An 11-kilogram cart is pulled with a horizontal force at a constant velocity of 8.0 meters per second, as shown in the diagram. The force of friction between the cart and the floor is 12 newtons. What is the magnitude of the horizontal force?

Answer and Explaination:

To solve this problem, we can analyze the forces acting on the mass as it travels up the inclined plane. We'll consider the gravitational force and the force exerted by the spring.

1. Gravitational force:

The force due to gravity can be broken down into two components: one perpendicular to the inclined plane (mg * cosθ) and one parallel to the inclined plane (mg * sinθ), where m is the mass and θ is the angle of the inclined plane.

2. Force exerted by the spring:

The force exerted by the spring can be calculated using Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position. The force can be written as F = -kx, where F is the force exerted by the spring, k is the spring constant, and x is the displacement from the equilibrium position.

Given:

Mass (m) = 5.0 kg

Compression of the spring (x) = 20.0 cm = 0.20 m

Angle of the inclined plane (θ) = 30°

First, let's find the force exerted by the spring (F_spring):

F_spring = -kx

To find k, we need the spring constant. Let's assume that the spring is ideal and obeys Hooke's Law linearly.

Next, let's calculate the gravitational force components:

Gravitational force parallel to the inclined plane (F_parallel) = mg * sinθ

Gravitational force perpendicular to the inclined plane (F_perpendicular) = mg * cosθ

Since the inclined plane is frictionless, the force parallel to the inclined plane (F_parallel) will be canceled out by the force exerted by the spring (F_spring) when the mass reaches its highest point.

At the highest point, the gravitational force perpendicular to the inclined plane (F_perpendicular) will be equal to the force exerted by the spring (F_spring).

Therefore, we have:

F_perpendicular = F_spring

mg * cosθ = -kx

Now, let's substitute the known values and solve for k:

(5.0 kg * 9.8 m/s^2) * cos(30°) = -k * 0.20 m

49.0 N * 0.866 = -k * 0.20 m

42.426 N = -0.20 k

k = -42.426 N / (-0.20 m)

k = 212.13 N/m

Now that we know the spring constant, we can calculate the maximum potential energy stored in the spring (PE_spring) when the mass reaches its highest point:

PE_spring = (1/2) * k * x^2

PE_spring = (1/2) * 212.13 N/m * (0.20 m)^2

PE_spring = 4.243 J

The maximum potential energy (PE_spring) is equal to the maximum kinetic energy (KE_max) at the highest point, which is also the energy the mass has gained from the spring.

KE_max = PE_spring = 4.243 J

Next, we can calculate the height (h) the mass reaches on the inclined plane:

KE_max = m * g * h

4.243 J = 5.0 kg * 9.8 m/s^2 * h

h = 4.243 J / (5.0 kg * 9.8 m/s^2)

h = 0.086 m

The height the mass reaches on the inclined plane is 0.086 m.

Now, we can calculate the distance traveled.

A 5.0 kg object compresses a spring by 0.20 m with a spring constant of 25 N/m. It climbs an incline, reaching a maximum height of 0.0102 m before coming back down, traveling a total distance of 0.0428 m.

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Answer:

g = 15.5 m/s²

Explanation:

In order to find the acceleration due to gravity near the surface of this planet can be calculated by using 2nd equation of motion. The 2nd equation of motion is given as:

h = Vi t + (0.5)gt²

where,

h = height covered by the wrench = 5 m

Vi = Initial Velocity = 0 m/s

t = Time Taken to hit the ground = 0.804 s

g = acceleration due to gravity near the surface of the planet = ?

Therefore,

5 m = (0 m/s)(0.804 s) + (0.5)(g)(0.804 s)²

g = (5 m)/(0.3232 s²)

g = 15.5 m/s²

Answer:

equator

Explanation:

in south & north pole you could have 20+ hours daylight or night, everyday!

Answer:

Q=cmΔT

Q1(steel)=Q2(water)

c1•m1• (t1-t) = c2•m2• (t-t2)

628•0.1•(80-t) = 4180•0.2• (t-10)

5024-62.8t = 836t -8360

5024+8360=(836+62.8)t

t=14.9°C

The cost of operation for an A.C for 10 hours per day for a month will be 71,100 francs.

Power is the amount of energy transferred or converted per unit time. The unit of power is the watt, equal to one joule per second. Power is a scalar quantity.

Cost of operation for 10 hours a day;

Daily consumption = 3kW x 10 hours

Daily Consumption = 30kW

Since 1kWH = 79 francs;

Daily consumption amount = 30 x 79 francs

Daily consumption amount = 2,370 francs

Therefore, the monthly consumption (using 30days) will be;

2,370 francs x 30 = 71,100 francs

In conclusion, 71,100 francs will be spent in a month (30 days) to run the 3kW rated A.C for 10 hours a day at 1kWH.

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If two mass dampers on a Lagos tower consist of a 373mg concrete block.that complete one oscillation in.6.80 secs. the oscillation amplitude in a high wind is 110cm. Then the spring constant of the mass-spring system is  6.90 N/m.

The spring constant is a measure of the stiffness of a spring, which describes how much force is required to stretch or compress the spring by a certain amount. It is typically measured in units of newtons per meter (N/m).

We can use the formula for the period of oscillation of a mass-spring system:

T = 2π√(m/k)

where T is the period of oscillation, m is the mass of the block, and k is the spring constant.

We can rearrange this formula to solve for k:

k = (4π²m) / T²

where we substitute the values given in the problem.

m = 373mg = 0.373g = 0.000373kg (convert milligrams to kilograms)

T = 6.80 s

π ≈ 3.14159

Plugging in these values, we get:

k = (4π² × 0.000373) / (6.80)²

≈ 6.90 N/m

Therefore, the spring constant of the mass-spring system is approximately 6.90 N/m.

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Answer: 707.11m

Explanation:

since the well is at 45 degrees, we can use trig ratios to figure out the vertical depth of the well as u can see image attached.

then since we are looking for the vertical depth and we have information on the hypotenuse we can say

sin45= \(\frac{verticle height}{1000}\)

therefore, we can say.

1000sin(45) = vertical height

hence

vertical height = 707.11m

Answer:

i honestly think its 21

Explanation:

da memes

10 + 10 =21

First we must calculate the current power the curling iron can handle:

where

I = current

V = tension

Then:

For the hair dryer we get:

Lets suppose all appliances are working in parallel together. The total current must be:

As we can see the appliances are drawning all current from the outlet fused.

Answer: the current that can be safely drawn from the outlet fused is zero.

The angle between vector A and B is 90 degrees.

Let’s consider the vectors A and B with equal magnitudes of 5.

Thus, we can assume that the angle between A and B is θ.

Now, if the sum of A and B is vector 6j, then we can write the vector equation below:

\(A + B = 6j\)

Let's first express vector A and B in terms of their components.

Let’s assume that vector A has components Ax and Ay, while vector B has components Bx and By.

Thus, the vector equation above can be rewritten in terms of components below:

\(Ax + Bx = 0\)       ------------(1)

\(Ay + By = 6\)       ------------(2)

We know that the magnitudes of vectors A and B are equal to 5, thus we can write the following equations:

\(x^2+y^2 = 5^2\)       ------------(3)

\(x^2+y^2 = 25\)      ------------(4)

From equation (4), we can write:

\(y = \sqrt{(25-x^2)}\)      ------------(5)

By substituting equation (5) into equation (2), we have:

\(Ay + By = 6Ay + \sqrt{(25-x^2)} = 6Ay\)

\(= 6 - \sqrt{(25-x^2)}\)    ------------(6)

We can now substitute equation (6) into equation (3):

\(x^2 + (6-\sqrt{(25-x^2)})^2 = 25\)

Solving for x:

\(2x^2 + 12\sqrt{(25-x^2)} = 0x^2 + 6\sqrt{(25-x^2)}\)

\(= 0x^4 + 36x^2 - 225\)

\(= 0x^2\)

\(= 3, -15\)

We choose \(x^2 = 3\) since it is positive and obtain:

\(y = 4By\)

substituting x and y into the original equations \(A = Ax + Ay\) and

\(B = Bx + By\), we obtain:

\(A = (-\sqrt{3}, 6-\sqrt{3})\)

\(B = (\sqrt{3}, -1+\sqrt{3})\)

Thus, the dot product of vectors A and B can be expressed as:

\(A \cdot B = |A||B| cos(\theta)\)

Now, we know that

\(|A| = |B| = 5\)

thus we can write:

\(A \cdot B = 25 cos(\theta)\)

Using the formula above, we can obtain the angle θ between vectors A and B as follows:

\(cos(\theta) = \frac{(A \cdot B)}{|A||B|}\)

\(cos(\theta) = \frac{[(\sqrt{3}(-\sqrt{3}) + (6-\sqrt{3})(-1+\sqrt{3})] }{(5)(5)}\)

\(cos(\theta) = \frac{ [-3 + 3]}{25}\)

\(cos(\theta) = 0\)

\(\theta= cos^{-1}(0)\)

\(\theta =90^{\circ}\)

Therefore, the angle between vector A and B is 90 degrees.

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Answer:

To solve this problem, we can use the formula:

d = (v^2)/(2μg)

d = distance traveled

v = speed of the car

μ = coefficient of kinetic friction

g = acceleration due to gravity

First, let's calculate the distance traveled when the car is traveling at 23 m/s:

d = (23^2)/(2*0.7*9.81) ≈ 67.97 meters

Now, let's calculate the distance traveled when the car is going twice as fast (46 m/s):

d = (46^2)/(2*0.7*9.81) ≈ 271.88 meters

Therefore, the car would travel approximately 271.88 meters if it were going twice as fast.

In Edgar Allan Poe's poem "The Raven," the speaker's description of the bird evolves throughout the poem, reflecting the changing emotions and perceptions of the speaker. By the end of the poem, the speaker's description of the bird is one of eerie and unsettling admiration.

Initially, the speaker describes the raven as a "stately" and "ebony" bird, highlighting its majestic and imposing presence. As the poem progresses, the speaker's description becomes more vivid and eerie. The bird is referred to as a "prophet" and a "devil," emphasizing its ominous and supernatural qualities. Its eyes are described as "burning" and "demon's," intensifying the sense of unease.

Towards the end of the poem, the speaker's attitude towards the bird shifts. The raven becomes a symbol of despair and sorrow, representing the speaker's torment. The speaker's repeated questioning of the raven about the possibility of being reunited with his lost love, Lenore, showcases his desperation and longing for answers.

In the final stanza of the poem, the speaker describes the bird as a "thing of evil" and a "demon." This description emphasizes the bird's malevolent nature and its power to haunt the speaker's thoughts and torment his soul. Despite its dark and foreboding presence, the speaker cannot help but be captivated and entranced by the raven's presence.

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The net force on q₂ will be  1.07 x 10⁻² N, pointing to the left.

To find the net force on particle q₂, we need to calculate the force due to q₁  and q₃ individually and then add them up vectorially. We can use Coulomb's law to calculate the force between two point charges:

F = k × (q₁ × q₂) / r²

where F is the magnitude of the force, k is Coulomb's constant (k = 8.99 x 10⁹ Nm²/C²), q1 and q2 are the charges of the two particles, and r is the distance between them.

The force due to q₁ on q₂ can be calculated as:

F₁ = k × (q₁ × q₂) / r₁²

where r1 is the distance between q₁ and q₂ (r₁ = 0.180 m).

Similarly, the force due to q₃ on q₂ can be calculated as:

F₂ = k × (q₃ × q₂) / r₃²

where r₃ is the distance between q₂ and q₃ (r₃= 0.230 m).

The direction of each force can be determined by the direction of the electric field due to each charge. Since q₁ and q₃ have opposite signs, their electric fields point in opposite directions. Therefore, the force due to q₁ points to the left and the force due to q₃ points to the right.

To find the net force, we need to add up the forces vectorially. Since the forces due to q₁ and q₃ are in opposite directions, we can subtract the magnitude of the force due to q₃ from the magnitude of the force due to q₁ to get the net force on q₂:

Fnet = F₁ - F₃

Substituting the values we get:

Fnet = k × (q₁ × q₂) / r₁² - k × (q₃ × q₂) / r₃²

Plugging in the values we get:

Fnet = (8.99 x 10⁹ Nm²/C²) × [(9.33 x 10⁻⁶ C) × (4.22 x 10⁻⁶ C) / (0.180 m)² - (-8.42 x 10⁻⁶ C) × (4.22 x 10⁻⁶ C) / (0.230 m)²]

Fnet = 1.07 x 10⁻² N

Therefore, the net force on q₂ is 1.07 x 10⁻² N, pointing to the left.

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The graph of the velocity and the time  can be shown by option D.

We know that the movement of an object as it is falling under gravity would have a constant acceleration. The constant acceleration means that the velocity of the object is also held a constant.

We now have to look at the graphs as we have them here. The graph as it has been shown has the the velocity on the vertical axis and it has the time on the horizontal axis. The gradient of the slope is what we would refers to as the acceleration of the body.

We also need to recall that the acceleration has to be a constant since tje tow object would have to reach the ground at the same time if they are released from the same height at the same time.

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Answer:

Explain

Explanation:

Answer:

The can was dropped from a height of 0.74 meters.

Explanation:

We can use the Conservation of Energy to evaluate the height.

The formula for the Conservation of Energy is

\(\frac{1}{2} mv^2=mgh\)

Lets solve for \(h\).

Cancel the common factor of \(m\).

\(\frac{1}{2} v^2=gh\)

Rewrite \(\frac{1}{2} v^2\) as \(\frac{v^2}{2}\) .

\(\frac{v^2}{2}=gh\)

Multiply both sides by 2.

\(v^2=2gh\)

Divide both sides by \(2g\).

\(\frac{v^2}{2g}=h\)

Numerical Evaluation

We are given

\(v=3.8\\g=9.81\)

Substituting our values into our equation for height gives us

\(h=\frac{3.8^2}{2*9.81}\)

Evaluate \(3.8^2\).

\(h=\frac{14.44}{2*9.81}\)

Multiply \(2\) and \(9.81\).

\(h=\frac{14.44}{19.62}\)

\(h=0.736235\)

Note: We also could have solved this using the kinematics equations. Both methods give you the same answer.

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The length of wire whose resistivity is 3 x 10^-6ohm, and radius is 0.2 mm, with a given value of 15.552 resistance is 6.5268 m.

Given data: r = 0.2 mm = 0.2 x 10^-3m Resistivity = 3 x 10^-6 ohm R = 15.552 ohm

Formula Used: Resistivity (ρ) = (RA)/L

Where, R is resistance, A is the area of cross-section, L is the length of the wire.

Resistance (R) = ρ (L/A)

Multiplying A on both sides, we get

Resistance (R) x A = ρ L ... equation (1)

Area of the cross-section of a wire of radius (r) is given by, A = πr^2

where, π is a constant whose value is 3.14

Substituting the given values, we get

A = πr^2= π (0.2 x 10^-3m)^2= 1.2566 x 10^-7 m^2

Substituting the values of R, A and ρ in equation (1), we get

Length of wire (L) = (Resistance x Area) / Resistivity= (15.552 ohm x 1.2566 x 10^-7 m^2) / (3 x 10^-6 ohm)= 6.5268 m

Therefore, the length of wire whose resistivity is 3 x 10^-6ohm, and radius is 0.2 mm, with a given value of 15.552 resistance is 6.5268 m.

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Answer:

6400km is the closest

Explanation:

Charge =

(current in Amperes) x (time in seconds)

1 Ampere means 1 Coulomb per second

240 Coulombs

90 Coulombs

150 Coulombs

Answer:

40 m/s ·

Explanation:

t= 5 s · a= 4 m/s².

we use the formula:V= u + atV

Answer:

[A] 20 m/s

Explanation:

Given:

Time (t)= 5 seconds

Acceleration (a)= 4 m/s²

We know v=u+at  

Speed = Velocity {in this question}

⇒ 40m/s=u+4×5 m/s

⇒ 40m/s=u+20 m/s

⇒ u=(40−20)  m/s

     u =20m/s

Hence, the initial speed of a car if its speed is 40 m/s after 5 seconds of accelerating at 4 m/s² is 20 m/s.

RevyBreeze

Complete question is;

A fisherman’s boat moves up and down periodically due to water waves. The boat travels from its highest to its lowest point, a vertical distance of 0.60 m, in 2.0 s. The horizontal distance between wave crests is 7.0 m. (a) What is the period of the wave motion? (b) What is the frequency of the wave motion? (c) What is the amplitude of each wave

Answer:

A) Period = 4 s

B) Frequency = 0.25 Hz

C) Amplitude = 0.3 m

Explanation:

A) We are told that the distance it takes for the boat to travel from its highest to its lowest point is 2 s.

Thus, t = 2 s

Now, in waves, period (T) it the time between two successive waves.

This means that;

T = 2t

T = 2 × 2

T = 4 s

B) Also, the frequency(f) is given by the formula;

f = 1/T

f = 1/4

f = 0.25 Hz

C) We are given a vertical distance of 0.60 m from highest to lowest point of waves.

Now, amplitude is half of this distance.

Thus;

Amplitude(A) = 0.6/2

A = 0.3 m

The potential energy of the roller coaster is 176,400 J (joules).

The potential energy of an object is given by the formula PE = mgh, where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height or vertical position of the object.

In this case, the roller coaster is at a peak of 20m and has a mass of 900kg. The acceleration due to gravity, g, is approximately 9.8 \(m/s^2\).

Using the formula, we can calculate the potential energy:

PE = mgh

= (900 kg)(9.8 \(m/s^2\))(20 m)

= 176,400 J

Therefore, the potential energy of the roller coaster is 176,400 J (joules).

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Answer:

F_suv= 49050 N

Explanation:

We are told that a 2000 kg car moving down the road runs into a 5000 kg stationary suv. The car applies a force of 1400 N on the suv.

Now, according Newton's first law of motion, an object will continue in it's present state of rest except it is acted upon by an external body.

This means the force acting on the stationary Suv is force of gravity.

Thus; F_suv = 5000 × 9.81

F_suv= 49050 N

Answer:

The wave moves with a velocity of 37.5 m/s

Explanation:

We know that the speed of a wave is given by:

V = f*λ

Where f is the frequency (the inverse of the period)

Then:

f = 1/T

And we know that T = 2 s/cycle

f = 1/(2 s/cycle) = (1/2) cycle/s

And λ is the wavelength, we know that:

λ = 75m/cycle.

Then the speed of the wave is:

v = ( (1/2) cycle/s)*(75m/cycle) = (75/2) m/s = 37.5 m/s

Answer:

14 secs and velocity will be 48

Explanation:

(1) The distance of the image formed by the lens is determined as 6 cm.

(2) The image formed is real.

The distance of the image formed by the lens is calculated by applying the following formula as follows;

1/f = 1/v + 1/u

where;

The distance of the image formed by the lens is calculated as;

1/v = 1/f - 1/u

1/v = 1/2 - 1/3

1/v = 1/6

v = 6 cm

Since the sign of the image of the image is positive, the image formed is real.

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The magnitude of the magnification indicates the size change of the image relative to the object. In this case, the magnitude is 0.2, indicating that the image is one-fifth the size of the object.

To determine the magnification of a real image formed by a mirror, we can use the magnification formula:

Magnification (m) = - (Image distance) / (Object distance)

Given:

Image distance (di) = 10.0 cm

Object distance (do) = 50.0 cm

Substituting the given values into the formula, we have:

m = \(- (10.0 cm) / (50.0 cm)\)

Simplifying the equation, we find:

m = -0.2

The negative sign indicates that the real image formed by the mirror is inverted compared to the object.

Therefore, the magnification of the real image is -0.2.

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The velocity of the wind with respect to the cyclist is 9.173 m/s its direction is 67.33⁰ from the southeast.

It states that "when two vectors are represented in a direction and magnitude by two sides of a triangle in the same order then its results will be represented in magnitude and direction of the closing side of the triangle in the opposite order."

then the resultant will be calculated as:

R= \(\sqrt{F1^{2} +F2^{2} +2F1F2cos\alpha }\)

Here in the given question

F1= -12m/s because the wind is opposing the cyclist who is moving with 12m/s so its direction is now east to west.

F2=5m/s

here angle between the two vectors is =45 degrees

now resultant of the vectors are

Vwc=\(\sqrt{(-12^{2}+5^{2} -2*12*5cos(45) }\)

=9.173km/h

Its direction will be applying sine the law

\(\frac{sin(45)}{9.173} =\frac{sine(\alpha) }{12}\)

\(\alpha =\)67.67⁰

now \(\beta =180-75-67.67\)

=67.33⁰

Hence the velocity of wind w.r.t. cyclist is 9.173m/s and its direction is towards the southeast.

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The resistance indicated by the platinum thermometer at 200°C is 1.648 times the reference resistance Ro at 0°C.

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