A crane lifts a 450 kg concrete to the top of a 50 m building in 5 s.
Assuming g= 10 m/s
)
2
a) The potential energy of the concrete.
, calculate;
b) The power developed by the crane

A metal bar is in the xy-plane with one end of the bar at the origin, [tex]\[r = (3.87 \, \text{m}) \mathbf{i} + (3.21 \, \text{m}) \mathbf{j}\][/tex], [tex]\theta\approx 55.16^\circ\][/tex], magnitude of torque is 22.58 Nm.

a) Position Vector r can be calculated as:

Given:

[tex]\(x = 3.87 \, \text{m}\)[/tex]

y = 3.21 m

The position vector r for the point where the force is applied is:

[tex]\[r = (3.87 \, \text{m}) \mathbf{i} + (3.21 \, \text{m}) \mathbf{j}\][/tex]

b) Magnitude of Torque can be calculated as:

Magnitude of r:

[tex]\[|r| = \sqrt{(3.87 \, \text{m})^2 + (3.21 \, \text{m})^2} \approx 5.019 \, \text{m}\][/tex]

Magnitude of F:

[tex]\[|F| = \sqrt{(6.82 \, \text{N})^2 + (-3.24 \, \text{N})^2}\\\\ \approx 7.610 \, \text{N}\][/tex]

Calculate the dot product of r and F:

[tex]\[r \cdot F = (3.87 \, \text{m}) (6.82 \, \text{N}) + (3.21 \, \text{m}) (-3.24 \, \text{N})\\\\ \approx 16.658 \, \text{N} \cdot \text{m}\][/tex]

Calculate the angle [tex]\(\theta\)[/tex] using the dot product and magnitudes:

[tex]\[\cos(\theta) = \frac{r \cdot F}{|r| \cdot |F|} \\\\= \frac{16.658 \, \text{N} \cdot \text{m}}{(5.019 \, \text{m})(7.610 \, \text{N})}\\\\ \approx 0.5526\][/tex]

[tex]\[\theta \approx \cos^{-1}(0.5526)\\\\ \approx 55.16^\circ\][/tex]

Now calculate the magnitude of the torque using the sine of the angle:

[tex]\[|\tau| = |r| \cdot |F| \cdot \sin(\theta)\\\\ = (5.019 \, \text{m}) (7.610 \, \text{N}) \sin(55.16^\circ)\\\\ \approx 22.58 \, \text{N} \cdot \text{m}\][/tex]

c) Direction of Torque:

According to the right-hand rule, the torque points either into or out of the plane formed by r and F. Its direction is perpendicular to that plane. The sign of the angle determines the precise orientation.

In this case, since [tex]\(\theta \approx 55.16^\circ\)[/tex] is positive (counterclockwise rotation), the torque points out of the plane formed by r and F.

Thus, the direction of the torque is outward from the xy-plane.

For more details regarding torque, visit:

https://brainly.com/question/30338175

#SPJ12

Your question seems incomplete, the probable complete question is:

A metal bar is in the xy-plane with one end of the bar at the origin. A force F=(6.82)i+ -3.24j is applied to the bar at the point x=3.87m , y=3.21m .

What is the position vector r for the point where the force is applied?

a Express your answer in terms of the unit vectors i and j .

b What are the magnitude of the torque with respect to the origin produced by F?

c What are direction of the torque with respect to the origin produced by F?

The magnitude of the electrical force between the two identical electrical charges is 8.98755 × 10⁹N.

Given the data in the question;

Coulomb's law states "that the force between two electrical charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them".

It is expressed as;

[tex]F = k\frac{q_1q_2}{r^2}[/tex]

Here, [tex]q_1\ and\ q_2[/tex]  are the two electrical charges, r is the distance between them and k is the Coulomb constant (  [tex]k = 8.98755*10^9 kgm^3/s^2C^2[/tex])

To determine the electrical force between the two charges, we substitute our values into the expression above.

[tex]F = k\frac{q_1q_2}{r^2}\\\\F = (8.98755*10^9 kgm^3/s^2C^2)*\frac{(1C)(1C)}{(1m)^2}\\\\F = (8.98755*10^9 kgm^3/s^2C^2)*\frac{1C^2}{1m^2}\\\\F = 8.98755*10^9 kgm/s^2\\\\F = 8.98755*10^9 N[/tex]

Therefore, the magnitude of the electrical force between the two identical electrical charges is 8.98755 × 10⁹N.

Learn more about coulomb's law: brainly.com/question/506926

The magnitude of the electrical force between the two charges is 8.987×10⁹ N.

As per the coulomb's law,  the electrical force between any two charges separated by a distance of r is given by the formula,

[tex]F = k\dfrac{q_1q_2}{r^2}[/tex]

Given that the value of q₁ and q₂ is 1 coulomb, while the distance between them is 1 meter. Also, the value of k is 8.987×10⁹ N·m²·C⁻², therefore, the force can be written as,

[tex]F = k\dfrac{q_1q_2}{r^2}\\\\F = (8.987 \times 10^{9}) \times (\dfrac{1 \times 1}{1^2})\\\\F= 8.987 \times 10^{9}\rm\ N[/tex]

Hence, the magnitude of the electrical force between the two charges is 8.987×10⁹ N.

Learn more about Coulomb's Law:

https://brainly.com/question/506926

#SPJ4

The entropy at constant pressure is always greater than that at constant volume and the change in entropy for the two processes is greater for gas B.

According to the second law of thermodynamics, entropy in the isolated system always stays the same or increases.

Since gas does work in isobaric (constant pressure) change processes, the entropy at constant pressure will be greater than that at constant volume.

Thus, for gas A the process is carried out at constant volume while for gas B that is carried out at constant pressure. The change in entropy is greater for gas B.

Learn more about work done by gas at constant pressure here: https://brainly.com/question/11982158

Answer:

Force=10N

Velocity=13m/s

Explanation:

Given,

Mass = 5kg

initial velocity=3m/s

Final velocity=7m/s

Time=2s

Now acceleration= v-u/t

=7-3/2

=4/2

=2m/s²

So, acceleration=2m/s²

Now,

F=ma

=5*2

=10N

Answer:

both

Explanation:

gravity is the same for both

A ball rolls down an inclined plane, starting from rest. if the total time it takes to reach the end of the inclined plane is t, how much time has elapsed when it is halfway down the incline 0.5t

An inclined plane is a straightforward device with a sloping surface that is used to lift heavy objects. When friction is taken into account, the force needed to move an object up an incline is less than the weight being raised. The needed force is closer to the real weight the higher the slope or incline.

The inclined plane is the most basic of all simple machines because nothing needs to move for it to function. In order to save effort, you have to move objects farther when using an inclined plane. A variety of techniques can be used to create an inclined plane. It can be as simple as a log leaning against a tree in the woods or a piece of wood placed on the edge of a stair.

To learn more about the inclined plane please visit

brainly.com/question/14983337

#SPJ2

Conversion of succinylcoA to succinate is the reaction that link acid cycle to the electron‑transport chain and amino acid synthesis.

SuccinylCoA is converted into succinate through the hydrolytic release of coenzyme A by succinyl-CoA synthetase Also succinyl-CoA is porphyrin synthesis, where it combine with glycine by ALA synthase to form δ-aminolevulinic acid.

Succinyl CoA is catalytically converted to succinate. The enzyme stimulates the hydrolysis of succinyl CoA into succinate and ATP and this represents a remarkable point of substrate level phosphorylation. After this, it link up to the electron transport chain via citric acid cycle.

Therefore, Conversion of succinylcoA to succinate is the reaction that link citric acid cycle to the electron‑transport chain and amino acid synthesis.

Learn more about Citric acid cycle conversion here.

https://brainly.com/question/11238674

The electron‑transport chain reaction connects the citric acid cycle to the electron‑transport chain and amino acid synthesis.

The electron transport chain is a set of protein complexes that link redox processes to create an electrochemical potential that leads to the production of ATP in a process known as

Both photosynthesis and cellular respiration occur in mitochondria.

As a result, the process that connects the citric acid cycle to the electron transport chain and amino acid synthesis is succinyl-CoA to succinate conversion.

Hence the electron‑transport chain reaction connects the citric acid cycle to the electron‑transport chain and amino acid synthesis.

To learn more about the electron‑transport chain reaction refer to:

https://brainly.com/question/13975046

#SPJ4

Explanation:

i think is per the International System of Units is Kelvin which is represented by the symbol K.

The acceleration of the runner in the given time is 2.06m/s².

Given the data in the question;

Since the runner begins from rest,

Acceleration of the runner; [tex]a = \ ?[/tex]

Velocity is the speed at which an object moves in a particular direction.

Acceleration is simply the rate of change of the velocity of a particle or object with respect to time. Now, we can see the relationship from the First Equation of Motion

[tex]v = u + at[/tex]

Where v is final velocity, u is initial velocity, a is acceleration and t is time elapsed.

To determine the acceleration of the runner, we substitute our given values into the equation above.

[tex]v = u + at\\\\13.4m/s = 0 + (a * 6.5s)\\\\13.4m/s = a * 6.5s\\\\a = \frac{13.4m/s}{6.5s}\\ \\a = 2.06m/s^2[/tex]

Therefore, the acceleration of the runner in the given time is 2.06m/s².

Learn more about Equations of Motion: https://brainly.com/question/18486505

Two equations will be needed to solve for the energy used in this procedure.

This is defined as the ability or capacity to do work. Ice being converted to vapor requires energy and the equations are seen below:

H₂O₍s₎  ⇒ H₂O₍l₎

H₂O₍l₎ ⇒ H₂O₍g₎

These are the equations which are used to calculate energy with heat being involved in both reactions.

Read more about Energy here https://brainly.com/question/19666326

Answer:

86.73 kg

Explanation:

Remember that F=mg

Let's plugin our numbers

850N=m9.8m/s^2

850N=9.8m/s^2m

86.73=m

first we need omega

Hence

[tex]\\ \rm\rightarrowtail \omega=\dfrac{2\pi}{T}=2\pi[/tex]

Now

Total energy:-

[tex]\\ \rm\rightarrowtail \dfrac{1}{2}m\omega ^2A^2[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{1}{2}(1)(2\pi)^2(1)^2[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{1}{2}(4\pi ^2[/tex]

[tex]\\ \rm\rightarrowtail 2\pi ^2[/tex]

[tex]\\ \rm\rightarrowtail 2(3.14)^2[/tex]

[tex]\\ \rm\rightarrowtail 19.72J[/tex]

Answer:

An asteroid is a minor planet of the inner Solar System. Historically, these terms have been applied to any astronomical object orbiting the Sun.

The time taken by the runner to do the work is 1.42 seconds.

Given the data in the question;

Power can be simply referred to as the quantity of energy transferred per unit time.

It is expressed as;

[tex]P = \frac{W}{t}[/tex]

Where W is work done and t is time elapsed.

To determine the time it took the runner to do the work, we substitute our given values into the expression above.

[tex]P = \frac{W}{t} \\\\t = \frac{W}{P} \\\\t = \frac{457J}{321W} \\\\t = \frac{457 kgm^2/s^2}{321 kgm^2/s^3}\\\\t = 1.42s[/tex]

Therefore, the time taken by the runner to do the work is 1.42 seconds.

Learn more about Power and Work: https://brainly.com/question/2962104

In the motion of the medium particles in a longitudinal wave, the medium vibrates parallel to the direction of the wave.

A longitudinal wave is a wave that is transversing along the length. When the displacement of medium and travel of wave is the same in that condition wave is known as the longitudinal wave.

It requires some medium to travel. A mechanical and sound wave is an example of a longitudinal wave.

Hence in the motion of the medium particles in a longitudinal wave, the medium vibrates parallel to the direction of the wave.

To learn more about the longitudinal wave refer to the link;

https://brainly.com/question/8497711

Answer:

d the medium vibrates parallel to the direction of the wave.

Explanation:

The speed of the brick dropped by the builder as it hits the ground is 17.32m/s.

Given the data in the question;

Since the brick was initially at rest before it was dropped,

Final speed of brick as it hits the ground; [tex]v = \ ?[/tex]

velocity is simply the same as the speed at which a particle or object moves. It is the rate of change of position of an object or particle with respect to time. As expressed in the Third Equation of Motion:

[tex]v^2 = u^2 + 2gh[/tex]

Where v is final velocity, u is initial velocity, h is its height or distance from ground and g is gravitational field strength.

To determine the speed of the brick as it hits the ground, we substitute our giving values into the expression above.

[tex]v^2 = u^2 + 2gh\\\\v^2 = 0 + ( 2\ *\ 10m/s^2\ *\ 15m)\\\\v^2 = 300m^2/s^2\\\\v = \sqrt{300m^2/s^2}\\ \\v = 17.32m/s[/tex]

Therefore, the speed of the brick dropped by the builder as it hits the ground is 17.32m/s.

Learn more about equations of motion: https://brainly.com/question/18486505

If the distance between the two charges is doubled, the attraction or repulsion becomes weaker.

Explanation:

Objects with the same charge repel each other, and objects with opposite charges attract each other

According to Coulomb, the electric force for charges at rest has the following properties: Like charges repel each other; unlike charges attract. Thus, two negative charges repel one another, while a positive charge attracts a negative charge. The attraction or repulsion acts along the line between the two charges.

Learn more about charges here: https://brainly.com/question/25922783

Comets have an extremely eccentric orbit around the Sun. They can travel hundreds of thousands of years through the solar system before returning to the Sun at perihelion. Comets, like all orbiting bodies, obey Kepler's Laws, which state that the closer they get to the Sun, the faster they move.

A comet is a dirty snowball many kilometers across that exists at a considerable distance from the Sun. However, when it gets closer to the Sun, the comet's surface warms up, causing its components to melt and vaporize, resulting in the comet's distinctive tail. The distance between the Earth and the Sun can be measured in comet tails.

Answer:

Here's the answer

Explanation:

since an electromagnet has a magnetic field, it will always follow the electromagnet.

The answers to your questions are as listed below

A) The total momentum of the system is :  < - 167, 133, 87 >   kg m/s

B) Velocity of the center of mass of this system : < - 10.44 , 8.31, 5.44 > m/s

C) Total kinetic energy of the system : 5159.5 J  

D) Translational kinetic energy of the system :  1660.84 J

E) kinetic energy relative to the center of mass : 3498.66 J

Given data :

m₁ = 4 kg ,   V₁ = < 10, -5, 15 > m/s

m₂ = 9 kg,   V₂ = < -15, 5, -3 > m/s

m₃ = 3 kg    V₃ = < -24, 36, 18 > m/s.

Total momentum = Σ mv

= < 4*10 + 9*(-15) + 3*(-24), 4*(-5) + 9*5 + 3*36, 4*15 + 9 (-3) + 3*18 >

= < - 167, 133, 87 >   kg m/s

Velocity = < - 167 / 16 , 133/ 16, 87/ 16 >

              =  < - 10.44 , 8.31, 5.44 > m/s

Total Kinetic energy = 1/2 m₁v₁² + 1/2 m₂v₂²  + 1/2 m₃v₃²  --- ( 1 )

where : v² = v₁² + v₂² + v₃²

therefore

Total kinetic energy = 700 + 1165.5 + 3294

                                  = 5159.5 J  

Translational kinetic energy ( Kcm ) = 1/2 ( m₁ + m₂ + m₃ ) * Velocity²

                                                           = 1/2 ( 16 ) * (  - 10.44² + 8.31² + 5.44² )

Hence translational kinetic energy = 1660.84 J

E) The Kinetic energy of the system relative to the center of mass

Krel = Ktotal - Kcm

       = 5159.5 - 1660.84

       = 3498.66 J

Hence we can conclude that the answers to your questions are as listed above.

Learn more about Translational kinetic energy :https://brainly.com/question/25959744

Answer:

If the Lego building is shaken side to side, it will withstand up to 60 seconds because front to back will cause the top of the building to collapse.

Answer:

Convert your wavelength into meters. Divide the speed of light, ~300,000,000 m/s, by the wavelength in m. This gives you the wave's frequency

Explanation:

The direction of the normal contact force of the road on the wheels is : ( B ) Left

The contact force of the road on the wheels will act in a direction opposite to the movement of the wheel on the road. therefore as the wheel moves forward ( right ), the contact force will move backwards ( left ) of the direction of motion.

Hence we can conclude that the direction of the normal contact force of the road on the wheels is : ( B ) Left

Learn more about contact force : https://brainly.com/question/18451249

#SPJ2

Answer:

2 kg

Explanation:

K.E. = 1/2 m v^2

81   = 1/2  m (9^2)

1 = 1/2 m

m = 2 kg

Answer:

a particular level of electical potential from a power source

Answer:

8 oz

Explanation:

Since the kinetic energy is equal to the potential energy then the speed of the object is √2gh.

The term work refers to the product of force and distance moved by force while energy is the ability to do work. The question is incomplete as the figure is not shown.

We know that the kinetic energy is equal to the potential energy hence;

mgh = 1/2mv^2

gh= 1/2v^2

v = √2gh

Learn more about kinetic energy: https://brainly.com/question/999862

Answer:

The energy of a mechanical wave can travel only through matter. The matter through which the wave travels is called the medium (plural, media). The medium in the water wave pictured above is water, a liquid. But the medium of a mechanical wave can be any state of matter, even a solid.

Explanation:

Brainlest pls if can thank you ! i hope its helped

Answer:

B. 240Ω

Explanation:

The formula between voltage, current and resistance is:

voltage = current × resistance

So resistance = voltage ÷ current

Therefore resistance = 120 ÷ 0.5

Resistance = 240Ω

Since chloride ions are not part of the ionic equilibrium, addition of chloride ions will only increase the concentration of the anions in the solution.

An ionic equilibrium is an equilibrium that exists between two or more ions in an aqueous solution.

The ionic equilibrium between iron (iii) ion and thiocyanate ions is given below:

[tex]Fe^{3+}\rightleftharpoons SC \: N^{-}[/tex]

From the principle of equilibrium, addition of either ions in the ionic equilibrium will alter equilibrium position to the left or right.

Addition of chloride ions, Cl- which is not a part of the ionic equilibrium will only increase the concentration of the anions in the solution.

Learn more about ionic equilibrium at: https://brainly.com/question/13879496

The chloride ions are not part of the ionic equilibrium, adding them to the solution will merely raise the concentration of anions.

When a chemical reaction does not convert all reactants to products, it reaches equilibrium. Many processes attain a state of balance, or dynamic equilibrium, in which both reactants and products are present.

The following is the ionic equilibrium between iron (III) ion+ and thiocyanate ions:

[tex]\rm Fe^{3+} \rightleftharpoons SC \ N^{-}[/tex]

The addition of either ion in the ionic equilibrium will shift the equilibrium position to the left or right, according to the principle of equilibrium.

The inclusion of chloride ions, Cl-, which are not components of the ionic equilibrium, increases the levels of anions in the solution.

Thus, the chloride ions are not part of the ionic equilibrium, adding them to the solution will merely raise the concentration of anions.

Learn more about the equilibrium here:

https://brainly.com/question/13458865

#SPJ4