A boy is playing with a ball of mass 72g attached to a string. He is moving it at constant speed in a horizontal circle of radius 0.9m. a. State the net work done on the ball in one complete revolution. (1) b. The tension in the string is 60N. Determine the angular velocity of the ball. (4) c. Calculate the time it takes for the ball to complete 20 revolutions. (2)

Answer:

make a pineapple schematic

Explanation:

Answer: the angular velocity of a particle at the Earth's surface is approximately 7.27 x 10^-5 rad/s, and the linear velocity of the particle is approximately 464.1 m/s.

Explanation:

When you see yourself in a plane mirror, the image is always virtual, erect and the image formed has same size as that of the object

Besides that, the image will be at the same distance behind the mirror as the object is in the front of the mirror, so we can say that the image formed by the plane mirror is an exact copy of ourselves

Because the light does not actually pass through the image, that's why  the image formed by plane mirror is called a virtual image and the real images are formed by curved mirror and they are produced on the same side as that of the mirror

But the only difference is that the image formed by plane mirror is laterally inverted, means if raise our right hand then it would appear in the mirror as if we have raised our left hand

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To construct a semi-ellipse fireplace arch with a height of 2 feet and a base width of 6 feet, the contractor can use the following steps:

Determine the center point of the arch. Mark this point on the floor and call it point C.Measure the height of the arch, which is 2 feet. Mark this point above point C and call it point A.Measure the base width of the arch, which is 6 feet. Mark two points on either side of point C at a distance of 3 feet each. Call these points B and D.

Tie a string to a tack at point A, and loop it around two more tacks at points B and D.Adjust the length of the string until it is taut, but not too tight.Using a pencil, trace the curve of the string from point B to point D. This will create the semi-ellipse shape.

The required positions of the tacks and the length of the string will depend on the specific measurements and dimensions of the fireplace arch. By following these steps, the contractor can ensure that the semi-ellipse fireplace arch is constructed accurately and meets the desired specifications.

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Answer:

T = 365.58 K

Explanation:

Given that,

The concentration of solution, C = 0.750M

Osmotic pressure, P = 22.5 atm

We need to find the temperature of the solution.

The formula for the osmotic pressure is given by :

\(P=CRT\)

Where

R is gas constant, \(R=0.08206\ L\ atm/mol-K\)

\(T=\dfrac{P}{CR}\\\\=\dfrac{22.5}{0.75\times 0.08206}\\\\=365.58\ K\)

So, the temperature of the solution is 365.58 K.

The magnetic field inside the new solenoid is half as strong as the magnetic field inside the original solenoid is  (B) Bo/2 is correct option.

The magnetic field inside a solenoid is given by the equation:

B = μ₀nI

where B is the magnetic field strength, μ₀ is the permeability of free space, I is the current, and n is the number of turns per unit length. For a solenoid, n = N / l, where N is the total number of turns and l is the length of the solenoid.

Using this equation,  can find the magnetic field strength inside the original solenoid:

Bo = μ₀NIl / lN = μ₀NI

Now, for the new solenoid with radius 2r, the number of turns per unit length would be half of that in the original solenoid, since the turns are spaced twice as far apart. Therefore, the magnetic field strength inside the new solenoid would be:

B' = μ₀(N/2)Il / l(N/2) = μ₀NI/2

Comparing B' to Bo, we get:

B' / Bo = (μ₀NI/2) / (μ₀NI) = 1/2

Therefore, the magnetic field inside the new solenoid would be half as strong as the magnetic field inside the original solenoid.

The answer is (B) Bo/2.

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Convection currents are set up in the boiling water and in the surrounding air.

Convection is the transfer of thermal energy by the actual movement of the molecules of a substance. A convection current is set up when the molecules of a fluid is heated, rises and is replaced by cooler molecules from below.

The two transfers of energy in this system are;

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Answer:

Explanation:

ill try to help

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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Explanation:

Becuse the coin has a Lesser Density than water.

An action which would help in preventing and coping with heat-related conditions is: A. Drinking water.

Heat can be defined as a form of energy that is transferred from a physical object (body) to another, as a result of a difference in temperature. Also, heat is a condition of weather that is generally characterized by a high degree of temperature.

This ultimately implies that, heat is most likely to cause dehydration and high body temperature.

In order to prevent and cope with heat-related conditions, you should ensure that you drink water at regular intervals for hydration.

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The density of the second liquid is 0.812 g/cm³

To calculate the density of the second liquid, we need to use the principle of displacement. The mass of the liquid can be found by subtracting the mass of the empty density bottle from the mass of the bottle filled with the liquid. Therefore, the mass of the liquid is:

mass of liquid = mass of bottle + liquid - mass of empty bottle

mass of liquid = 39.84g + x - 18.00g

where x is the mass of the liquid.

We can now use the density formula, which is:

density = mass/volume

The volume of the liquid is equal to the volume of the density bottle that is filled with the liquid, which can be calculated by subtracting the volume of the empty bottle from the volume of the bottle filled with the liquid. Therefore, the volume of the liquid is:

volume of liquid = volume of bottle filled with liquid - volume of empty bottle

We can now substitute this expression into the density formula to get:

density of liquid = mass of liquid / (volume of bottle filled with liquid - volume of empty bottle)

We know that the density of water is 1000 kg/m³, which is equal to 1 g/cm³. We can use this to find the volume of the liquid by dividing the mass of water by its density:

volume of water = mass of water / density of water

volume of water = 44.00g / 1 g/cm³

volume of water = 44.00 cm³

Now, we can calculate the volume of the density bottle filled with the second liquid by using the principle of displacement:

volume of bottle filled with liquid = volume of water - volume of liquid

volume of bottle filled with liquid = 44.00 cm³ - (39.84g - 18.00g) / 1 g/cm³

volume of bottle filled with liquid = 44.00 cm³ - 21.84 cm³

volume of bottle filled with liquid = 22.16 cm³

Finally, we can substitute these values into the density formula to get:

density of liquid = x / 22.16 cm³

Solving for x, we get:

x = density of liquid x 22.16 cm³

Substituting x back into the mass equation, we get:

mass of liquid = 39.84g + (density of liquid x 22.16 cm³) - 18.00g

Solving for the density of the liquid, we get:

density of liquid = (mass of liquid - 21.84g) / 22.16 cm³

Substituting the given values, we get:

density of liquid = (39.84g - 21.84g) / 22.16 cm³ = 0.812 g/cm³

In conclusion, the density of the second liquid is 0.812 g/cm³. This value is less than the density of water, which means that the second liquid is less dense than water and will float on top of water.

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Answer:

B

Explanation:

Simply take all forces pointing to the right of the box as positive and all of the forces pointing to the left of the box as negative and add all values.

ΣF = 7 + 18 + (-20) = 5N to the right

Answer:

4161 J/kg·°C

Explanation:

We can use the principle of conservation of energy to solve this problem, which states that the total heat energy in a closed system is constant. The heat lost by the tea is equal to the heat gained by the milk.

Let's first calculate the heat lost by the tea:

Q(tea) = mcΔT

Q(tea) = (0.27 kg)(3910 J/kg·°C)(90.0°C - 85.0°C)

Q(tea) = 6555 J

where m is the mass of tea, c is the specific heat of tea, and ΔT is the change in temperature.

Next, let's calculate the heat gained by the milk:

Q(milk) = mcΔT

Q(milk) = (0.02 kg)(c)(85.0°C - 6.0°C)

Now we can equate the two expressions:

Q(tea) = Q(milk)

6555 J = (0.02 kg)(c)(79.0°C)

Solving for c, we get:

c = 4161 J/kg·°C

Therefore, the specific heat of milk is approximately 4161 J/kg·°C.

The acceleration of the given mass is equal to 2 m/s².

Acceleration can be described as the change in velocity with respect to time. The acceleration is a vector parameter because it has both magnitude and direction.

According to Newton's 2nd law, the force is the mass (m) times of acceleration (a) of an object.

F = ma

And, a  = F/m

Therefore, the acceleration (a) of a body is inversely proportional to the mass(m).

Given, the force acting on the mass, F = 12 N

The value of the mass, m = 6 Kg

The acceleration of the mass, a = F/m = 12/6 = 2 m/s²

Therefore, the acceleration of the mass 6 Kg is 2 m/s².

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Answer:

45 meters

Explanation:

The distance travel by the white-backed vulture can be calculated as:

Since the velocity is 25 m/s and the time is 1.8 s, we get:

Therefore, the answer is 45 meters

Answer:

The graph of the velocity of an object in free fall would look like a straight line sloping downward. As the object falls, its velocity increases at a constant rate, so the graph of its velocity versus time will be a straight line with a negative slope. This is because acceleration due to gravity is a constant -9.8 meters per second squared, so the velocity of a free-falling object will increase by 9.8 meters per second every second.

Therefore, the graph that shows the change in velocity of an object in free fall is a straight line with a negative slope. Here is an example of such a graph:

Free Fall Velocity Graph

Answer: C

Explanation:

The bigger the satellite, the longer it will take to get around the satellite. Hence, the velocity would get smaller.

r*v=4r*?

r*v/4r=?

r/4r * v=?

1/4 * v=?

?=v/4 ==> C

The drawing of the wave in the slinky shows the node and antinode

in the form of a standing wave pattern.

The speed of the wave pulse through the slinky, v = 18 m/s

The frequency with which the student vibrates the slinky, f = 4.5 Hz

Number of nodes in the slinky, n = 4 nodes

The wavelength of the slinky, λ, is given as follows;

\(\displaystyle \lambda = \mathbf{ \frac{v}{f}}\)

Therefore;

\(\displaystyle \lambda = \frac{18 \, m/s }{4.5 \, Hz} = \mathbf{4.0 \, m}\)

The attached drawing of the situation shows the wavelength of the

wave equal to the distance between three consecutive nodes, N

The number of loops = 3 complete loops + Half of a loop = 3.5 loops

The length of the wavelength, λ = Length of two complete loops

Height of the stairwell = 3.5 loops

2 loops = λ

Therefore;

\(\displaystyle Height \ of \ stairwell = \frac{\lambda}{2 } \times 3.5 = \mathbf{1.75 \cdot \lambda}\)

Which gives;

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Answer: The angular velocity of a car tire is 1 rad/s.

Definition: Angular velocity is the speed at which the angle between two bodies changes when an object rotates or revolves around an axis. This displacement is depicted in the image by the angle formed by a line on one body and a line on the other.

Answer:

In a collision, there is a collision force which endures for some amount of time to cause an impulse. This impulse acts upon the object to change its velocity and thus its momentum

Answer:

a) The minimum thickness of the oil slick at the spot is 313 nm

b) the minimum thickness be now will be 125 nm

Explanation:  

Given the data in the question;

a) The index of refraction of the oil is 1.20. What is the minimum thickness of the oil slick at that spot?

t\(_{min\) = λ/2n

given that; wavelength λ = 750 nm and  index of refraction of the oil n = 1.20

we substitute

t\(_{min\) = 750 / 2(1.20)

t\(_{min\) = 750 / 2.4

t\(_{min\) = 312.5 ≈ 313 nm

Therefore, The minimum thickness of the oil slick at the spot is 313 nm

b)

Suppose the oil had an index of refraction of 1.50. What would the minimum thickness be now?

minimum thickness of the oil slick at the spot will be;

t\(_{min\) = λ/4n

given that; wavelength λ = 750 nm and  index of refraction of the oil n = 1.50

we substitute

t\(_{min\) = 750 / 4(1.50)

t\(_{min\) = 750 / 6

t\(_{min\) = 125 nm

Therefore, the minimum thickness be now will be 125 nm

Answer:

The dependent variable is the cook time of the egg

The higher the temperature of the water, the faster the egg will cook, then the dependent variable is the temperature of the water, therefore the correct answer is the option C

It can be defined as the form of the energy in which heat is transferred from one body to another body due to their molecular movements, thermal energy is also known as heat energy.

Thermal energy can be produced with help of various means such as by burning fossil fuels, with the help of solar energy.

The correct direction for heat flow is from hot to cold because heat always moves naturally from a higher thermal potential to a lower thermal potential unless additional work is provided by an external machine.

Thus, The dependent variable is the water's temperature, and since the egg will cook more quickly at higher water temperatures, option C is the best choice.

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Hi there!

Part A:

The only quantities explicitly given to us are:

3. mass (m)

4. Maximum velocity (vmax)

5. Amplitude (A)

8. Position x from equilibrium

Part B:

To solve, we must begin by calculating the force constant, 'k'.

We can use the following relationship:

\(v = \sqrt{\frac{k}{m}(A^2-x^2)\)

We are given the max velocity which occurs at a displacement of 0 m, because the mass is the fastest at the equilibrium point. We can rearrange the equation for k/m:

\(\frac{v^2}{(A^2-x^2)} = \frac{k}{m}\)

\(\frac{3.2^2}{(0.06^2-0)} = \frac{k}{m} = 2844.44\)

Now, we can find the velocity at 4.7cm (0.047m) using the equation:

\(v = \sqrt{(2844.44)(0.06^2-0.047^2)} = 1.989 m/s\)

Plug this value into the equation for kinetic energy:

\(KE = \frac{1}{2}mv^2\\\\KE = \frac{1}{2}(0.05)(1.989^2) = \boxed{0.0989 J}\)

Part C:

The potential energy of a spring is given as:

\(U = \frac{1}{2}kx^2\)

Find 'k' using the derived quantity above:

\(\frac{k}{m} = 2844.44\\\\k = 2844.44m = 142.22 N/m\)

Now, calculate potential energy:

\(U = \frac{1}{2}(142.22)(0.047^2) = \boxed{0.157 J}\)

Frequency=  30 Hz, Period= 0.0333 s, Wave Number=15.708 rad/m, Wave Function= y(x, t) = 0.05 sin(15.708x - 94.248t), Transverse displacement= -0.013 m, Time= 0.297 s.

(a) To find the frequency (f), we can use the equation: wave speed = frequency x wavelength. Rearranging this equation, we get:

frequency = wave speed / wavelength

Substituting the given values, we get:

frequency = 12 m/s / 0.4 m = 30 Hz

Therefore, the frequency of the wave is 30 Hz.

To find the period (T), we can use the equation:

period = 1 / frequency

Substituting the frequency value we just calculated, we get:

period = 1 / 30 Hz = 0.0333... s (rounded to four decimal places)

Therefore, the period of the wave is approximately 0.0333 s.

To find the wave number (k), we can use the equation:

wave number = 2π / wavelength

Substituting the given values, we get:

wave number = 2π / 0.4 m = 15.708 rad/m (rounded to three decimal places)

Therefore, the wave number of the wave is approximately 15.708 rad/m.

(b) The wave function for a transverse wave on a string is given by:

y(x, t) = A sin(kx - ωt + φ)

where A is the amplitude, k is the wave number, x is the position of the point on the string, t is the time, ω is the angular frequency, and φ is the phase constant.

We already know the values of A, k, and ω from the previous calculations. To find φ, we can use the given initial condition: "at t = 0 end of the string has zero displacement and is moving upward". This means that y(0,0) = 0 and ∂y/∂t(0,0) > 0. Substituting these conditions into the wave function, we get:

0 = A sin(0 + φ)

∂y/∂t = -Aω cos(0 + φ)

Since sin(0 + φ) = sin(φ) = 0 (because sin(0) = 0), we get:

φ = nπ, where n is an integer

Since cos(0 + φ) = cos(φ) = 1 (because cos(0) = 1) and ∂y/∂t(0,0) > 0, we get:

n = 0 or 2

Therefore, the possible values of φ are 0 or 2π.

Substituting the values of A, k, ω, and φ, we get:

y(x, t) = 0.05 sin(15.708x - 94.248t)

Therefore, the wave function describing the wave is:

y(x, t) = 0.05 sin(15.708x - 94.248t)

(c) To find the transverse displacement of a wave at x = 0.25 m and t = 0.15 s, we can use the wave function we just found:

y(0.25, 0.15) = 0.05 sin(15.708(0.25) - 94.248(0.15))

y(0.25, 0.15) ≈ -0.013 m (rounded to three decimal places)

Therefore, the transverse displacement of the wave at x = 0.25 m and t = 0.15 s is approximately -0.013 m.

(d) To find how much time must elapse from the instant in part (c) until the point at x = 0.25 m has zero displacement,

From part (c), we know that the transverse displacement of the wave at x = 0.25 m and t = 0.15 s is approximately -0.013 m. We need to find the time it takes for this point to return to zero displacement.

We can use the wave function we found in part (b) and set y(0.25, t) = 0:

0 = 0.05 sin(15.708(0.25) - 94.248t)

Since sin(θ) = 0 when θ = nπ (where n is an integer), we get:

15.708(0.25) - 94.248t = nπ

Solving for t, we get:

t = (15.708(0.25) - nπ) / 94.248

To find the smallest positive value of t that satisfies this equation, we need to use the smallest positive value of n that makes the right-hand side of the equation positive (because we want to find the time it takes for the point at x = 0.25 m to return to zero displacement, which happens after the point has completed a full cycle). We can see from the equation that n must be an even integer to make the right-hand side positive. The smallest even integer greater than zero is 2. Substituting n = 2, we get:

t = (15.708(0.25) - 2π) / 94.248

t ≈ 0.297 s (rounded to three decimal places)

Therefore, the time it takes for the point at x = 0.25 m to return to zero displacement is approximately 0.297 s.

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The velocity of the ball just before it hits the ground is 14.0 m/s

Let's solve the problem using the given equation:

\(v^2 = u^2 + 2as\)

We know that u (initial velocity) is zero, s (distance traveled) is 10 meters, and a (acceleration due to gravity) is 9.81 m/s^2. We want to find the final velocity (v) just before the ball hits the ground.

Plugging in the given values, we get:

v^2 = 0 + 2(9.81)(10)

v^2 = 196.2

Taking the square root of both sides, we get:

v = sqrt(196.2)

v = 14.0 m/s

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--The complete Question is, A ball is dropped from a height of 10 meters. What is its velocity just before it hits the ground, assuming no air resistance? (Assume that the acceleration due to gravity is 9.81 m/s^2)

Hint: You can use the equation v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity (which is zero in this case), a is the acceleration due to gravity, and s is the distance traveled.--

question 1 is option D

question 2 is option B

Explanation for question 1: The quantum theory of light, as proposed by Albert Einstein, explained the outcome of the photoelectric effect experiment by proposing that light travels in discrete packets of energy called photons, and that the energy of a photon is directly proportional to its frequency. In the photoelectric effect, the material only absorbs photons with a certain minimum frequency, called the threshold frequency. When a photon with sufficient energy is absorbed by an electron in the material, the electron is ejected with kinetic energy equal to the energy of the photon minus the energy required to overcome the binding energy of the electron to the material. This explains why increasing the intensity of the light does not increase the kinetic energy of the ejected electrons, but increasing the frequency of the light above the threshold frequency does.

Explanation for question 2: When an electric current is passed through a gas or vapor, some of the electrons in the gas are excited to higher energy levels. When these electrons return to their lower energy levels, they emit light in the form of photons. The energy of the emitted photons corresponds to the energy difference between the excited state and the lower energy state. Different elements have different electron configurations and energy levels, and therefore they emit light at different wavelengths (colors) when excited.

For example, sodium vapor lamps emit yellow light because the excited sodium atoms emit photons with a characteristic wavelength in the yellow part of the spectrum. Mercury vapor lamps emit blue-green light because the excited mercury atoms emit photons with a characteristic wavelength in the blue-green part of the spectrum.

The acceleration will be 0.2m/s^2 while the velocity will be 1m/s

Force = 300N

Mass = 1500kg

Time = 5 seconds

We know that

Force = ma

a = F/m

a = 300/1500

a = 0.2 m/s^2

Also, the expression for Velocity is given as

Ft = mv

300*5 = 1500*v

Making velocity the subject of the formula we have

1500 = 1500*v

v = 1 m/s

The rate of change of an object's velocity with respect to time is defined as acceleration.

Acceleration implies that the speed is changing, but this is not always the case. When an object moves in a circular path at a constant speed, it is still accelerating because its velocity direction changes.

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When the segment is shrunk to one-third of its original length, the ratio of the final linear charge density (?f) to the initial linear charge density (?i) is f/?i = 3

This is because the charge is the same, but the length of the segment has decreased to one-third of its original length. Therefore, the charge density has increased by a factor of 3.

The ratio of the electric force on the proton after the segment is shrunk (Ff) to the force before the segment was shrunk (Fi) is also 3. This is because the electric force is directly proportional to the charge density, so if the charge density increases by a factor of 3, the electric force will also increase by a factor of 3.

If the original segment of wire is stretched to 15 times its original length, the charge density will decrease by a factor of 15. To keep the linear charge density unchanged, we need to add 14 times the original charge to the wire. This is because the original charge will be spread out over 15 times the original length, so we need to add 14 times the original charge to make up for the decrease in charge density.

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The kinetic energy of the flywheel after 1 minute of rotation, given that it has a mass of 50 and radius of 40 cm is 32.4 KJ (Option D)

We'll begin by obtaining the velocity of the flywheel. This is shown below:

v = at

v = 0.6 × 60

v = 36 m/s

Finally, we shall determine the kinetic energy of the flywheel. Details below:

KE = ½mv²

KE = ½ × 50 × 36²

KE = 25 × 1296

KE = 32400 J

Divide by 1000 to express in KJ

KE = 32400 / 1000

KE = 32.4 KJ

Thus, the kinetic energy is 32.4 KJ (Option D)

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10.0g of ice at -20.0°C needs 120°C of steam in order to become steam, so: \(9.92 *10^{6} J\)

When a given mass of ice at -20.0°C is converted into steam at 120°C, the following processes take place:

1. The ice absorbs heat to raise its temperature from -20.0°C to 0°C.

2. The ice then melts to form water at 0°C.

3. The water absorbs heat to raise its temperature from 0°C to 100°C.

4. The water then evaporates to form steam at 120°C.

The amount of heat absorbed by the ice is calculated using the equation Q = m * c * ΔT, where  ΔT is the change in temperature, c is the specific heat capacity, and m is the mass.

The amount of heat that the ice absorbs during Process 1 is:

\(Q = 10.0g * 2060J/kg\°C * (0 - (-20.0))\°C = 4.12 * 10^4 J\)

The latent heat of fusion of ice is equal to the amount of heat absorbed by the water in process 2:

\(Q = 10.0g * 3.34 * 10^5 J/kg \\= 3.34 *10^5 J\)

The quantity of heat that the water absorbed in step three is:

\(Q = 10.0g * 4200J/kg\°C * (100 - 0)\°C \\= 4.2 * 10^6 J\)

The latent heat of vaporisation of steam is equal to the amount of heat absorbed by the steam in Process 4:

\(Q = 10.0g * 2.26 * 10^{6}J/kg \\\\ =2.26 * 10^{6 }J\)

The total amount of heat added to the 10.0g of ice at -20.0°C to convert it into steam at 120°C is:

\(Q = 4.12 * 10^4 J + 3.34 * 10^5 J + 4.2 * 10^6 J + 2.26 * 10^{6} J \\\\= 9.92 *10^{6} J\)

As a result, the total heat required to turn 10.0g of ice at -20.0°C into steam at 120°C is: \(9.92 *10^{6} J\)

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