At least how many Calories does a mountain climber need in order to climb from sea level to the top of a 5.42 km tall peak assuming the muscles of the climber can convert chemical energy to mechanical energy with an efficiency of 16.0 percent. The total mass of the climber and the equipment is 78.4 kg. (Enter your answer as a number without units.)

Answer:

686 Hz

Explanation:

Here we must remember the following relationship.

where v = speed of sound, λ = wavelength, and f = frequency.

Now in our case, we know that the speed of sound at 20°C is 343 m/s.

Furthermore, we also know that sound intensity decreases to a minimum every 50.0 cm; this means that the wavelength of the sound wave must be 50 cm. Why? because the wavelength is defined as the distance between two minima or two maxima.

Now, since we know that

v = 343 m/s and λ = 50.0 cm = 0.50 m, our formula gives

Dividing both sides by 0.50 m gives

Hence, the frequency of sound is 686 Hz.

Answer:

a) 1.082 × 10⁻¹⁹C  ( e = 1.6 × 10⁻¹⁹C)  

b) 3.466 × 10¹¹ N/C

Explanation:

a)

p(r) = -A exp ( - 2r/a₀)

Q = ₀∫^∞ ₀∫^π ₀∫^2xπ p(r)dV  =  -A  ₀∫^∞ ₀∫^π ₀∫^2π   exp ( - 2r/a₀)r² sinθdrdθd∅

Q = -4πA ₀∫^∞ exp ( - 2r/a₀)r²dr = -e

now using integration by parts;

A = e / πa₀³

p(r) =  - (e / πa₀³) exp (-2r/a₀)

Now Net charge inside a sphere of radius a₀ i.e Qnet is;

= e - (e / πa₀³)  ₀∫^a₀ ₀∫^π ₀∫^2π  r² exp (-2r/a₀)dr

= e - e + 5e exp (-2) = 1.082 × 10⁻¹⁹C  ( e = 1.6 × 10⁻¹⁹C)  

b)

Using Gauss's law,

E × 4πa₀ ² = Qnet / ∈₀

E = 4πa₀ ² × Qnet × 1/a₀²

E = 3.466 × 10¹¹ N/C

Answer:

A

Explanation:

The amount of load lifted by the pulley when the efficiency is 60% and effort is 50 N is determined as 30 N.

The amount of load lifted by the pulley is calculated by applying the formula for efficiency of a machine as follows;

E = L / E   x  100%

where;

The amount of load lifted by the pulley is calculated as;

60 = L / 50   x 100%

60 = 100L / 50

100L = 50 x 60

100 L = 3000

L = 3000 / 100

L = 30 N

Thus, the amount of load lifted by the pulley is 30 N.

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The models provide important tools for understanding the strong force interactions within a proton.

The strong force interactions between quarks and gluons within a proton are described by Quantum Chromodynamics (QCD), which is a fundamental theory of the strong nuclear force in particle physics. QCD is a non-Abelian gauge theory, meaning that the interactions between the quarks and gluons are highly nonlinear and non-perturbative.

One of the most promising theoretical models for describing the strong force interactions within a proton is lattice QCD, which is a numerical approach that uses a discrete grid to represent the space-time continuum. Lattice QCD allows for the calculation of QCD observables from first principles, without resorting to perturbative expansions. This method can handle non-perturbative effects such as confinement and chiral symmetry breaking by allowing for the simulation of the strong interactions on a discrete space-time grid

Another promising model is effective field theory, which provides a way to describe the low-energy behavior of QCD by constructing an effective Lagrangian that contains only the degrees of freedom relevant to a particular energy scale. This allows for the calculation of QCD observables in a systematic expansion in powers of a small parameter, such as the ratio of the quark mass to the QCD energy scale.

Chiral perturbation theory is another effective field theory that focuses on the dynamics of light quarks, which are the building blocks of pions, the lightest hadrons. Chiral perturbation theory provides a systematic expansion for the interactions between pions and nucleons, and can be used to calculate the properties of these particles at low energies.

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The acceleration of the cheetah is 4.29 m/s².

Acceleration can be defined as the rate of change of velocity.

To calculate the acceleration of theb cheetah, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the acceleration of the cheetah is 4.29 m/s².

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(a) A 1 000 kg car is pulling a 300 kg trailer, together the car and trailer move forward with an acceleration of 2. 15 m/s² the net force acting on the car (and trailer) is approximately 2,795 Newtons (N).

To determine the net force on the car, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.

The total mass of the car and trailer combined is the sum of their individual masses: 1,000 kg + 300 kg = 1,300 kg.

The acceleration of the car and trailer system is given as 2.15 m/s².

Using Newton's second law:

Net force = mass × acceleration

Net force = 1,300 kg × 2.15 m/s²

Net force ≈ 2,795 N

Therefore, the net force acting on the car (and trailer) is approximately 2,795 Newtons (N).

This net force is responsible for accelerating the combined mass of the car and trailer in the forward direction. It represents the sum of all external forces acting on the system, such as the force exerted by the car's engine and the tension in the connection between the car and trailer.

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The velocity of the horse is 0 m/s, so the correct option is C.

The velocity is a vector that is given by the rate of change of the displacement.

\( v = \frac{d}{t} \)

Where:

d: is the displacement

t: is the time      

Since in the horse track the starting point and the finish line are at the same point, the velocity of the horse is zero because the velocity depends on the direction of the displacement, and here the displacement is zero (the horse returns to the starting point).  

Therefore, the correct option is C: 0 m/s.

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I hope it helps you!      

Answer:

The velocity of the horse is 0 m/s:

Correct answer is C.

Given the scenario described above:

The philosophy of individual worth is of the opinion that everyone is worthy of some respect.

In that light, the breastfeeding mother should not be frowned at for breastfeeding her child in the waiting room. If there is a more appropriate area, she should be directed there respectfully.

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Answer: B

Explanation: the energy stored in the bowstring is a result of the elastic nature of the string (k) how far the bow has been stretched (x).

elastic potential energy is the energy stored in any elastic material when stretched.

Answer:

The volume of the block is equal to the volume of water displaced by the block.

Explanation:

Volume refers to the amount of space occupied by a given object (in this case the block). When an object such as the block is immersed in water, it displaces its own volume of water. This volume of water displaced is equal to the volume of the block. Hence we can write;

Final Volume of water - Initial Volume of water= Water Displaced = Volume of the block

Recall that the density of a body is given by;

Density= mass/volume

If we obtain the volume of the block by measuring the volume of water displaced by the block, then we weigh the block using a weighing balance, we can obtain the density of the block easily from the relationship shown above.

We will have the following:

So:

We will find the data we can with the given information:

Also:

So:

So, the velocity at the bottom of the funnel is 0.045m/s.

Approximately 0.123 kg of liquid water at 26 degrees Celsius would be needed to melt 41 grams of ice.

To calculate the minimum amount of liquid water required to melt 41 grams of ice at 0°C, we need to consider the energy required for the phase change from solid to liquid, which is known as the specific heat of fusion of ice.

The energy required to melt 1 kg of ice is 3.33×105 J/kg.

Therefore, the energy required to melt 41 grams of ice is (3.33×105 J/kg) × (41/1000) kg = 13653 J.

To calculate the amount of liquid water required, we use the specific heat capacity of water, which is 4180 J/kg/°C.

Assuming the initial temperature of water is 26°C, the amount of water needed can be calculated as (13653 J) ÷ (4180 J/kg/°C) ÷ (26°C) = 0.123 kg or approximately 123 ml of water.

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Complete question is;

A particle moves along a line so that its velocity at time t is

v(t) = t² − t − 6

(measured in meters per second).

(a) Find the displacement of the particle during the time period 1 ⩽ t ⩽ 4.

(b) Find the distance traveled during this time period.

Answer:

A) -4.5 m

B) 10.17 m

Explanation:

We are given;

v(t) = t² − t − 6

We know that v = ds/dt

Thus,

S = v dt

s(4) - s(1) = (4,1)∫t² − t − 6 dt

= (4,1)[(t³/3) - (t²/2) - 6t]

= ((4³/3) - (4²/2) - 6(4)) - ((1³/3) - (1²/2) - 6(1))

= 64/3 - 8 - 24 - 1/3 + 1/2 + 6

= -4.5 m

B) Since v(t) = t² − t − 6, then factorizing we can write it as;

v(t) = (t + 2)(t - 3)

Thus, v(t) ⩽ 0 at the interval (1, 3) and v(t) ≥ 0 at the interval (3, 4)

Thus;

-x1 = (1, 3)∫t² − t − 6 dt

-x1 = (1,3)(t³/3 - t²/2 - 6t)

-x1 = (3³/3 - 3²/2 - 6(3)) - (1³/3 - 1²/2 - 6(1))

-x1 = 9 - 9/2 - 18 - 1/3 + 1/2 + 6

-x1 = -3 - 4 - 1/3

-x1 = -22/3 m

x1 = 22/3 m

x2 = (3, 4)∫t² − t − 6 dt

x2 = (3, 4)(t³/3 - t²/2 - 6t)

x2 = ((4³/3) - (4²/2) - 6(4)) - (3³/3 - 3²/2 - 6(3))

x2 = 64/3 - 8 - 24 - 9 + 9/2 + 18

x2 = -23 + 64/3 + 9/2

x2 = (-138 + 128 + 27)/6

x2 = 17/6 m

Thus, total distance = x1 + x2 = 22/3 + 17/6 = 10.17m

The region a represents the distance of the electron from the nucleus.

According to the wave mechanical model of the atom, the probability of finding an electron within a given volume element (representing the atom) is the square of the wave function psi.

Since a is the region in space where there is the greatest probability of finding the electron in the atom, it follows that distance of the electron form the atom is always a.

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Answer:

Explanation:

10.00 5

Answer:

1. 10 ft/s² straight up

2. 4 Km north-west

3. 20 m/s South

Explanation:

To successfully categorize the quantities given above as vectors, we must understand what vector quantity is.

A vector quantity is a quantity that has both magnitude and direction.

Considering the question given above, the vector quantities are:

1. 10 ft/s² straight up

2. 4 Km north-west

3. 20 m/s South

The remaining quantities in the question are not considered as vectors because they only have magnitude but no direction. They are therefore referred to as scalar quantities.

(a) The molar heat capacity at pressure is 29.1 J/K.mol.

(b) The molar heat capacity at volume is 20.785 J/K.mol.

Molar heat capacity of a gas at constant volume is defined as the quantity of heat required to raise the temperature of one mole of the gas by 1 degree Kelvin when its volume is constant.

Cv = R/(γ - 1)

where;

Cv = (8.314) / (1.4 - 1)

Cv = 20.785 J/K.mol

Molar heat capacity of a gas at constant volume is defined as the quantity of heat required to raise the temperature of one mole of the gas by 1 degree Kelvin when its pressure is constant.

γ = Cp/Cv

Cp = γCv

Cp = 1.4 x 20.785

Cp = 29.1 J/K.mol

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On research on animals they must given proper care and housing. And the purpose of the research must have a scientific reason. Thus option B  is  correct.

Animal research includes various scientific investigation on animals such as testing various doses of some drugs, effect of various chemicals, level of toxicity of some compounds etc.

According to the research ethics, no animals can be used to conduct any unscientific works. There must be a scientific purpose which is very important to conduct any animal research.

If any animals irrespective of its nature,it must be provided proper care, food and housing. No harmful things must be there which make them more suffering. Hence, option B is correct.

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The speed of the mass when it hits the ground from the given height is \(\sqrt{2gh}\).

The given parameters:

The final velocity of the ball when it hits the ground is calculated as follows;

\(v_f^2 = v_0_y^2 + 2gh\\\\\)

where;

\(v_f^2 = 0 + 2gh\\\\v_f^2 = 2gh\\\\v_f = \sqrt{2gh}\)

Thus, the speed of the mass when it hits the ground from the given height is \(\sqrt{2gh}\).

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The magnitude of the resultant vector to round the answer to the nearest tenth, we look at the digit in the hundredth's place. If this digit is 5 or greater, we round up. If it is less than 5, we round down.

In the study of physics, we use vectors to represent quantities that have both direction and magnitude. It is often the case that we want to add two or more vectors together to obtain a single vector that represents the net result of these additions. The process of adding two or more vectors together is known as vector addition.The magnitude of the resultant vector is the length of the line that represents it on a scale drawing.

When we add two or more vectors together, the resultant vector is the vector that represents the net result of these additions. To find the magnitude of the resultant vector, we use the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

In the case of vector addition, the hypotenuse is the resultant vector, and the other two sides are the component vectors. If we have two vectors a and b, the magnitude of the resultant vector is given by the following equation:|R| = √(ax2 + bx2)where R is the resultant vector, a and b are the component vectors, and x is the angle between the vectors.

For example, if the answer is 12.345, we would round it to 12.3.

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The distance travelled by the vehicle around the circular track is 1,052.4 m.

The distance travelled by the vehicle in one complete cycle is calculated by using the following equation as show below.

d = 2πr

d = πd

Where;

In one complete cycle, the  vehicle will travel the circular track only once.

d = π(335 m)

d = 1,052.4 m

Thus, the distance travelled by the vehicle around the circular track is a function of the diameter of the circular track.

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The complete question is below:

A vehicle, starting from rest, accelerates on a circular track with a 335m diameter. What is the distance travelled by the vehicle when it makes one complete cycle?

The features of a Desert Climate sare mainly associated with the absence of precipitation and high solar radiation (question a), plants adapt to live in that type of climate due to the close of stomata and avoiding the presence of many leaves that lose too much water and or succulence in the plant shoot (questions b and c).

The relationship between desert conditions and plant adaptations in terms of evolution is based on certain anatomical and or physiological features used by these organisms to avoid the excessive loss of water under extreme desertic conditions such as the presence of small leaves and close stomata.

Therefore, with this data, we can see that plant adaptations in terms of evolution in desert environments are mainly associated with small leaves and also close stomata for gas exchange.

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Answer:

Centripetal acceleration must involve a change in a. an object's tangential speed.

Explanation:

Centripetal acceleration must involve a change in direction of motion of the object.

centripetal acceleration is the acceleration of a body traversing a circular path. Because velocity is a vector quantity (that is, it has both a magnitude, the speed, and a direction), when a body travels on a circular path, its direction constantly changes and thus its velocity changes, producing an acceleration. The acceleration is directed radially toward the center of the circle.

In your daily existence, you must have encountered numerous instances of centripetal acceleration. A centripetal acceleration occurs when you drive in a circle, and a centripetal acceleration also occurs when a satellite orbits the earth. Centripetal refers to being in the center.

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The change in motion, visible effects of the collision, and temperature increase would all serve as evidence that energy was transferred during the collision between the cart and the track after the removal of electrostatic forces.

If the electrostatic forces on the cart and track were suddenly removed and the cart hits the track, there would be several pieces of evidence indicating that energy was transferred during the collision.Firstly, there would be a noticeable change in the motion of the cart. The cart would decelerate as it collides with the track, and its velocity would decrease due to the loss of energy. This change in motion demonstrates that energy has been transferred from the cart to the track.

Secondly, there may be visible effects of the collision, such as deformation or damage to the cart or the track. This deformation or damage occurs because the energy transferred during the collision is transformed into other forms, such as heat or sound energy. These visible effects provide evidence of energy transfer.Additionally, there could be an increase in the temperature of the cart and/or the track due to the conversion of kinetic energy into thermal energy upon impact. This temperature change would be another indication that energy has been transferred.

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