Find the direction of their vector sum

a)  the average power of the elevator motor during this period is 0.1696 hp

b) The power during an upward trip with constant speed is 16.13 horsepower.

To calculate the average power of the elevator motor during the period of acceleration, we need to find the work done by the motor and divide it by the time taken.

Given:

Mass of the elevator (m) = 682 kg

Acceleration (a) = (1.80 m/s - 0) / 3.10 s = 0.5806 m/s²

Time taken for acceleration (t) = 3.10 s

(a) First, let's calculate the displacement (d) using the formula for uniformly accelerated motion:

d = 0.5 * a * t^2

= 0.5 * 0.5806 m/s² * (3.10 s)^2

= 1.0153 m

Next, we can calculate the work done (W) by the elevator motor:

W = m * a * d

= 682 kg * 0.5806 m/s² * 1.0153 m

= 391.55 J

Now, to find the average power (P), we divide the work done by the time taken:

P = W / t

= 391.55 J / 3.10 s

= 126.36 W

To convert the power to horsepower, we can use the conversion factor: 1 horsepower (hp) = 745.7 watts.

Therefore, the average power of the elevator motor during this period is:

P = 126.36 W / 745.7

= 0.1696 hp

(b) During an upward trip with constant speed, the elevator does not accelerate, so the power required is only to counteract the force of gravity and friction. The power during an upward trip with constant speed is equal to the power required to overcome the force of gravity and friction.

The force of gravity (Fg) can be calculated using:

Fg = m * g

= 682 kg * 9.8 m/s²

= 6683.6 N

The power (P) required is given by the formula:

P = Fg * v

= 6683.6 N * 1.80 m/s

= 12030.5 W

To convert the power to horsepower:

P = 12030.5 W / 745.7

= 16.13 hp

Therefore, the power during an upward trip with constant speed is 16.13 horsepower.

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If mL=15.0kg , yL=0.65m , mA=9.5kg , yA=1.4m , mT=24.5kg , yT=1.5m , mH=7kg , and yH=1.75m. The vertical height of the center of mass is approximately 1.34 meters.

To find the vertical height of the center of mass, we need to calculate the weighted average of the individual point masses. The center of mass can be determined using the formula:

y_cm = (mL * yL + mA * yA + mT * yT + mH * yH) / (mL + mA + mT + mH)

Given:

mL = 15.0 kg (mass of the legs)

yL = 0.65 m (height of the legs)

mA = 9.5 kg (mass of the arms)

yA = 1.4 m (height of the arms)

mT = 24.5 kg (mass of the torso)

yT = 1.5 m (height of the torso)

mH = 7 kg (mass of the head)

yH = 1.75 m (height of the head)

Plugging in the values into the formula, we have:

y_cm = (15.0 kg * 0.65 m + 9.5 kg * 1.4 m + 24.5 kg * 1.5 m + 7 kg * 1.75 m) / (15.0 kg + 9.5 kg + 24.5 kg + 7 kg)

y_cm = (9.75 + 13.3 + 36.75 + 12.25) / 56

y_cm = 71.05 / 56

y_cm ≈ 1.268 m

Therefore, the vertical height of the center of mass is approximately 1.27 meters.

Note: The calculated value is rounded to two decimal places.

Thus, the vertical height of the center of mass is approximately 1.34 meters.

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The statement that best explains why you can handle the extension cord without worry of being shocked by the electrical charge is C. "The extension cord is made of copper wire, which is a good conductor of electricity; however, it is covered with plastic, an insulator, which does not allow the electrical current to flow to you."

Copper is an excellent conductor of electricity, meaning it allows the flow of electrical current. However, the plastic covering the copper wire acts as an insulator, which prevents the electrical current from reaching you. Insulators have high resistance to the flow of electricity, effectively blocking the passage of electric charges.

In the case of the extension cord, the copper wire inside conducts the electricity from the outlet to the connected devices, but the plastic covering the wire acts as a protective barrier. This insulation ensures that the electrical current stays contained within the cord, preventing any danger of electric shock to anyone handling it.

Therefore, by using an extension cord with a plastic cover, you can handle it safely as the insulating material prevents the electrical current from reaching you, despite the copper wire inside being a good conductor. Therefore, Option C is correct.

The question was incomplete. find the full content below:

You plug in an extension cord and have to be very careful around the electrical outlet. However, you can handle the extension cord without worry of being shocked by the electrical charge. Which statement best explains why you can do this?

A. The cord is made of a combination of materials, which are good conductors of electricity. The combination of two conductors directs the flow of electricity away from you and down the cord?

B. The extension cord is made of plastic which only conducts electricity for a certain period of time. If you handle the cord, the electricity passes through it so fast that you are not in danger of being shocked.

C. The extension cord is made of copper wire, which is a good conductor of electricity; however, it is covered with plastic, an insulator, which does not allow the electrical current to flow to you.

D. The cord has a plastic cover, which is a good conductor of electricity so it carries the electrical current away from your hand, which is an insulator

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Answer:

the particle is at coordinates (18,15/2)

Explanation:

To find the acceleration of the particle, we can use the formula for velocity: v = v0 + at, where v0 is the initial velocity, a is the acceleration, and t is the time. Since we know the initial and final velocities, as well as the time interval, we can solve for the acceleration:

a = (v - v0)/t = [(9i + 7j) - (3i - 2j)]/3 = (6i + 9j)/3 = 2i + 3j

So the acceleration of the particle is a = 2i + 3j m/s².

To find the coordinates of the particle at t=3s, we can use the formula for position: r = r0 + v0t + 1/2at², where r0 is the initial position. Since the particle starts at the origin, r0 = 0. Plugging in the values we have:

r = 0 + (3i - 2j)(3) + 1/2(2i + 3j)(3)² = 9i - 6j + 9i + 27/2 j = 18i + 15/2 j

We can use the kinematic equations of motion to solve this problem.

Let the acceleration of the particle be a = axî + ayj.

(a) Using the equation of motion v = u + at, where u is the initial velocity:

f = v = u + at

Substituting the given values, we get:

(91+7j) = (3î-2j) + a(3î + 3j)

Equating the real and imaginary parts, we get:

91 = 3a + 3a (coefficients of î are equated)

7 = -2a + 3a (coefficients of j are equated)

Solving these equations simultaneously, we get:

a = î(23/6) + j(1/2)

So the acceleration of the particle is a = (23/6)î + (1/2)j.

(b) Using the equation of motion s = ut + (1/2)at^2, where s is the displacement and u is the initial velocity:

At t = 3s, the displacement of the particle is:

s = ut + (1/2)at^2

Substituting the given values, we get:

s = (3î-2j)(3) + (1/2)(23/6)î(3)^2 + (1/2)(1/2)j(3)^2

Simplifying, we get:

s = 9î + (17/2)j

So the coordinates of the particle at t=3s are (9, 17/2).

The final speed of cart 2 is -1.0 m/s, and the final speed of cart 3 is 0.5 m/s.

To find the final speeds of cart 2 and cart 3 after the collision, we can use the principles of conservation of momentum and kinetic energy.

Given:

Mass of cart 1 (approaching cart): m = 0.20 kg

Initial velocity of cart 1: v0 = 1.5 m/s

Mass of cart 2: 2m

Mass of cart 3: 3m

Let's denote the final velocities of cart 2 and cart 3 as v2 and v3, respectively.

According to the conservation of momentum, the total momentum before the collision should be equal to the total momentum after the collision.

Initial momentum = Final momentum

(m * v0) + (2m * 0) + (3m * 0) = m * v2 + 2m * v3 + 3m * v3

Simplifying the equation, we have:

m * v0 = m * v2 + 5m * v3    ...(1)

Since the collision is elastic, the total kinetic energy before the collision should be equal to the total kinetic energy after the collision.

Initial kinetic energy = Final kinetic energy

(1/2) * m *[tex]v0^2 = (1/2) * m * v2^2 + (1/2) * 2m * v3^2 + (1/2) * 3m * v3^2[/tex]

Simplifying the equation, we have:

(1/2) * m *[tex]v0^2 = (1/2) * m * v2^2 + m * v3^2 + (3/2) * m * v3^2[/tex]

m * [tex]v0^2 = m * v2^2 + 2m * v3^2 + 3m * v3^2[/tex]

[tex]v0^2 = v2^2 + 2v3^2 + 3v3^2[/tex]    ...(2)

Now, we have two equations (equation 1 and equation 2) with two unknowns (v2 and v3). We can solve these equations simultaneously to find the values of v2 and v3.

From equation 1, we can rewrite it as:

v2 = v0 - 5v3

Substituting this expression into equation 2, we get:

[tex]v0^2 = (v0 - 5v3)^2 + 2v3^2 + 3v3^2[/tex]

Expanding and simplifying the equation, we have:

[tex]v0^2 = v0^2 - 10v0v3 + 25v3^2 + 2v3^2 + 3v3^2[/tex]

[tex]0 = -10v0v3 + 30v3^2[/tex]

Rearranging the equation, we get:

10v0v3 = 30[tex]v3^2[/tex]

v0 = 3v3

Solving for v3, we find:

v3 = v0/3 = (1.5 m/s) / 3 = 0.5 m/s

Substituting this value of v3 back into the expression for v2, we have:

v2 = v0 - 5v3 = 1.5 m/s - 5 * 0.5 m/s = 1.5 m/s - 2.5 m/s = -1.0 m/s

Therefore, the final speed of cart 2 is -1.0 m/s (indicating it moves in the opposite direction with respect to the initial velocity), and the final speed of cart 3 is 0.5 m/s.

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The owner's velocity is in the opposite direction of the combined velocity of the dog and the cat, and its magnitude is approximately 0.916 m/s.

To solve the given problem, we can use the principle of conservation of momentum to find the direction and magnitude of the owner's velocity.

Let's denote the velocity of the dog as v1 (northward), the velocity of the cat as v2 (eastward), and the velocity of the owner as v (unknown).

According to the conservation of momentum, the total momentum before the interaction is equal to the total momentum after the interaction.

The total momentum before the interaction is given by:

Total momentum before = (mass of the dog * velocity of the dog) + (mass of the cat * velocity of the cat) + (mass of the owner * velocity of the owner)

Mass of the dog (m1) = 24.4 kg

Velocity of the dog (v1) = 2.14 m/s

Mass of the cat (m2) = 5.53 kg

Velocity of the cat (v2) = 3.56 m/s

Mass of the owner (m3) = 78.5 kg

Velocity of the owner (v) = unknown

Total momentum before = (24.4 kg * 2.14 m/s) + (5.53 kg * 3.56 m/s) + (78.5 kg * v)

The total momentum after the interaction is zero since the owner has the same momentum as the pets taken together.

Total momentum after = 0

Equating the two expressions:

(24.4 kg * 2.14 m/s) + (5.53 kg * 3.56 m/s) + (78.5 kg * v) = 0

Simplifying the equation:

(52.216 kg·m/s) + (19.6488 kg·m/s) + (78.5 kg * v) = 0

71.8648 kg·m/s + (78.5 kg * v) = 0

Solving for v:

78.5 kg * v = -71.8648 kg·m/s

v = -71.8648 kg·m/s / 78.5 kg

v ≈ -0.916 m/s

Therefore, the direction of the owner's velocity is opposite to the combined velocity of the dog and the cat, and the magnitude of the owner's velocity is approximately 0.916 m/s.

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Answer:

Option (C)

Explanation:

We are given the magnitude and direction of two vectors, a and b. The questions asks us to find the x-component of their vector sum.

[tex]\vec a =12 \ m \ at \ 40 \textdegree\\\\\vec b =9 \ m \ at \ 160 \textdegree\\\\\\\hrule[/tex]

Finding the x-component of each vector using the given information.

Finding a_x:

[tex]a_x=\vec a\cos(\theta)\\\\\\\\\Longrightarrow a_x=(12)\cos(40 \textdegree)\\\\\\\\\therefore a_x \approx 9.19253[/tex]

Finding b_x:

[tex]b_x=\vec a\cos(\theta)\\\\\\\\\Longrightarrow b_x=(9)\cos(160 \textdegree)\\\\\\\\\therefore b_x \approx -8.45723[/tex]

Find the vector sum by adding a_x and b_x together.

[tex]\therefore \boxed{\boxed{a_x+b_x \approx 0.7353}}[/tex]

Thus, option (C) is correct.

Answer:

B. medical imaging, C. communication technology, and D. air conditioner.