can some one help me answer this qustion

Answer:

tube (sufficiently) long / not too short.

To move with the same acceleration as the 10kg box, the 50kg box needs higher net force.

The term "net force" refers to the combined effects of all the forces exerted on a moving body, including gravitational, frictional, and normal forces. FNet equals Fa, Fg, Ff, and FN.

Newton's Second Law of Motion states that

A mass-proportional force is needed to accelerate an item.

The following formula determines the net force necessary to move an item at a given acceleration:

net force = mass x acceleration

The 50kg box and the 10kg box both accelerate at the same rate, but the 50kg box's net force need is more than the 10kg box's because of its heavier mass.

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The maximum current in the circuit is 17.46 A.

To find the maximum current in the circuit, we need to find the time at which the current reaches its maximum value. This occurs when the derivative of the current with respect to time is zero:

di/dt = (V/L) e^(-Rt/L) = 0

Solving for t, we get:

t = (L/R) ln(V/I)

where I is the maximum current.

Substituting the given values, we get:

t = (3.5/6.2) ln(38.2/I) = 0.3

Solving for I, we get:

I = 17.46 A

Inductance is a property of an electrical circuit that describes the ability of a component to store energy in a magnetic field. It is measured in henries (H) and is denoted by the letter L. Inductors are components that are specifically designed to have high inductance.

If the current is changing, then the magnetic field also changes, and this change induces a voltage in nearby conductors. This is known as electromagnetic induction, and it is the basis for many important electrical devices, including transformers and electric motors. The inductance of a component depends on several factors, including the number of turns in the coil, the size of the coil, and the material from which the coil is made.

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Para encontrar el punto donde están enterradas las llaves del Porsche nuevo, debemos sumar los tres desplazamientos dados en el problema.

Primero, el desplazamiento de A tiene una magnitud de 72.4 m y una dirección de 32.0° al este del norte. Usando trigonometría, podemos descomponer este desplazamiento en sus componentes vertical y horizontal: Componente vertical = 72.4 m sin(32.0°) ≈ 38.9 m hacia el norte. Componente horizontal = 72.4 m cos(32.0°) ≈ 61.5 m hacia el este. Por lo tanto, el desplazamiento de A se puede representar como un vector de 61.5 m hacia el este y 38.9 m hacia el norte. Segundo, el desplazamiento de B tiene una magnitud de 57.3 m y una dirección de 36.0° al sur del oeste. De manera similar, podemos descomponer este desplazamiento en sus componentes vertical y horizontal: Componente vertical = 57.3 m sin(36.0°) ≈ 34.4 m hacia el sur. Componente horizontal = 57.3 m cos(36.0°) ≈ 46.0 m hacia el oeste. Por lo tanto, el desplazamiento de B se puede representar como un vector de 46.0 m hacia el oeste y 34.4 m hacia el sur. Finalmente, el desplazamiento de C tiene una magnitud de 17.8 m hacia el sur. Este desplazamiento solo tiene una componente vertical. Ahora, podemos sumar los tres vectores de desplazamiento para obtener la resultante. Podemos hacer esto sumando las componentes horizontal y vertical por separado: Componente horizontal total = 61.5 m - 46.0 m = 15.5 m hacia el este

Componente vertical total = 38.9 m - 34.4 m - 17.8 m = -13.3 m hacia el norte. La magnitud de la resultante se puede encontrar usando el teorema de Pitágoras: |magnitud resultante| = sqrt((15.5 m)^2 + (-13.3 m)^2) ≈ 20.2 m. Por lo tanto, el concursante ganador debería ir en una dirección de aproximadamente 29.7° al este del norte para encontrar las llaves del Porsche nuevo.

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I agree with the student's statement that if we look at a star's absorption line spectrum and see that it has many lines at the blue end of the spectrum, the star must be hot because the blue lines are higher energy lines.

This is because hotter stars have more energy than cooler ones, which means that their atoms are more excited and have a higher probability of emitting photons of higher energy levels. When a star emits light, it passes through a cloud of gas before reaching Earth, and as the light passes through this cloud, it interacts with the gas atoms. The photons of light with just the right amount of energy will be absorbed by the atoms, causing the electrons to jump up to higher energy levels, and this is what creates the absorption lines in the spectrum. The amount and position of these lines can provide useful information about the chemical composition, temperature, and other properties of the star.

As a result, a star's temperature is proportional to the energy of the photons it emits, which are responsible for creating the lines in its absorption spectrum. Since blue lines have higher energy than red lines, a star with many blue lines will be hotter than one with more red lines. In conclusion, the student's statement is correct because the blue lines represent higher energy levels, which are found in hotter stars, and thus, a star with many blue lines in its absorption spectrum will be hotter.

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The component of the force acting in the direction of an object's motion determines how much force is doing work on that object. The "parallel component" of the force is referred to as this.

A force that is applied perpendicular to an object's motion has no effect since it does not add to the object's kinetic energy.

It follows that the force exerted on the item will increase if the applied force's direction is adjusted to make it more parallel to the direction of motion.

The amount of force accomplishing work will decrease, on the other hand, if the direction of the applied force becomes increasingly perpendicular to the direction of motion.

Take the movement of a box across a rough surface as an illustration.

Only a fraction of the force will be parallel to the surface of the force delivered at a 45-degree angle to the surface, contributing to the motion of the box.

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The amount of non-conservative work done on the sofa is 3833.83 Joules .

The total work done by the wave is expressed as;

Workdone = Potential energy + Kinetic energy

Workdone = mgh + 1/2mv²

m is the mass = 77kg

g is the acceleration due to gravity = 9.8m/s²

v is the velocity = 8.2m/s

h is the height = 1.65m

Substitute into the formula;

Workdone = 77(9.8) (1.65) + 1/2(77)8.2²

Workdone = 1245.09 + 2588.74

Workdone = 3833.83 Joules

It is a scalar quantity that depends on both the mass and velocity of an object. The formula for calculating kinetic energy is KE = 0.5 * m * v^2, where KE is the kinetic energy, m is the mass of the object, and v is its velocity.

When an object is in motion, it possesses kinetic energy because it has the ability to do work on other objects when it interacts with them. For example, a moving ball has the potential to do work when it collides with another ball, causing it to move and potentially change its direction or speed.

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The estimated terminal speed of the wooden sphere falling through air is approximately 8.68 m/s.

To estimate the terminal speed of the wooden sphere falling through air, we can use the following equation:

[tex]V_{terminal}[/tex] = [tex](2mg) / (p_{air} \times Cd \times A \times v^2)[/tex]

Where:

[tex]V_{terminal}[/tex] is the terminal velocity (m/s)

m is the mass of the sphere (kg)

g is the acceleration due to gravity (9.81 m/[tex]s^2[/tex])

[tex]p_{air}[/tex] is the density of air (1.20 kg/[tex]m^3[/tex])

[tex]C_d[/tex] is the drag coefficient (0.500)

A is the cross-sectional area of the sphere ([tex]m^2[/tex])

v is the velocity of the sphere relative to the air (m/s)

First, we need to calculate the mass of the sphere:

[tex]m = (4/3) \times \pi \times r^3 \times p[/tex]

where:

r is the radius of the sphere (m)

ρ is the density of the sphere (kg/[tex]m^3[/tex])

Substituting the given values, we get:

[tex]m = (4/3) \times \pi \times (0.0850 m)^3 \times 830 kg/m^3\\m = 0.980 kg[/tex]

Next, we need to calculate the cross-sectional area of the sphere:

[tex]A = \pi \times r^2\\A = \pi \times (0.0850 m)^2\\A = 0.0228 m^2[/tex]

Now, we can substitute the values into the equation for terminal velocity and solve for [tex]V_{terminal}[/tex] :

[tex]V_{terminal}[/tex] = [tex](2mg) / (p_{air} \times Cd \times A \times v^2)[/tex]

[tex]V_{terminal}[/tex] =[tex](2 \times 0.980 kg \times 9.81 m/s^2) / (1.20 kg/m^3 \times 0.500 \times 0.0228 m^2 \times v^2)[/tex]

[tex]V_{terminal}[/tex] = 8.68 m/s

Therefore, the estimated terminal speed of the wooden sphere falling through air is approximately 8.68 m/s.

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To produce a current in a circuit without a voltage source, it is necessary to induce a voltage in the circuit by changing the magnetic field passing through it.

This is achieved through a process called electromagnetic induction. According to Faraday's law of electromagnetic induction, a voltage is induced in a circuit when there is a change in the magnetic flux through the circuit. To meet this condition, there are three basic methods: Moving a magnet relative to a coil of wire: When a magnet is moved close to a coil of wire or away from it, the magnetic flux through the coil changes and induces a voltage in the coil. This is the basic principle behind generators. Changing the current in a nearby coil: When the current in a coil of wire is changed, the magnetic field surrounding the coil changes, inducing a voltage in a nearby coil of wire. This is the basic principle behind transformers. Moving a coil of wire in a magnetic field: When a coil of wire is moved in a magnetic field, the magnetic flux through the coil changes, inducing a voltage in the coil. This is the basic principle behind electric motors. By using one of these methods, it is possible to produce a current in a circuit without a voltage source.

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When there is zero voltage across an ideal photocell, the amount of current that flows from the photocell is zero.

What is a photocell? A photocell is a transducer that converts light energy into electrical energy. It is also known as a photoresistor or light-dependent resistor (LDR). It is a sensor that detects light and converts it into electricity.

A photocell is a component that senses light levels and reacts to them. It is a semiconductor device that has an electrical resistance that changes depending on the amount of light it receives.

The amount of light received by a photocell is proportional to the current generated. As the light intensity decreases, the resistance of the cell increases.

The current through the circuit and the voltage across the circuit decrease when the resistance of the cell increases.The current that flows from an ideal photocell when there is zero voltage across it is zero.

The photocell produces a current proportional to the amount of light it receives. As a result, the ideal photocell has zero current when there is zero voltage across it. The photoelectric effect is responsible for the current generated by a photocell.

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The volumetric strain rate is zero, the vorticity is -1/2μ (∂p/∂x) y, the rate of angular deformation is 1/2μ (∂p/∂x) y, and the shear stress at the plate surface is -1/2 (∂p/∂x) [tex]h^2[/tex].

Given:

x-velocity: u = 1/2μ (∂p/∂x) ([tex]y^2 - h^2[/tex])

y-velocity: υ = 0 (no variation in y-direction)

where,

μ = dynamic viscosity

p = pressure

x, y = coordinates

h = distance between the plates

To determine the volumetric strain rate, we can start by considering the continuity equation for incompressible flow, which states that the product of velocity and cross-sectional area is constant:

u × (h-y) = Q/A

where A is the cross-sectional area and Q is the volumetric flow rate.

Taking the derivative of both sides with respect to time and simplifying, we get:

dQ/dt = -u × dA/dy

Since the y-velocity is zero, we have dA/dy = 0, so:

dQ/dt = 0

This means that the volumetric flow rate is constant and there is no change in volume with time. Therefore, the volumetric strain rate is zero.

The velocity vector's curl is used to define the vorticity.

ω = ∇ x v

where ∇ is the del operator. For two-dimensional flow, the vorticity is a scalar and can be expressed as:

ω = (∂υ/∂x) - (∂u/∂y)

Substituting the given values for u and υ, we get

ω = 0 - (∂/∂y)[1/2μ (∂p/∂x) ([tex]y^2 - h^2[/tex])]

Simplifying and integrating with respect to y, we get:

ω = -1/2μ (∂p/∂x) y

The formula for angular deformation rate is:

D = (∂u/∂y + ∂υ/∂x) = ∂u/∂y

Substituting the given value for u, we get:

D = (∂/∂y)[1/2μ (∂p/∂x) [tex](y^2 - h^2)[/tex]]

Simplifying and integrating with respect to y, we get:

D = 1/2μ (∂p/∂x) y

To find the shear stress at the plate surface, we can use the following relation:

τ = μ (∂u/∂y)|y=h

Substituting the given value for u, we get:

τ = μ (∂/∂y)[1/2μ (∂p/∂x) ([tex]y^2 - h^2[/tex])]|y=h

Simplifying, we get:

τ = -1/2 (∂p/∂x) [tex]h^2[/tex]

Therefore, the volumetric strain rate is zero, the vorticity is -1/2μ (∂p/∂x) y, the rate of angular deformation is 1/2μ (∂p/∂x) y, and the shear stress at the plate surface is -1/2 (∂p/∂x) [tex]h^2[/tex].

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The labels for vectors A, B, and C ought to be determined by their magnitudes and directions. It is essential to keep track of their angles in relation to the +x axis.

We need to use trigonometry to figure out the y and x-components of each vector in order to find Ay, Ay, B., B, C, and C. The magnitude of the vector is divided by the cosine of its angle with the +x-axis to get the y-component, and the magnitude of the vector is divided by the sine of its angle with the +x-axis to get the x-component.

The Pythagorean theorem can be used to determine the net force. We really want to add the x and y-parts of the vectors to acquire the resultant vector. The Pythagorean theorem can then be used to determine the magnitude of the net force.

In conclusion, we can use the Pythagorean theorem to determine the net force and trigonometry to determine the components of each vector.

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A uniform stick has length l, The combined moment of inertia with mass M at one end of the rod is  I₀ + M(L² ÷ 4).

The stick is I₀. The particle is MR² about the point of rotation but R = 1/2 the stick length so for the particle,

I = M × (L ÷ 2)²

I = M × L² × (1 ÷ 2)²

I = (1/4) × M × L²

Therefore, The total I is the sum of the separate is I₀ + (1/4) M L².

Then the combined moment of inertia with mass M at one end of the rod is:

I₀ = (mL²) ÷ 12

I = (mL²) ÷ 12  + M(L ÷ 2)²

I = I₀ + M(L ÷ 2)²

I = I₀ + M(L² ÷ 4)

Therefore, the combined moment of inertia with mass M at one end of the rod is  I₀ + M(L² ÷ 4).

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Answer:

m g H = 1/2 m v^2     conservation of energy

v = (2 g H)^1/2 = (2 * 9.8 * .2)^1/2 = 1.98 m/s    (call it 2 m/s)

Total momentum of people

N m v = 6E9 * 72 * 2 = 8.6E11 kg m/s       momentum of people

M V = N m v        to get recoil speed of people (conservation momentum)

V = N m v / M = 8.6E11 / 6.0E24 = 1.4E-13

The speed  of the earth would be less than 1/trillionth m/s

The estimated recoil speed of the earth is -1.44 x 10-14 m/s.

First, we need to calculate the total mass of all the people jumping on the earth's surface. This can be done by multiplying the average mass of a person by the total number of people:

Mass of all people = (72 kg)(6 x 109) = 4.32 x 1011 kg

Next, we need to calculate the total momentum of all the people jumping. This can be done by multiplying the total mass of all the people by the distance they jump:

Momentum of all people = (4.32 x 1011 kg)(0.2 m) = 8.64 x 1010 kg m/s

Now, we can use the law of conservation of momentum to find the recoil speed of the earth.

This law states that the total momentum before an event is equal to the total momentum after an event. Therefore, the momentum of the earth before the jump is equal to the negative of the momentum of all the people after the jump:

Momentum of earth = -Momentum of all people = -8.64 x 1010 kg m/s

Finally, we can use the formula for momentum (p = mv) to find the recoil speed of the earth:

v = p/m = (-8.64 x 1010 kg m/s)/(6 x 1024 kg) = -1.44 x 10-14 m/s

Therefore, the estimated recoil speed of the earth is -1.44 x 10-14 m/s.

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Answer:

7/20

Explanation:

0.35 as a fraction =35/100

35/100 can b divided by 5 so =7/20

0.350 simplified as a fraction is 7/20

Answer:

7/20

Explanation:

Electric potential in y direction (a) will be constant and in x direction (b) will decrease as you move in direction of the electric field.

The electric field E in a region is uniform if it is the same at all points. Specifically, if E has a magnitude of 5 V/m and points in the x direction, then we can say the following about the behavior of the electric potential:

a) In the y direction, the electric potential will be constant. This is because the electric field is perpendicular to the y direction, and therefore does not affect the electric potential in that direction.

b) In the x direction, the electric potential will decrease as you move in the direction of the electric field.

This is because the electric field is parallel to the x direction, and therefore affects the electric potential in that direction. Specifically, the electric potential will decrease by 5 V for every meter you move in the x direction.

To summarize, the electric potential will be constant in the y direction, and will decrease in the x direction as you move in the direction of the electric field. This is due to the fact that the electric field is uniform and points in the x direction.

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The work W done from x = 5 m to x = 10 m by the one-dimensional force depicted in the graph is 250 J

The work done by the force is the product of the force and distance traveled.

The product of the force and distance traveled is the sum of the area of the two triangles that are formed from x = 5 to x = 10

The area of the first triangle = 1/2 * 100 * 1

The area of the first triangle = 50 J

The area of the second triangle = 1/2 * √(100² + 1²) * 4

The area of the second triangle = 0.5 * √10001 * 4

The area of the second triangle = 200 J

Therefore, the work done = 200 + 50 J

Work done = 250 J

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1. C. Mass and speed

2. B. Speed

3. B. Speed

4. C. 5.7 * 10^5 J

5. C. 71 km/h

The acceleration due to gravity at the surface of the planet would be one-twelfth (1/12) of the acceleration due to gravity at the surface of the Earth.

The acceleration due to gravity at the surface of a planet is given by the formula:

g = G * M / R^2

Where:

g is the acceleration due to gravity

G is the gravitational constant

M is the mass of the planet

R is the radius of the planet

we are given that the planet has twice the Earth's radius (2R) and one-third of its mass (1/3M).

now, the acceleration due to gravity at the surface of the planet would be:

g = G * (1/3M) / (2R)^2

= G * (1/3M) / 4R^2

= (1/12) * (G * M / R^2)

= (1/12) * gEarth

where gEarth is the acceleration due to gravity at the surface of the Earth.

Hence, the acceleration due to gravity at the surface of the planet would be one-twelfth (1/12) of the acceleration due to gravity at the surface of the Earth.

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1. The horizontal component of the force on the box, given that at force of 18 N was applied at angle of 34° to the horizontal is 15 N

2. The vertical component of the force on the box is 10 N

From the question given above, the following data were obtained:

The horizontal component of the force can be obtained as illustrated below:

Horizontal component of force (Fx) = F × Cosθ

Horizontal component of force (Fx) = 18 × Cos 34

Horizontal component of force (Fx) = 15 N

From the question given above, the following data were obtained:

The vertical component of the force can be obtained as illustrated below

Vertical component of force (Fy) = u × Sine θ

Vertical component of force (Fy) = 18 × Sine 34

Vertical component of force (Fy) = 10 N

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(a) Increasing the reheat in a simple, ideal Rankine cycle with a constant mass flow rate will result in an increase in pump power input. (b) Increasing the reheat in a simple, ideal Rankine cycle with a constant mass flow rate will result in a decrease in turbine power output.
(c) Heat input required increases due to the addition of reheat stages.
(d) Waste heat rejected increases due to the additional heat input required for reheating.
(e) Thermal efficiency slightly decreases due to the lower steam temperature after reheating.
(f) Steam quality at the turbine exit decreases slightly due to the lower steam temperature after reheating.

The Rankine cycle or Rankine Vapor Cycle is the process widely used by power plants such as coal-fired power plants or nuclear reactors. In this mechanism, a fuel is used to produce heat within a boiler, converting water into steam which then expands through a turbine producing useful work.

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The correct option is C.In the excerpt, Mowgli begins to learn the ways of men, forgetting the ways of the jungle, beginning to learn the ways of men, and despising his previous life and family.

Mowgli struggles with his in-betweenness, his liminal status, his sense of belonging to two worlds. He loves the jungle but despairs being kicked out of the pack. He rues the fact that he cannot smell as well as the animals can, that he does not know all the stories of the jungle, and that he does not participate in the Time of New Talk.

Conversely, while he likes Messua, he hates the greedy and superstitious villagers as well as many of their customs, and chafes at life in the village. Thus, Mowgli's identity takes a long time to develop because he is constantly torn between these two worlds. He chooses the life of man at the end.Thus,the correct option is C.

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Question:

How does Mowgli develop in the excerpt?

a)Mowgli becomes fearful of Messua.

b)Mowgli forgets the ways of the jungle.

c) Mowgli begins to learn the ways of men.

d) Mowgli despises his previous life and family.

The steam engine moves a piston back and forth inside a cylinder using the force created by the pressure of the steam. A connecting rod and crank can convert this pushing force into a rotational force for wo

Because electric and diesel locomotives are faster, more effective, and simpler to operate, steam locomotives are no longer utilized to transport people or goods. The locomotives that are still in operation are historical artifacts from the 1800s that serve as a great reminder of how far we've come.

Simply explained, steam engines generate heat energy by boiling water and producing steam using fire and coal (chemical energy). This heat energy is then used to push the cylinder and piston, which in turn moves the wheels (kinetic).

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Answer: The difference between lava and magma is if they have breached the surface yet. If the molten rock is still inside the earth, it is considered magma. once the volcano or opening erupts and the molten rock is on the surface, it is lava.

250N   is the amount of force required to stretch the same material from 20m to 20.05m​

A force is an effect in physics that causes the motion of a mass object to alter its velocity (e.g., moving from a state of rest), i.e., to accelerate. It can be a shove or a draw, with magnitude and direction always present, rendering it a vector quantity. It is measured in newtons (N) and is denoted by the sign F. (formerly P).

Newton's second law, in its initial version, says that the total force operating on an object is equivalent to the rate at which its momentum varies with time.

Original length = 20m

first new length = 20.01m

first increase in length = 20.01m - 20m = 0.01m

Second new length = 20.05m

second increase in length = 20.05 - 20m = 0.05m

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Full Question: If a force of 50N stretches a wire from 20m to 20.01m, what is the amount of force required to stretch the same material from 20m to 20.05m?

A. 250N

B. 200N

C. 100N

D. 50N

The magnitude of accelration is 0.23 m/s^2 and the distance is 8.7 m

final speed , v = 2 m/s

time taken , t = 8.6 s

a)

Let the magnitude of accelartion be a

v = u + a * t

2 = 0 + a * 8.6

solving for a

a = 0.23 m/s^2

b)

The distance travelled in this time , s = v^2 /2a

s = 2^2 /( 2 * 0.23) m

s = 8.7 m

Magnitude refers to the size or extent of something, and it is often used in physics and mathematics to describe the strength or intensity of a physical quantity or phenomenon. Magnitude can be measured using various units, depending on the type of quantity being measured.

For example, in physics, the magnitude of a force is the strength or intensity of the force, and it is typically measured in units such as newtons (N) or pounds-force (lbf). The magnitude of a vector quantity, such as velocity or acceleration, is the length of the vector and is measured in units such as meters per second (m/s) or meters per second squared (m/s^2).

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Complete Question: -

A snowboarder on a slope starts from rest and reaches a speed of 2.0 m/s after 8.6 s.

(a) What is the magnitude of the snowboarder's average acceleration?

_____ m/s2

(b) How far does the snowboarder travel in this time?

_____ m

Making multiple trials and averaging them is a good laboratory skill for several reasons such as, it reduces random error, increases precisions, increases accuracy and confidence in the result.

Why  multiple trials necessary as a good laboratory skill is that Random errors can occur in any laboratory experiment due to small variations in measurement or other factors that are beyond the experimenter's control. By conducting multiple trials and averaging the results, these random errors are minimized, since they will be averaged out across the different trials.

Also by averaging multiple trials, the overall precision of the measurement is increased. This is because averaging reduces the effect of outliers or other anomalous results that may occur in individual trials

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Answer:m = 0.7

Explanation:

Answer:

m = 705 kg

Explanation:

PE = m * g * h

m = PE / (g * h)

m = 19,000 (J) kg m/s² / (9.8 m/s² * 2.75 m)

m = 19,000 / (9.8  * 2.75 )

m = 19000 / 26.95

m = 705.009276438 kg

chatGPT

The required value to determine the value of the tangential velocity of the beetle is 25.13 m/s.

Write the provided data with suitable variables.

[tex]\omega = 360^o s^-1\\r = 4m[/tex]

Here, [tex]\omega[/tex] is the angular velocity and r is the radius.

Write the expression for the angular velocity and substitute the required values to determine the value of the period.

[tex]\omega = 2\pi / T\\360^o s^{-1}[/tex]× [tex]2\pi / 360^o =2\pi / T[/tex]

[tex]2\pi s^{-1} = 2\pi / T[/tex]

T = 1 s

Write the provided expression for the tangential velocity and substitute the required values to determine the value of the tangential velocity of the beetle.

[tex]\nu = 2r / T\\\nu = 2(4m) / 1 s\\\nu = 8m / s[/tex]

Write the expression for the tangential velocity when the beetle is moved to r = 4 m and substitute the required values to determine the value of the tangential velocity of the beetle.

[tex]\nu = 2\pi r/T\\\nu = 2\pi (4m) / 1 s\\\nu = 25.13 m/s[/tex]

B. If the beetle were moved to a radius of 4 m, its tangential velocity would still be given by v = 2r/T, where T is still 1 rotation/s. So, we can calculate the tangential velocity as:

v = 2r/T

v = 2(4 m)/(1 rotation/s)

v = 8 m/s

Tangential velocity is the component of an object's velocity that is perpendicular to its radial vector. In other words, it is the velocity of an object moving along a circular path, perpendicular to the radius of that circle.

When an object is moving in a circular path, it experiences a constant change in direction, and thus, its velocity is constantly changing. Tangential velocity measures the speed at which the object is moving along this circular path. The magnitude of the tangential velocity is equal to the object's speed, which is the distance covered by the object per unit time. The direction of the tangential velocity is always tangent to the circle at the point where the object is located.

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A- The tension of the rope is 490.5N, when box is at rest , B- when box moves 5m/s tension is 500N, C- when  the box has vx tension is 10Vx² N..

a)The tension in the rope when the box is at rest is equal to the weight of the box. Thus, the tension in the rope would be 50 kg x 9.81 m/s= 490.5 N.

b)When the box is moving at a steady 5.0 m/s, we need to use the equation of motion to find the tension in the rope. The equation of motion for a steady velocity is: F= ma+maF=2m(F=2m) (Since acceleration is zero)F=2(50kg)(0m/s²+5m/s²)F= 500N

c)When the box has a velocity component in the x-direction (Vx), the tension in the rope can be calculated as follows: F=ma+maF=2m(F=2m) (Since acceleration is zero)F=2(50kg)(Vx²/10m/s²)F= 10Vx² NThe tension in the rope when the box has a velocity component in the x-direction (Vx) is F = 10Vx² N.

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