Can momentum be negative?
A. No.
B. Yes, if it has a very small mass.
C. Yes, if it is moving very slow.
D. Yes, if it is moving backward.

(a) The magnitude of the magnetic field at point P1 , midway between the wires is  1.005 x 10⁻⁴ T and the direction will be out of the page.

(b) The magnitude of the magnetic field at point P2 , 25.0 cm to the right of P1 is 2.67 x 10⁻⁶ T and the direction is into the page.

(c) The magnitude of the magnetic field at point P3 , 20.0 cm directly above P1  is 3.88 x 10⁻⁶ T and the direction is downwards.

B = μ/2π[I₁/0.5r + I₂/0.5r]

B = (μ/2π) x (I/0.5r + I/0.5r)

B = (μ/2π) x (2I/0.5r)

B = μI/0.5r

B = 2μI/r

where;

B = (2 x 4π x 10⁻⁷ x 4)/(0.1)

B = 1.005 x 10⁻⁴ T

The direction of the magnetic field is out of the page.

B = μI/2πd

d = 5 cm + 25 cm = 30 cm

B =  (4π x 10⁻⁷ x 4)/(2π x 0.3)

B = 2.67 x 10⁻⁶ T

The direction of the magnetic field is into the page towards P1.

B = μI/2πd

d = √(20² + 5²)

d = 20.62 cm

B =  (4π x 10⁻⁷ x 4)/(2π x 0.2062)

B = 3.88 x 10⁻⁶ T

The direction of the magnetic field is downwards towards P1.

Thus, the magnitude of the magnetic field at point P1 , midway between the wires is  1.005 x 10⁻⁴ T and the direction will be out of the page.

The magnitude of the magnetic field at point P2 , 25.0 cm to the right of P1 is 2.67 x 10⁻⁶ T and the direction is into the page.

The magnitude of the magnetic field at point P3 , 20.0 cm directly above P1  is 3.88 x 10⁻⁶ T and the direction is downwards.

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Answer:

See below

Explanation:

T = period of orbit = sqrt ( 4  pi^2  r^3  /  (G  Me)  )

   G = gravitational constant   6.6743 x 10^-11  m^3 / (kg-s^2)

Me = mass of earth      =  6 x 10^24 kg

 r = radius = 6600 km = 6,600,000 m

plug in the values to find T = 5323.75 seconds

(check my math)

Answer:

 no

Explanation:

The angle subtended by the radius of the target at Emily's distance can be found using the tangent relation.

 tan(α) = opposite/adjacent = (1/4 ft)/(150 ft) = 1/600

The angle is found using the inverse relation -

α = arctan(1/600) ≈ 0.095°

If Emily's aim is off by 0.2°, she will miss the target by several inches.

Emily's projectile will miss her aiming point by ... (150 ft)tan(0.2°) ≈ 0.524 ft ≈ 6.28 in

The horizontal distance XQ traveled by the bomb is 250 m.

Let the XQ be the horizontal distance traveled by the bomb.

h = vt + ¹/₂gt

Let the vertical velocity = 0

h = 0 + ¹/₂gt²

h = ¹/₂gt²

2h = gt²

t² = 2h/g

t = √(2h/g)

t = √(2 x 100 / 9.8)

t = 4.5 s

XQ = vx(t)

where;

vx is horizontal speed, = 200 km/hr = 55.56 m/s

XQ = 55.56 x 4.5

XQ = 250 m

Thus, the horizontal distance XQ traveled by the bomb is 250 m.

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The force F, necessary to support an object with a mass of 991 kg placed on piston 2. is 20.61J.

It should be noted that by Pascal Law, the pressure on piston 1 will have the same value as the pressure on piston 2.

This will be:

(991 × 10) /(π × 0.0946/2)²

= 9910/0.022

= 450454.6 Pa

F1 = A1 × 450454.6 = 3.14 × (0.0187/2)² × 450454.6

= 123.64

F = 123.64/6

F = 20.61

Therefore, the force F, necessary to support an object with a mass of 991 kg placed on piston 2. is 20.61J.

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Answer:

To give light yo people and the neutron are to give you health care

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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The amount of heat needed to raise the temperature of 6.00 g of copper by 15.0°C is 34.65J (option A).

The amount of heat absorbed or released by a substance can be calculated using the following formula:

Q = mc∆T

Where;

Q = 6 × 0.385 × 15

Q = 90 × 0.385

Q = 34.65J

Therefore, the amount of heat needed to raise the temperature of 6.00 g of copper by 15.0°C is 34.65J.

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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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The vertical component of force exerted by the hi.nge on the beam will be,142.10N.

To find the answer, we need to know more about the tension.

                      [tex]F_V+T sin\alpha -mg=0\\F_V=mg-Tsin\alpha \\[/tex]

                     [tex]Tlsin\alpha - mg\frac{l}{2}sin\beta =0\\ \\Tlsin\alpha = mg\frac{l}{2}sin\beta\\\\Tsin57=\frac{mg}{2}sin90\\\\T=\frac{mg}{2sin57} =169.43N[/tex]

                [tex]F_V=(29*9.8)-(169.43*sin57)=142.10N[/tex]

Thus, we can conclude that, the vertical component of force exerted by the hi.nge on the beam will be,142.10N.

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The hi.nge will apply a force of 142.10N on the beam in the vertical direction.

We must learn more about the tension in order to find the solution.

                           [tex]F_V=mg-Tsin\alpha[/tex]

                            [tex]Tlsin\alpha =mg\frac{l}{2}sin\beta \\T=\frac{mgsin90}{2sin57} =169.43N[/tex]

                     [tex]F_v=(29*9.8)-(169.43*sin57)=142.10N[/tex]

This leads us to the conclusion that the vertical component of the force the hi.nge exerts on the beam will be 142.10N.

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The point where m3 experiences a zero net gravitational force due to M1 and m2 is 57.42 m.

m1<------(x)------> m3 <-----------(94.8 m - x)-------->m2

a point, x, where m3 experiences a zero net gravitational force due to M1 and m2;

Force on m3 due to m1 = Force on m3 due to m2

Gm1m3/d² = Gm2m3/r²

m1/d² = m2/r²

where;

m1/(x²) = m2/(94.8 - x)²

m1(94.8 - x)² = m2x²

(94.8 - x)² = (m2/m1)x²

(94.8 - x)² = (10.6/25)x²

(94.8 - x)² = 0.424x²

(94.8 - x)² = (0.651)²x²

94.8 - x = 0.651x

94.8 = 1.651x

x = 94.8/1.651

x = 57.42 m

Thus, the point where m3 experiences a zero net gravitational force due to M1 and m2 is 57.42 m.

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The angle of projection given that the range is 256√3 m and the maximum height reached is 64 m is 30°

R = u²Sine(2θ) / g

256√3 = u²Sine(2θ) / 9.8

Cross multiply

256√3 × 9.8 = u²Sine(2θ)

Divide both sides by Sine(2θ)

u² = 256√3 × 9.8 / Sine(2θ)

H = u²Sine²θ / 2g

64 = [256√3 × 9.8 / Sine(2θ)] × [Sine²θ / 2 × 9.8]

64 = [256√3 / Sine(2θ)] × [Sine²θ / 2]

Recall

Sine²θ = SineθSineθ

Sine2θ = 2SineθCosθ

Thus,

64 = [256√3 / 2SineθCosθ] × [SineθSineθ / 2]

64 = 256√3 × Sineθ / 4Cosθ

Recall

Sineθ / Cosθ = Tanθ

Thus,

64 = 256√3 / 4 × Tanθ

Divide both side by 256√3 / 4

Tanθ = 64 ÷ 256√3 / 4

Tanθ = 0.5774

Take the inverse of Tan

θ = Tan⁻¹ 0.5774

θ = 30°

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The kinetic energy of the projectile at the highest point of its motion will be E/4.

When a projectile will be thrown obliquely near the surface of the earth, it travels a curved path under uniform acceleration directed toward the center of the Earth. The path of a particle is called a projectile while the motion of a projectile is projectile motion.

Given, the angle of projection  with horizontal, [tex]\theta = 60 ^o[/tex]

Consider that 'E' is the initial value of the kinetic energy of the projectile.

The equation for the initial kinetic energy is : [tex]E =\frac{1}{2}mu^2[/tex]

where m is the mass of the given projectile.

The component of the velocity of the projectile in the horizontal direction:

uₓ = u cosθ

uₓ = u cos 60°

uₓ = u/2

From the equation of motion: v = u +at

v = (u/2) + (0) t

v = u/2

The final kinetic energy of the projectile:

[tex]E_f = \frac{1}{2}mv^2[/tex]

[tex]E_f = \frac{1}{2}m(\frac{u}{2} )^2[/tex]

[tex]E_f = \frac{1}{4} (\frac{1}{2}mu^2 )[/tex]

[tex]E_f = \frac{E}{4}[/tex]

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5.8 moles of nitrogen gas are needed to pressurize the air bag.

= (2.37×60)/(0.0821×298)

= 5.8 moles

Thus, we can conclude that 5.8 moles of nitrogen gas are needed to pressurize the air bag.

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The deceleration of the bullet over 0.2 second, given the data from the question is –2500 m/s²

This is defined as the rate of change of velocity which time. It is expressed as

a = (v – u) / t

Where

a is the acceleration

v is the final velocity

u is the initial velocity

t is the time

NOTE: Deceleration is the opposite of acceleration

With the above equation for acceleration, we can obtain the deceleration of the bullet. Details below:

a = (v – u) / t

a = (0 – 500) / 0.2

a = –500 / 0.2

a = –2500 m/s²

Thus, the deceleration of the bullet is –2500 m/s²

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Answer:

4 C

Explanation:

The strength of an electric field can be defined as: [tex]E = \frac{f}{q}[/tex] where f=force and q=charge, and e=strength

Since we're given the strength and the force we can simply rearrange the equation so that we solve for Q:

Original Equation:

[tex]E=\frac{f}{q}[/tex]

Multiply both sides by q

[tex]E*q = f[/tex]

Divide both sides by E

[tex]q=\frac{f}{e}[/tex]

So now plug the known values into the equation

[tex]q=\frac{1000 N}{250 N/C}[/tex]

Simplify:

[tex]q = 4 c[/tex]

The voltage between the plates is 3.9 × [tex]10^-^3[/tex] V.

The work-energy theorem states that the delta in the equation equals the change in kinetic energy plus the change in potential energy. Here, a charge's potential energy is expressed as qV, where V is the position's electric potential.  The greater the change in voltage per unit distance, the greater the electric field.

The kinetic energy of the electrons = 4.1 × [tex]10^-^1^5[/tex] J

Charge of the electron = 1.602 × [tex]10^-^1^9[/tex] coulomb

Using,

     ΔU = q × ΔV

4.1 × [tex]10^-^1^5[/tex] = 1.602 × [tex]10^-^1^9[/tex] × ΔV

      ΔV  = 3.9 × [tex]10^-^3[/tex] V

Therefore, the voltage between the plates is 3.9 × [tex]10^-^3[/tex] V.

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The volume of the helium balloon in order to lift the weight is 17,760m³.

To find the answer, we need to know about the buoyant force.

     => V= 3179/0.179 = 17,760m³

Thus, we can conclude that the volume of the helium balloon in order to lift the weight is 17,760m³.

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The original kinetic energy of the player and the average power is required to stop him are 1200 J and 1200 W respectively.

The energy possessed by a body in motion is known as Kinetic Energy. The S. I unit is Joule.

Given that an 87-kg football player traveling 5.2 m/s is stopped in 1.0 s by a tackler. The given parameters are;

The original kinetic energy of the player can be calculated by using the formula K.E = 1/2m[tex]v^{2}[/tex]

Substitute all the parameters into the formula

K.E = 1/2 x 87 x [tex]5.2^{2}[/tex]

K.E = 1176.24

K.E = 1200 J

Power is the rate at which work is done.

Work done = energy

The average power is required to stop him can be calculated by using the formula P = E/t

Substitute all the parameters into the formula

P = 1200/1

P = 1200 W

Therefore, the original kinetic energy of the player and the average power is required to stop him are 1200 J and 1200 W respectively.

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5.48 V is the potential drop across the cable for a copper transmission cable of 50.0 km long and 10.0 cm in diameter carries a current of 105 A

Ohm's Law states that the potential drop is determined by the equation: V = IR, where I is the current and R is the wire resistance.
R=PL/A
Under the assumption that all physical parameters and temperatures remain constant, Ohm's law asserts that the voltage across a conductor is directly proportional to the current flowing through it.

Only when the given temperature and the other physical variables remain constant does Ohm's law apply. Increasing the current causes the temperature to rise in some components. The filament of a light bulb serves as an illustration of this, where the temperature increases as the current increases. Ohm's law cannot be applied in this situation. The filament of the lightbulb defies Ohm's Law.

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The output current for the given step down transformer is 30A.

What is the step down transformer?

A step down transformer is a passive device that converts high voltage power to low voltage power, while the output current is higher than the  input current. They are used in power adaptors and rectifiers to decrease the voltage to the desired level. It works according to Faraday's law of Electromagnetic induction.

The current in the windings of a step down transformer is inversely proportional to the voltage in windings as:

Input voltage / Output voltage = Output current / Input current

220 / 110 = Outout current / 15

Output current = 30A

Hence, the output current (30A) obtained is higher than the given input current (15A).

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An object is considered to be in a condition of equilibrium when it is balanced with regard to all external forces.

Equilibrium:

An object is considered to be in equilibrium if both its angular acceleration and the acceleration of its center of mass are equal to zero. In layman's terms: The item must either be at rest or moving at a constant speed if it is not accelerating because F = ma (force = mass x acceleration). Even in motion, a body can be in equilibrium. This kind of equilibrium is referred to as a dynamic equilibrium.

A weight suspended by a spring or a brick laying on a flat surface is an example. The equilibrium is unstable if the force with the smallest deviation tends to increase the displacement. As an example, imagine a ball bearing on the edge of a razor blade.

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(a) The initial vertical velocity of the stone is 16.85 m/s and the initial horizontal velocity is 14.14 m/s.

(b) The final vertical velocity is 0 and the final horizontal velocity is 14.14 m/s.

The initial vertical velocity of the stone is calculated as follows;

Vi = Vsinθ

Vi = 22 x sin(50)

Vi = 16.85 m/s

Vxi = V cosθ

Vxi = 22 x cos(50)

Vxi = 14.14 m/s

Vf = Vi - gt

where;

Vfx = Vxi = 14.14 m/s

Thus, the initial vertical velocity of the stone is 16.85 m/s and the initial horizontal velocity is 14.14 m/s.

The final vertical velocity is 0 and the final horizontal velocity is 14.14 m/s.

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The initial momentum of the yellow and the orange train is 1000kgm/s.

Momentum is the product of the mass and velocity of any object.

Momentum is denoted by P.

Momentum P = mv , where m = mass and v = velocity.

Mass of the orange train = 200kg

Velocity of the orange train = 1m/s

So, the momentum of the orange train will be,

                            ∴    P = mv

                                  P = 200 x 1

                                  P = 200 kgm/s

∴   The initial momentum of the orange train is 200kgm/s.

Mass of the yellow train = 100kg

Velocity of the yellow train = 8m/s

So, the momentum of the yellow train will be,

                            ∴    P = mv

                                  P = 100 x 8

                                  P = 800 kgm/s

∴ The initial momentum of the yellow train is 800kgm/s.

Therefore, the initial momentum of the yellow and the orange train is 1000kgm/s.

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As, per the buoyancy force,the volume that the balloon should have is 2863[tex]m^{3}[/tex]

What is buoyancy force?

Air buoyancy is the upward force exerted on an object by the air that is displaced by object. Air buoyancy is responsible for the buoyancy created by the displaced air.

[tex]F_{b}[/tex] = -Vρg ,       where V= volume of the object

                                   ρ = density of the object

                                   g = acceleration due to gravity

                                   [tex]F_{b}[/tex] = buoyant force

The buoyancy force must be equal to the total load lifted

ρ[tex]_{He}[/tex] × V × g + 269 + 2910 = ρ[tex]_{air}[/tex] × V × g

0.179 × V + 3179 = 1.29 V

0.179V + 3179 = 1.29V

0.179V- 1.29V = - 3179

1.11V = 3179

On solving , we get

V = 2863 [tex]m^{3[/tex]

Therefore, the volume that the balloon should have is 2863[tex]m^{3}[/tex].

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The magnitude of the magnetic field and the direction of the magnetic field at point P is mathematically given as

B=1.9*10^{-5}T

To determine the magnetic field direction, use the right-hand -rule on the page magnetic field is going.

Generally, the equation for Biot savant law is  mathematically given as

[tex]B=(\frac{u}{4\pi}*{\frac{Ilsin\theta}{r^2})[/tex]

Their net field is

Bn=2B

[tex]Bn=2* B=(\frac{u}{4\pi}*{\frac{Ilsin\theta}{r^2})[/tex]

Hence

[tex]B=(\frac{4*\p *10^{-7}}{4\pi}*{\frac{(30)(2*10^{-3}sin45)}{\sqrt{(3*10^{-2})^2+((3*10^{-2})^2)}/2})[/tex]

B=1.9*10^{-5}T

In conclusion, To determine the magnetic field direction, use the right-hand -rule on the page magnetic field is going.

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Answer:

The magnitude of the magnetic field at the point P is [tex]1.57*10^{-5}T[/tex] and the field is pointing into the page.

Explanation:

The general form of a similar question to this is:

[tex]\vec{B} = \frac{\mu _{0} }{4\pi } * \oint \frac{Id\vec{l} \times \hat{r}}{r^{2} }[/tex]

where [tex]\vec{B}[/tex] is the vector of the Magnetic Field, [tex]\mu _{0}[/tex] is the Free Space Permeability Constant (equal to [tex]4\pi * 10^{-7} \frac{N}{A^2}[/tex]), [tex]I[/tex] is the current, and [tex]r[/tex] is the distance from the segment to the point P. (I will get to the [tex]d\vec{l} \times \hat{r}[/tex] term in a bit)

This equation is fairly complicated. Luckily, it can be simplified by looking at the magnitude and direction separately.

The first thing to simplify is the cross product. Due to the fact that a cross product can be simplified from [tex]\vec{x} \times \vec{y}[/tex] to [tex]xy\sin(\theta)[/tex], where [tex]\theta[/tex] is the angle between the 2 vectors, and [tex]\hat{r}[/tex] is the unit vector of [tex]r[/tex] (i.e. [tex]\hat{r} = \vec{r}/r[/tex]) we can simplify [tex]d\vec{l} \times \hat{r}[/tex] to just [tex]dl \sin(\theta)[/tex].

Next, we will look at the integral. In this scenario, everything will function as a constant, so we can essentially ignore it.

Finally, [tex]\frac{\mu_{0}}{4\pi}[/tex] simplifies down to [tex]10^{-7}[/tex].

This gives us our new equation for the Magnetic Field produced by a single segment at a point:

[tex]B = \frac{Il\sin\theta}{r^{2}}*10^{-7}[/tex]

Now we need to find values for [tex]r[/tex] and [tex]\theta[/tex]. Luckily, we are dealing with a 45-45-90 triangle with sides of [tex]1.5 cm[/tex]. This means the distance [tex]r[/tex] is [tex](1.5\sqrt2)cm[/tex]! Similarly, because it is a 45-45-90 triangle, our [tex]\theta[/tex] is [tex]45\textdegree[/tex]!

Now we can start plugging things in:

[tex]B = \frac{(25A)(2*10^{-3}m)\sin(45\textdegree)}{(1.5\sqrt2*10^{-2}m)^2}*10^{-7}\frac{N}{A^2}[/tex]

[tex]B = 7.86^{-6} \frac{N}{A}[/tex] or [tex]T[/tex]

This is the magnitude due to only one single segment. In order to find the total field, we need to know the direction of the field due to each segment.

Finding the direction is really easy. Just use the right hand rule. Point your thumb in the direction of the current and curl the rest of your fingers around an imaginary pole. The direction your fingers point is the direction of the field. In this case, the field lines due to the segments point into the page in the 4th quadrant (the origin is the bend). This means that at point P, both segments induce the same field in the same direction. Therefore, we can take our value from before and double it, giving us our final answer:

[tex]B = 1.57*10^{-5} T[/tex]; into the page.

Answer:

36 cm

Explanation:

Mass of stick; m1 = 0.20kg at midpoint.

Total length; L=1.0 m

Pivot at 0.40m

Atached mass m2 = 0.50kg

Applying rotational equilibrium we have;

Ʈnet = 0

(m1g) • r1 = (m2g) • r2

(0.2) (0.1m) = (0.5)(x)

x = 0.04m =4cm

measured away from 40cm mark gives a position on the stick of; 40cm - 4cm = 36 cm

The primary means by which heat is transferred through fluids is convection currents (option D).

Convection is the transmission of heat in a fluid by the circulation of currents.

Heat can be transferred by different methods depending on the medium. Fluids like gases and liquids transfer heat through the process of convection.

Therefore, the primary means by which heat is transferred through fluids is convection currents.

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