The kinematic viscosity of oxygen at 40 °C and a pressure of 160 kPa is 0.104 stokes. Determine the dynamic viscosity of the oxygen at this temperature and pressure. (Ro₂ = 0.2598 kPa.m³/kg.K)

​

The magnitude of the displacement of the vector A is determined as 6.2 units.

The magnitude of the displacement of the vector is calculated as follows;

| A | = √[ (x₂ - x₁ )²  +  (y₂ - y₁ )² +  (z₂ - z₁ )²]

where;

The magnitude of vector A is calculated as;

| A | = √[ (2 - 0 )²  +  (3 - 0 )² +  (5 - 0 )²]

| A | = √ (4 + 9 + 25)

| A | = √ ( 38)

| A | = 6.2 units

Learn more about magnitude of vectors here: https://brainly.com/question/3184914

#SPJ1

The complete question is below;

If vector A represents displacement from point O(x1, y1,z1) and P(x2, Yz, Z2). find the magnitude of the displacement of vector A.

Answer:

Alternating current

Explanation:

We know that electric current is defined as the electric charge divided by time.

There are two types of current i.e. direct current (D.C) and alternating current (A.C)

Direct current: The flow of electric charge in one direction is called as direct current. It was produced firstly by Alessandro Volta in 1800. One of the examples of direct current is the battery.

Alternating current: The flow of electric charges that reverses the direction periodically is known as alternating current.

it is a form of mechanical energy, this is not a characteristic of electrical potential energy. Hence option A is correct.

Electrical potential energy is the energy that is held in a system of charges as a result of their arrangements or positions. It is connected to a charge in an electric field and results from the interaction of charges.

The relative locations of the charges and how they interact with the electric field determine the potential energy. Electrical potential energy is not regarded as a type of mechanical energy, though. The energy connected to the motion or location of an object is referred to as mechanical energy.

Both kinetic energy (energy of motion) and potential energy (energy resulting from position or configuration) are included in it; however, electrical potential energy belongs to the potential energy category rather than the mechanical energy category.

To know more about Energy :

https://brainly.com/question/1932868

#SPJ1.

The spring constant of the spring is 20.78 N/m and the velocity of the cart when the cart is first located at x=8.47 cm is -0.082 m/s.

a) To find the spring constant of the spring, we can use the equation for the displacement of a mass undergoing simple harmonic motion on a spring.

x = A cos(ωt)

where x = displacement of the mass from its equilibrium position,

          A = amplitude of the motion, and

          ω = angular frequency of the motion.

Comparing this equation with the given equation, we can see that the amplitude of the motion is A = 12.4 cm = 0.124 m and the angular frequency is ω = 6.35 rad/s.

The equation for the displacement of a mass on a spring undergoing simple harmonic motion can also be written as:

[tex]x=\sqrt{m/k} *cos\omega t[/tex]

where m = mass of the object, and

            k = spring constant.

Comparing this equation with the given equation, we can see that  = [tex]\sqrt{m/k}[/tex] = 0.124 m.

Squaring both sides,

m/k = (0.124 m)² = 0.0154

Therefore, the spring constant of the spring is:

k = m / 0.0154

  = (0.32)/(0.0154)

  = 20.78 N/m

b) To find the velocity of the cart when it is first located at x = 8.47 cm, we need to take the derivative of the displacement equation w.r.t. time:

v = dx/dt

 = d{A cos(ωt)}/dt

 = -Aω sin(ωt)

Substituting the given values, we get:

v = -(0.124 m) * (6.35 rad/s) * sin(6.35t)

When the cart is located at x = 8.47 cm = 0.0847 m, using x = A cos(ωt):

0.0847 m = (0.124 m) * cos(6.35t)

cos(6.35t) = 0.6835

Taking the inverse cosine of both sides gives:

6.35t = 0.824 rad

      t = 0.130 s

Substituting this value of t into the velocity equation gives:

v = -(0.124 m) * (6.35 rad/s) * sin(6.35 * 0.130 s) = -0.082 m/s

Therefore, the velocity of the cart when it is first located at x = 8.47 cm is -0.082 m/s, that is in the negative direction.

Learn more about oscillations here

brainly.com/question/28994371

#SPJ1

Hello!

20c = 0.2€

number coins = 2.6/0.2 = 13

1 coin => 6g

13 coins => 6g x 13 = 78g

The answer is 78 grams.

The required length of L which is the distance from the grating to screen is: 8.696 cm

The event of deviating the wave from the original path of propagating due to obstruction of any obstacle. Diffraction happens near the slit, edges, or corners of the object. Interference differs from the diffraction in such a way that in interference, only some waves are considered.

We are given that:

Grating: n = 3300 lines/cm

The shortest wavelength is: λs = 400 nm

The longest wavelength is: λl = 700nm

The distance limited is: y = 2.15 cm

The expression for separation of slit is given for the second order as,

d sin θ = mλ

Here,

d is spacing,

m is the order.

Calculate the value of spacing.

d = 1/n

d = 1/3300

d = 0.0003030 cm

d = 3030.30 nm

Substituting the value in the above expression for shorter wavelength,

3030.30 sinθ = 2 * 400

sinθ_s = 800/3030.30

sinθ_s = 0.264

θ_s = 15.31°

Substituting the value in the above expression for longer wavelength,

3030.30 sinθ = 2 * 700

sinθ_l = 1400/3030.30

sinθ_l = 0.462

θ_l = 27.52°

Now, for expression for the distance from the grating to screen is calculated as:

L = y/(tan θ_l - tan θ_s)

L = 2.15/(tan 27.52° - tan 15.31)

L = 8.696 cm

Read more about diffraction Grating at: https://brainly.com/question/13104464

#SPJ1

r = √9/2(pg¹/₂) / (P-0)g. The expression is proved as follows:

The following expression:

r = √9/2(pg¹/₂) / (P-0)g

where r is the radius of a cylindrical container filled with a liquid of density ρ, g is the acceleration due to gravity, and P is the pressure at the bottom of the container.

To prove this expression, express the equation for the pressure at a depth h in a fluid:

P = P0 + ρgh

where P0 is the pressure at the surface of the fluid, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the depth of the fluid.

Supposing that the fluid is incompressible and that the pressure at the surface of the fluid is atmospheric pressure, P0 = 0. Rearrange the above equation to solve for h:

h = (P - P0) / (ρg)

Substituting the above expression for h into the formula for the volume V with height h and radius r:

V = πr²h

and simplifying using the expression for h derived above:

V = πr²(P - P0) / (ρg)

Solving for r:

r = √(V / (π(P - P0) / (ρg)))

= √(Vρg / π(P - P0))

Now, the mass of the fluid in the container is given by:

m = ρV

Substituting this expression into the equation for r above, we get:

r = √(mρg / π(P - P0))

Since the density of the fluid is given as ρ and the acceleration due to gravity is g, we can substitute these values to get:

r = √(mg / π(P - P0))

Finally, substitute the expression for P - P0 in terms of h and simplify to get:

r = √9/2(pg¹/₂) / (P-0)g

Therefore, we have proven the given expression for r.

learn more about derivation of fluid pressure: https://brainly.com/question/8033367

#SPJ1

Answer:

gamma rays (or x-rays)

Explanation:

Example when you get x-rays at the dentist and they put the lead vest over you to protect the rays from passing through your body.

Two forces f1=(8i+3j)N and f2=(4i+6j) are acting on 5kg object then  the magnitude of the resultant force is 15 N and the direction of the resultant force is approximately 36.87 degrees from the positive x-axis.

The acceleration of the object in the x-component ([tex]a_x[/tex]) is 2.4  [tex]m/s^{2}[/tex], and the acceleration in the y-component ([tex]a_y[/tex]) is 1.8  [tex]m/s^{2}[/tex].

The magnitude of the acceleration of the object is 3  [tex]m/s^{2}[/tex].

To find the magnitude and direction of the resultant force, we need to add the two given forces together.

Given:

f1 = (8i + 3j) N

f2 = (4i + 6j) N

To find the resultant force ([tex]F_res[/tex]), we simply add the corresponding components:

[tex]F_res[/tex] = f1 + f2

= (8i + 3j) + (4i + 6j)

= (8 + 4)i + (3 + 6)j

= 12i + 9j

The magnitude of the resultant force ([tex]|F_res|[/tex]) can be found using the Pythagorean theorem:

[tex]|F_res|[/tex]= [tex]\sqrt{(12^2) + (9^2)}[/tex]

= [tex]\sqrt{144 + 81}[/tex]

= [tex]\sqrt{225}[/tex]

= 15 N

So, the magnitude of the resultant force is 15 N.

To find the direction of the resultant force, we can use trigonometry. The direction can be represented by the angle θ between the positive x-axis and the resultant force vector. We can calculate θ using the inverse tangent function:

θ = arctan(9/12)

= arctan(3/4)

≈ 36.87 degrees

Therefore, the direction of the resultant force is approximately 36.87 degrees from the positive x-axis.

Now let's calculate the acceleration of the object in the x and y components. We know that force (F) is related to acceleration (a) through Newton's second law:

F = ma

For the x-component:

[tex]F_x[/tex]= 12 N

m = 5 kg

Using  [tex]F_x[/tex]= [tex]ma_x[/tex], we can solve for [tex]a_x[/tex]:

12 N = 5 kg * [tex]a_x[/tex]

[tex]a_x[/tex]= 12 N / 5 kg

[tex]a_x[/tex] = 2.4 [tex]m/s^{2}[/tex]

For the y-component:

[tex]F_y[/tex] = 9 N

m = 5 kg

Using [tex]F_y[/tex] = [tex]ma_y[/tex], we can solve for [tex]a_y[/tex]:

9 N = 5 kg * [tex]a_y[/tex]

[tex]a_y[/tex] = 9 N / 5 kg

[tex]a_y[/tex]= 1.8  [tex]m/s^{2}[/tex]

So, the acceleration of the object in the x-component ([tex]a_x[/tex]) is 2.4  [tex]m/s^{2}[/tex], and the acceleration in the y-component ([tex]a_y[/tex]) is 1.8  [tex]m/s^{2}[/tex].

To find the magnitude of the acceleration (|a|), we can use the Pythagorean theorem:

|a| = [tex]\sqrt{(a_x^2) + (a_y^2)}[/tex]

= [tex]\sqrt{(2.4^2) + (1.8^2}[/tex]

= [tex]\sqrt{5.76 + 3.24}[/tex]

= [tex]\sqrt{9}[/tex]

= 3  [tex]m/s^{2}[/tex]

Therefore, the magnitude of the acceleration of the object is 3  [tex]m/s^{2}[/tex]

For more such information on: force

https://brainly.com/question/25239010

#SPJ11

Conduction and Convection is the two ways by which heat energy can be transmitted.

Heat energy can be transferred by the following ways-

To learn more about heat energy,

https://brainly.com/question/14505067

#SPJ1

The gauge pressure at a depth of 80 cm in oil with specific gravity 0.8 is 6.2784 kPa.

The gauge pressure at a depth in a fluid can be found using the formula, P = ρgh, where gauge pressure is P, density of the fluid is ρ, acceleration due to gravity is g, and depth of the fluid is h. The specific gravity is given to be 0.8 hence, the density of oil is = 0.8 x 1000 kg/m³ = 800 kg/m³. The depth of the oil is given as 80 cm, which is equivalent to 0.8 m. The acceleration due to gravity is approximately 9.81 m/s².

Substituting these values into the formula for gauge pressure, we get,

P = ρgh = (800 kg/m³) x (9.81 m/s²) x (0.8 m) = 6278.4 N/m²

To express the pressure in kPa, we divide by 1000,

P = 6278.4 N/m² ÷ 1000 = 6.2784 kPa

Therefore, the gauge pressure at a depth of 80 cm in the oil with specific gravity 0.8 is 6.2784 kPa.

To know more about gauge pressure, visit,

https://brainly.com/question/30425554

#SPJ1

The final temperature of the mixture formed by adding the water is most likely 30°.

The rule of conservation of energy is demonstrated by the calorimetric principle, which states that the total amount of heat lost by a hot body is equal to the total amount of heat acquired by a cool body.

Heat lost = Heat gain

50 x 4.18 x (T - 10) = 50 x 4.18 x (80 - T)

T - 10 = (80 - T)

T - 10 = 80 - 2T

3T = 90

Therefore, the final temperature of the mixture,

T = 90/3

T = 30°

To learn more about calorimetric principle, click:

https://brainly.com/question/30884598

#SPJ1

Answer:

Hokkaido, Japan

Explanation:

earth quakes are natural there

The acceleration of the body is 4.5 m/s^2.

First, let's convert the initial velocity and final velocity from m/s to km/h:

Initial velocity = 30 m/s = (30/1000) * 3600 = 108 km/h

Final velocity = 80 m/s = (80/1000) * 3600 = 288 km/h

Let the time taken to accelerate to 288 km/h be t1, and the time taken to decelerate from 288 km/h to rest be t2. Since the time spent at constant velocity is twice the time spent accelerating, it is 2t1.

The distance covered during acceleration and deceleration can be calculated using the formula:

distance = (initial velocity * time) + (0.5 * acceleration * time^2)

For acceleration:

distance1 = (108 * t1) + (0.5 * a * t1^2)

For deceleration:

distance2 = (288 * t2) + (0.5 * (-a) * t2^2)

Since the total time taken for the journey is 40, we have:

t1 + 2t1 + t2 = 40

3t1 + t2 = 40

Also, the total distance traveled is given as 2550 km:

distance1 + distance2 = 2550

Substituting the expressions for distance1 and distance2, we get:

(108 * t1) + (0.5 * a * t1^2) + (288 * t2) - (0.5 * a * t2^2) = 2550

Simplifying the above equation:

108t1 + 144t1^2/a + 288t2 - 0.5t2^2a = 2550

Now, we have three equations with three variables (a, t1, t2). We can solve these equations to obtain the value of acceleration (a).

From the first equation, we have:

t2 = 40 - 3t1

Substituting this value of t2 in the equation for distance2, we get:

distance2 = 288(40 - 3t1) - 0.5*a(40 - 3t1)^2

Substituting the values of distance1 and distance2 in the equation for total distance, we get:

(108 * t1) + (0.5 * a * t1^2) + 288(40 - 3t1) - 0.5*a(40 - 3t1)^2 = 2550

Simplifying the above equation and solving for a, we get:

a = 4.5 m/s^2
For more such questions on acceleration ,click on:

https://brainly.com/question/460763

#SPJ11

The statement is true. A stanza, also known as a verse, of 12-bar blues usually consists of four phrases, each phrase consisting of three bars (measures) of music. The 12-bar blues is a standard chord progression commonly used in blues music, and it typically follows an AAB lyrical pattern where the first and second phrases are identical and the third phrase provides a contrasting resolution. The fourth phrase is often used as a turnaround, leading back to the beginning of the progression for the next stanza. This structure creates a cyclical and repetitive form that is characteristic of the blues genre.

here are a total of two electrons being shared between the atoms in the H-H bond diagram.

In the bond diagram H-H, the symbol "H" represents a hydrogen atom. Hydrogen is an element that exists as diatomic molecules, meaning it naturally forms pairs of atoms. In the case of H-H, two hydrogen atoms are bonded together.

Each hydrogen atom contributes one electron to the shared pair in the bond. Therefore, in the H-H bond diagram, there is a single pair of electrons being shared between the two hydrogen atoms.

Since each pair of electrons consists of two electrons, we can say that there are a total of two electrons being shared between the atoms in the H-H bond diagram. It is important to note that hydrogen forms a single covalent bond with another hydrogen atom, resulting in a stable H2 molecule.

For more such questions on electrons

https://brainly.com/question/860094

#SPJ11

The pattern of planetary speeds and distance does not support the amateur astronomer's estimated distance of the asteroid being 13.5 AU from the Sun.

According to Kepler's laws of planetary motion, the speed of a planet or asteroid in its orbit is inversely proportional to its distance from the Sun. This means that as the distance from the Sun increases, the speed of the object should decrease.

Looking at the known planets in our solar system, we observe that the outer planets, such as Neptune and Uranus, have slower speeds compared to the inner planets, such as Mercury and Venus. This is consistent with the inverse relationship between speed and distance. However, the estimated speed of the discovered asteroid, 8 km/sec, is relatively high.

Given that the asteroid is moving at such a high speed, it suggests that its distance from the Sun should be closer, rather than at 13.5 AU. At that distance, the asteroid would be expected to have a slower speed.

Therefore, based on the established pattern of planetary speeds and distance, the estimated distance of 13.5 AU for the asteroid does not align with the expected speed. It is more likely that the asteroid is closer to the Sun than the estimated distance, possibly within the inner regions of the solar system. Further observations and calculations would be necessary to accurately determine its true distance from the Sun.

For more such questions on planetary ,

https://brainly.com/question/28610721

#SPJ11

Answer:

The answer is flint glass.

Explanation:

(a) Let's use the law of conservation of mechanical energy to determine the speed with which the other end of the rod hits the floor. When the rod is released, it begins to rotate around its center of gravity and falls to the floor. At the moment of release, the rod has no kinetic energy or potential energy, but it has potential energy when it reaches the floor. The energy is conserved, so we can equate the initial potential energy to the final kinetic energy.

The initial potential energy of the rod is given by:

U_i = mgh

where m is the mass of the rod, g is the acceleration due to gravity, and h is the height of the center of gravity above the floor. Since the rod is vertical, h = L/2. The mass of the rod can be calculated using its density ρ and cross-sectional area A:

m = ρAL

The final kinetic energy of the rod is given by:

K_f = (1/2)Iω^2 + (1/2)mv^2

where I is the moment of inertia of the rod with respect to its center of gravity, ω is the angular velocity of the rod, and v is the linear velocity of the center of gravity. At the moment when the rod hits the floor, the angular velocity is zero, so the first term in the above equation is zero. We can simplify the equation to:

K_f = (1/2)mv^2

We can equate the initial potential energy and final kinetic energy to get:

mgh = (1/2)mv^2

Solving for v, we get:

v = sqrt(2gh)

Substituting the given values, we get:

v = sqrt(2gL/2) = sqrt(gL/2)

Now, we can substitute the values of g and L to get:

v = sqrt(9.81 m/s^2 x 1 m/2) = sqrt(4.905) m/s

Therefore, the other end of the rod hits the floor with a speed of approximately 2.216 m/s.

(b) If the length of the rod were 100 m instead of 1 m, the speed with which the end hits the floor would increase significantly. The potential energy of the rod when it is released is proportional to its height above the floor, so when the length of the rod is increased by a factor of 100, the potential energy increases by a factor of 100 as well. Therefore, the final speed of the end hitting the floor would be:

v' = sqrt(2gh') = sqrt(2g(100L)/2) = sqrt(100gL/2) = 10sqrt(gL/2)

Substituting the given values, we get:

v' = 10sqrt(9.81 m/s^2 x 100 m/2) = 10sqrt(490.5) m/s

Therefore, the end of the 100 m tall object would hit the floor with a speed of approximately 70.0 m/s, which is a significant increase compared to the initial speed of the 1 m rod.

The tension on the rope at the end where the painter is standing is 294 N, and the tension on the other rope is 196 N.

To find the tensions on the ropes, we can analyze the forces acting on the painter and the plank.

Considering the equilibrium of the system, the sum of the forces acting vertically must be zero. The weight of the painter acts downward with a force of 50 kg * 9.8 m/s^2 (acceleration due to gravity), which equals 490 N.

Let's denote the tension in the rope at the end where the painter is standing as T1 and the tension in the other rope as T2.

Since the plank is at equilibrium, the total upward force must be equal to the total downward force. At the end where the painter is standing, there are two forces acting upward: T1 and T2. Since the painter is 2 m away from this end, the plank experiences a torque due to the weight of the painter.

To calculate the torque, we use the formula: Torque = Force * Distance. The torque due to the painter is (490 N) * (2 m) = 980 Nm.

Since the plank is in equilibrium, the torques acting on it must balance. The torque due to T1 is 0 Nm (as it acts at the pivot point), and the torque due to T2 is (T2) * (5 m) = 5T2 Nm.

Therefore, 5T2 - 980 Nm = 0, which gives T2 = 196 N.

Now, to find T1, we can use the equation: T1 + T2 = Total vertical force. Thus, T1 + 196 N = 490 N, which gives T1 = 294 N.

Therefore, the tension on the rope at the end where the painter is standing is 294 N, and the tension on the other rope is 196 N.

For more such questions on tension

https://brainly.com/question/24994188

#SPJ11

To obtain the type, orientation, location and magnification of the image, we shall first obtain the location (i.e distance) of the image from the mirror. Details below:

The location i.e distance of the image can be obtained as follow:

1/f = 1/v + 1/u

Rearrange

1/v = 1/f - 1/u

v = (f × u) / (u - f)

v = (12 × 24) / (24 - 12)

v = 288 / 12

v = 24 cm

Thus, the the location of the image is 24 cm

Since the location of the image is positive (i.e 24 cm). Thus,

Now, we shall obtain the magnification of the image. Details below:

Magnification = image distance (v) / object distance (u)

Magnification = 24 / 24

Magnification = 1

Learn more about distance:

https://brainly.com/question/13152512

#SPJ1

The energy level from which is emitted is n = 6

The frequency is[tex]7.3 * 10^14[/tex] Hz

The Rydberg equation is a mathematical formula that relates the wavelengths of light emitted by an atom to the energy levels of its electrons.

Using the Rydberg equation;

1/λ= RH (1/[tex]n_{2}^2[/tex] - 1/[tex]n_{1} ^2[/tex])

1/[tex]410.2 * 10^-9[/tex] = [tex]1.097 * 10^7[/tex](1/[tex]2^2[/tex] - 1/  /[tex]n_{1} ^2[/tex])

1/[tex]4.102 * 10^-7[/tex] = [tex]1.097 * 10^7[/tex](1/4 - 1/[tex]n_{1} ^2[/tex])

1/[tex]4.102 * 10^-7[/tex] * 1/ [tex]1.097 * 10^7[/tex] = (1/4 - 1/[tex]n_{1} ^2[/tex])

0.22 = 0.25 -  1/[tex]n_{1} ^2[/tex]

0.22 - 0.25 = -  1/[tex]n_{1} ^2[/tex]

-0.03 = -  1//[tex]n_{1} ^2[/tex]

[tex]n_{1}[/tex] = 6

Using;

f = c/λ

[tex]3 * 10^8/4.102 * 10^-7 \\f = 7.3 * 10^14 Hz[/tex]

Learn more about Rydberg equation:https://brainly.com/question/22916962

#SPJ1

The weight of the 100 kg object on the surface of the planet is approximately 8.9 × 10¹² Newtons.

To calculate the weight of a 100 kg object on the surface of a planet, we need to use the formula for gravitational force:

F = (G * M * m) / r²

Where:

F is the gravitational force (weight)

G is the gravitational constant (approximately 6.67430 × 10⁻¹¹ N m²/kg²)

M is the mass of the planet (4.8 × 10²⁴ kg)

m is the mass of the object (100 kg)

r is the radius of the planet (diameter / 2)

Given that the diameter of the planet is 12,000 km, we can find the radius by dividing it by 2:

r = 12,000 km / 2 = 6,000 km = 6,000,000 m

Now, we can substitute the values into the formula:

F = (6.67430 × 10⁻¹¹ N m²/kg² * 4.8 × 10²⁴ kg * 100 kg) / (6,000,000 m)²

Simplifying the expression:

F = (6.67430 × 10⁻¹¹ N m²/kg² * 4.8 × 10²⁶ kg) / 36,000,000,000 m²

F ≈ 8.9 × 10¹² N

Therefore, the weight of the 100 kg object on the surface of the planet is approximately 8.9 × 10¹² Newtons.

For more such questions on weight visit:

https://brainly.com/question/86444

#SPJ11

a) The value of the vector A + B is i + 2j + k and |A + B| is √6 units.

Given:

A = i + j

B = j + k

A + B = i + j + j + k

= i + 2j + k

|A + B| is the magnitude of the vectors A and B

|A + B| = √(1² + 2² + 1²)

= √(1 + 4 +1)

= √6

b) The vector 3A - 2B has the value of 3i + j -2k

Given:

A = i + j

3A = 3i + 3j

B = j + k

2B = 2j + 2k

3A - 2B = 3i + 3j - 2j - 2k

= 3i + j -2k

c) The scalar product of the vector that is A • B is equal to 3 units

The scalar product is calculated as follows:

A • B = i + j • j + k

= 1 + 1 * 1 + 1

= 1 + 1 + 1

= 3 units

d) The vector product or A x B is i - j + k and the magnitude of the same is √3 units.

                   i          j        k

A                 1          1        0

B                 0         1         1

The vector product is calculated as follows:

A x B = (1 * 1 - 1 * 0) i + (0 * 0 - 1 * 0) j + (1 * 1 - 0 * 1) k

= (1 - 0) i + (0 - 1) j + (1 - 0) k

= i - j + k

| A x B | = √(1² + (-1)² + 1²

= √1 + 1 + 1

= √3 units

Learn more about Vectors:

https://brainly.com/question/30394406

#SPJ1

The maximum angle at which an object will not slip on an incline can be calculated using the coefficient of friction (μ).

When an object is on an inclined plane, there are two main forces acting on it: the gravitational force pulling it downward (mg) and the normal force (N) exerted by the inclined plane perpendicular to its surface. Additionally, there is a frictional force (F) acting parallel to the surface of the incline.

To prevent slipping, the frictional force must be equal to or greater than the force component pulling the object down the incline. This force component is given by the equation F = mg sin(θ), where θ is the angle of inclination.

The maximum frictional force that can be exerted between two surfaces is given by the equation F = μN, where μ is the coefficient of friction.

For an object not to slip, the maximum frictional force (F) must be equal to or greater than the force component pulling the object down the incline (mg sin(θ)). Therefore, we have:

F ≥ mg sin(θ)

Substituting F = μN, we get:

μN ≥ mg sin(θ)

Since N = mg cos(θ) (the normal force is equal to the component of the gravitational force perpendicular to the incline):

μmg cos(θ) ≥ mg sin(θ)

μ cos(θ) ≥ sin(θ)

Now, divide both sides of the equation by cos(θ):

μ ≥ tan(θ)

Taking the inverse tangent (arctan) of both sides, we get:

θ ≤ arctan(μ)

Therefore, the maximum angle at which an object will not slip on an incline is given by θ = arctan(μ).

More on inclined planes can be found here: https://brainly.com/question/29360090

#SPJ1

1. The electric field pattern due to charged sphere A can be represented by lines radiating outward from the sphere.

2. The magnitude of the charge on sphere A is approximately 0.0833 Coulombs.

3. The electrostatic force experienced by sphere B when placed at point P is approximately 2.675 x 10^-4 Newtons.

1. These lines should be evenly spaced and symmetric around the sphere, indicating a radial field pattern. Since the electric field at point P is directed towards sphere A, the field lines should point inward towards the sphere. Thus, the electric field pattern would resemble a series of concentric circles with lines converging towards the center of sphere A.

2. To calculate the magnitude of the charge on sphere A, we can use the formula for the electric field strength (E) due to a point charge:

E = k * (Q / r^2)

where k is the electrostatic constant (approximately 9 x 10^9 N m^2/C^2), Q is the charge on the sphere, and r is the distance from the sphere to the point P.

From the given information, we have E = 3 x 10^7 N/C and r = 0.5 m. Plugging these values into the formula and solving for Q:

3 x 10^7 N/C = (9 x 10^9 N m^2/C^2) * (Q / (0.5 m)^2)

Simplifying the equation, we find:

Q = (3 x 10^7 N/C) * (0.5 m)^2 / (9 x 10^9 N m^2/C^2)

Q ≈ 0.0833 C (Coulombs)

Therefore, the magnitude of the charge on sphere A is approximately 0.0833 Coulombs.

3. When sphere E, which has an excess of 105 electrons, is placed at point P, it will experience an electrostatic force due to the interaction with sphere A. The electrostatic force between two charges can be calculated using Coulomb's law:

F = k * (|q1| * |q2|) / r^2

where k is the electrostatic constant, q1 and q2 are the charges on the spheres, and r is the distance between them.

Since each electron carries a charge of approximately -1.6 x 10^-19 C, the excess charge on sphere E is:

q2 = 105 electrons * (-1.6 x 10^-19 C/electron)

Plugging in the values and the given distance of 0.5 m, we have:

F = (9 x 10^9 N m^2/C^2) * (|0.0833 C| * |-1.6 x 10^-19 C|) / (0.5 m)^2

Simplifying the equation, we find:

F ≈ 2.675 x 10^-4 N (Newtons)

Therefore, the electrostatic force experienced by sphere E when placed at point P is approximately 2.675 x 10^-4 Newtons.

For more such questions on electrostatic force

https://brainly.com/question/17692887

#SPJ11