For Ip, we have:

Ip = Io × [tex]10^{\frac{104 }{10} }[/tex]

Ip = Io × [tex]10^{10.4}[/tex]

For Ir, we have:

Ir = Io × [tex]10^{\frac{121 }{10} }[/tex]

Ir = Io × [tex]10^{12.1}[/tex]

Now, we can find the ratio of the intensity:

Ir/Ip = Io × [tex]10^{12.1}[/tex]/Io × [tex]10^{10.4}[/tex]

Ir/Ip = [tex]10^{12.1}[/tex]/[tex]10^{10.4}[/tex]

Ir/Ip = [tex]10^{12.1 -10.4}[/tex]

Ir/Ip = [tex]10^{1.7}[/tex]

Ir/Ip = 50.12.

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The speed of the satellite in a circular orbit around the Earth is 1.32 x 10⁵ m/s.

v = √(GM/r)

where;

v = √(6.67 x 10⁻¹¹ x 5.98 x 10²⁴/3.57 x 6.37x 10³)

v = 1.32 x 10⁵ m/s

Thus, the speed of the satellite in a circular orbit around the Earth is 1.32 x 10⁵ m/s.

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(a) The magnitude of the minimum magnetic field is 1.467 T.

(b) The direction of the minimum magnetic field will be eastwards.

F = qvB

mg = qvB

B = mg/qv

where;

B = (1.98 x 10⁻⁴ x 9.8) / (3.5 x 10⁻⁸ x 3.78 x 10⁴)

B = 1.467 T

The magnetic field will be directed towards the negative charge. Thus, the direction of the minimum magnetic field will be eastwards.

Thus, the magnitude of the minimum magnetic field is 1.467 T and the direction is eastwards.

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The symbol for a variable resistor is a line with a zig zag pattern with a diagonal line drawn across it.

What is a variable resistor ?

A resistor whose electric resistance value may be altered is known to as a variable resistor. A variable resistor, which works usually by sliding a contact (wiper) over a variable resistor, is basically an electro-mechanical transducer.

The flow of electrical current is restricted by a resistor. The resistivity of a fixed resistor is steady. By adjusting a slider's position, the resistance of this resistor can be altered. Some volume controls and dimmer switches employ variable resistors.

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The highest point of the wheel is the position of the wheel when its potential energy is greatest.

The position of the wheel when its potential energy is greatest when it is at the highest point because potential energy depends on the height of an object. If the object is at more height then it has more potential energy and vice versa.

So we can conclude that the highest point of the wheel is the position of the wheel when its potential energy is greatest.

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