Two projectiles a and b are thrown with same speed but at angle of 40° and 50° with the hohorizont. The horizontal range of A will be?

The net force on particle q₂ is 1.05 x 10¹³ N, directed towards particle q1.

To find the net force on particle q₂, we need to calculate the force between q₁ and q₂, and the force between q₂ and q₃, and then add these two forces together.

The force between two point charges can be calculated using Coulomb's law, which states that

F = k × q₁× q₂ / r²

where F is the force, k is Coulomb's constant (9.0 x 10⁹ N m² / C²), q₁ and q₂ are the magnitudes of the charges, and r is the distance between the charges.

The force between q₁ and q₂ is

F₁ = k × q₁ × q₂ / r₁²

where r₁ = 0.10 m.

Substituting the values, we get

F₁ = 9.0 x 10⁹ N m² / C²  × 8.0 C  × 3.5 C / (0.10 m)² = 2.52 x 10¹³ N

The force between q₂ and q₃ is

F₂ = k  × q₂  × q₃ / r₂²

where r₂ = 0.15 m.

Substituting the values, we get

F₂ = 9.0 x 10⁹ N m² / C²  × 3.5 C  × (-3.5 C) / (0.15 m)² = -1.47 x 10¹³ N

Note that the negative sign indicates that the force is attractive, since q₂ and q₃ have opposite signs.

The net force on q₂ is the vector sum of F₁ and F₂

\(F_{net}\) = F₁ + F₂ = 2.52 x 10¹³ N - 1.47 x 10¹³ N = 1.05 x 10³ N

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Answer:

0kgm/s

Explanation:

Given parameters:

Mass of the passenger  = 48.5kg

Unknown:

Momentum  = ?

Solution:

The momentum of a body is the quantity of motion a body possesses. A body not in motion has no momentum.

Mathematically;

  Momentum = mass x velocity

  So;

Since the train is stopped, velocity  = 0m/s

        Momentum  = 48.5 x 0 = 0kgm/s

We will have the following:

a. The gravitational potential energy will be:

So, the gravitational potential energy of C is 882 J.

b. The velocity of C right before it hits the ground will be:

So, the velocity will be approximately 10.84 m/s.

c.

1. We will have that Eg at the initial position will be: B < C

2. Vfinal upon impact with ground: B = C

3. Ek right before hitting he ground: B < C

f.

1. Eg: A > B

2. V final: A > B

3. Ek: A > B

4. V at 2 meters above the ground: A > B

5. Total energy at 2 m above the ground: A > B.

Answer:

Jared has earned 23% of the $52 he needs to buy a new jacket. Find 23% of $52.

Which expression can you use to find 23% of 52?

✔ 0.23 × 52

23% of $52 is $

✔ 11.96

.

An easy way to check your answer is to use the friendly

✔ 25%

and divide 52 by

✔ 4

to get

✔ 13

.

Explanation:

Answer:

B, the number of protons.

Explanation:

It is the number of protons found in the nucleus of the atom.

Answer:

Explanation:

Your body weighs more at the pole for two important reasons. Both have to do to the spin of the earth on its axis.

Because of its spin the earth is thicker around the equator than it is through the poles. This means that when you stand on the equator, you are farther away from the center of earth than you would be at the poles. As gravity decreases with the inverse of the square of distance, gravity will be weaker at the equator.

As you are also spinning with the earth, you will have a required centripetal acceleration and force to keep you attached to the ground, This force decreases the effect of gravity so again, you would weigh less at the equator.

A motion diagram of this scenario would show a ball being thrown upward and then falling back down, bouncing off the floor before being caught at the same height it was released from.

At the highest point, the ball would have a velocity of 0 m/s, since it has reached its maximum height and its velocity has changed from positive to negative.

This can be determined by the fact that the ball is momentarily at rest at the highest point, and the concept of conservation of energy, since the total energy of the ball must be conserved throughout the entire motion.

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The option that represents what the magnetic field look like above the North pole is an arrow that decreases as we go up and points up (E)

The magnetic field lines of a magnet point away from the north pole and towards the south pole. The field lines are strongest at the poles and weaken as you move away from the poles.

So, the arrow that represents the magnetic field above the north pole will be pointing up, but it will become smaller and smaller as you go up.

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1) The photoelectric effect is the phenomena by which, the metals release electrons when they are exposed to electromagnetic radiation with the suitable frequency. The photoelectrons are the electrons that are released in this process.

So, the statement is true.

2) In a particle model, energy transfer can be done through many ways such as:

The energy jumps between the particles in the form of photons.

Electrons can absorb or emit energy during energy transfer.

The energy is transferred between different objects in the form of photons.

So, all of them are true.

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Answer:  

Hence the answer is E inside \(= KQr_{1} /R^{3}\).

Explanation:  

E inside \(= KQr_{1} /R^{3}\)  

so if r1 will be the same then  

E  \(\begin{bmatrix}Blank Equation\end{bmatrix}\) proportional to 1/R3  

so if R become 2R  

E becomes 1/8 of the initial electric field.

Answer:

The electric field is E/8.

Explanation:

The electric field due to a solid sphere of uniform charge density inside it is given by

\(E =\frac{\rho r}{3}\)

where, \(\rho\) is the volume charge density and r is the distance from the center.

For case I:

\(\rho = \frac{Q}{\frac{4}{3}\pi R^3}\)

So, electric field at a distance r is

\(E = \frac { 3 Q r}{3\times 4\pi R^3}\\\\E = \frac{Q r}{4\pi R^3}\)

Case II:

\(\rho = \frac{Q}{\frac{4}{3}\pi 8R^3}\)

So, the electric field at a distance r is

\(E' = \frac { 3 Q r}{3\times 32\pi R^3}\\\\E' = \frac{Q r}{8\times 4\pi R^3}\\\\E' = \frac{E}{8}\)

The density of water is approximately 1 g/cm^3. Therefore, the volume of 2800 g of water would be 2800 cm^3 because density is mass/volume, and so volume is mass/density.

Since this volume is inside a cubic box, the length of each side of the cube (a, for instance) could be found by taking the cubic root of the volume. This is because the volume of a cube is calculated by a^3 (length of one side cubed). Hence, a = cube root of 2800 cm^3 ≈ 14.1 cm.

Converting centimeters to meters (as 1 meter is equal to 100 centimeters), we get approximately 0.141 meters.

So the filled cubic box has a side length of approximately 0.141 m.

The centripetal acceleration of the mass is 10 m/s².

The centripetal acceleration of the mass when it is at the lowest position is calculated as follows;

Tsinθ = ma - mg

where;

when the mass is at the lowest position, θ = 0

The centripetal acceleration of the mass is calculated as follows;

T sin (0) = ma - mg

0 = ma - mg

ma = mg

a = g

Given that g, acceleration due to gravity = 10 m/s²

Hence, a = 10 m/s²

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The complete question is below:

A mass m is suspended by a massless string forming a simple pendulum of length 2.0 m. The string of the pendulum is initially at an angle of 60° with the vertically downward direction when the mass is released from rest. Calculate the centripetal acceleration of the mass when it is at the lowest position ( take g = 10 m/s²).

The displacement of the train after 2.23 seconds is 25.4 m.

The resultant velocity of the train is calculated as follows;

R² = vi² + vf² - 2vivf cos(θ)

where;

R² = 8.81² + 9.66² - 2(8.81 x 9.66) cos(76)

R² = 129.75

R = √129.75

R = 11.39 m/s

The displacement is calculated as follows;

Δx = vt

Δx = 11.39 m/s x 2.23 s

Δx = 25.4 m

Thus, the displacement of the train after 2.23 seconds is 25.4 m.

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Because the mass and displacement are already given in Kg and m, respectively, in the first part of your question, there is no need to convert them. However, in the second part of your question, you must use the given equation to calculate the spring constant.

if the table data is given in grams and  cm you have to convert it using the following conversion,

1. To convert grams to kilograms, we divide the mass values by 1000.

2. To convert centimeters to meters, we divide the displacement values by 100.

But here in the given table it's already given the mass in kg and the displacement in meters (m). so no need to convert it.

Now comes the second part of your question,

To calculate the spring constants for the given data, we can use the equation:

k = -mg/Δx

where:

k is the spring constant (in N/m),

m is the mass (in kg), and

Δx is the displacement of the spring (in m).

Let's calculate the spring constants using the provided data:

Mass (kg): 0.05  0.1  0.2  0.3  0.4  0.5  0.6

Displacement of Spring (m): 0.012  0.027  0.065  0.1  0.135  0.17  0.199

Using the equation

k = -mg/Δx,

we can calculate the spring constant for each data point:

For the first data point (m = 0.05 kg, Δx = 0.012 m):

k = -0.05 kg * 9.8 m/s² / 0.012 m

k ≈ -40.833 N/m

Similarly, we can calculate the spring constants for the other data points:

For the mass of 0.05 kg, the spring constant is approximately -40.833 N/m.

For the mass of 0.1 kg, the spring constant is approximately -18.519 N/m.

For the mass of 0.2 kg, the spring constant is approximately -6.154 N/m.

For the mass of 0.3 kg, the spring constant is approximately -3.267 N/m.

For the mass of 0.4 kg, the spring constant is approximately -2.222 N/m.

For the mass of 0.5 kg, the spring constant is approximately -1.716 N/m.

For the mass of 0.6 kg, the spring constant is approximately -1.449 N/m.

Therefore, In the first part of the question, there is no need to convert the mass into kg and the displacement cm into m because it is already given in kg and m respectively, and in the second part question you have to calculate the spring constant using the given equation.

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Answer:

-12.1

Explanation:

i’m almost sure this is it, i’m checking my old answers

if not let me know and i’ll give you some more answers

Explanation:

gravitational potential energy = mgh (must be in S.I. unit)

m= 0.4 kg ; g= 10m/s (gravitational acceleration occurs); h=9.2 m

hence mgh=0.4×10×9.2= 36.8J

unit for energy is joules and since the variables are in S.I. unit, we can use Joules as the final unit for measurement

Answer:

36.06 J if you define g = 9.8 m/s² or 36.8 J if you define g = 10 m/s²

Explanation:

Potential Energy = Mass x Gravitational Acceleration x Height

It can be expressed as \(\displaystyle{PE = mgh}\) where PE is potential energy, m is mass, g is gravitational acceleration and h is height.

In this case, we know mass is 0.40 kg and height of 9.2 m as well as gravitational acceleration is defined to be 9.8 m/s² (You can also define g = 10 m/s²)

Therefore, substitute given information in formula:

\(\displaystyle{PE=0.40 \ \times \ 9.8 \ \times 9.2 }\\\\\displaystyle{PE=36.06 \ J}\)

With g = 10 m/s², you'll get:

\(\displaystyle{PE = 0.40 \ \times 10 \ \times 9.2}\\\\\displaystyle{PE = 36.8 \ J}\)

Note that J is for joule unit.

Therefore, the answer is 36.06 J if you define g = 9.8 m/s² or 36.8 J if you define g = 10 m/s² - both work.

The electrical change of oxygen ion is -2

An ion is an atom or molecule that has an unequal number of protons and electrons, which results in a net electrical charge. When an oxygen atom gains two electrons, it becomes negatively charged because electrons have a negative charge. This is because the number of negatively charged electrons now exceeds the number of positively charged protons in the nucleus of the atom. Therefore, the electrical charge of the oxygen ion is -2.

The electrical charge of an ion is represented by the symbol "n", which stands for the number of electrons gained or lost by the atom. In this case, the oxygen atom has gained two electrons, so n = -2. This is represented by the formula: O^2-.

In summary, when an oxygen atom gains two electrons, it becomes negatively charged and forms an oxygen ion. The electrical charge of the oxygen ion is represented by the symbol "n" and is equal to -2, which is reflected in the formula O^2-. This means that the oxygen ion has a net charge of -2, which reflects the excess of negatively charged electrons in the ion.

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The reading on a vernier caliper can be represented as 45.75mm.

1. Understand the components of a vernier caliper: A vernier caliper consists of two main scales - the main scale and the vernier scale. The main scale is typically graduated in millimeters, while the vernier scale is a smaller scale that slides along the main scale.

2. Locate the main scale: Identify the main scale on the vernier caliper. The main scale is usually marked on the fixed jaw of the caliper and extends in a linear fashion.

3. Identify the vernier scale: The vernier scale is attached to the movable jaw of the caliper. It slides along the main scale and consists of smaller divisions.

4. Align the zero marks: Close the jaws of the caliper and ensure that the zero marks on both the main and vernier scales are aligned.

5. Determine the main scale reading: Read the main scale value that aligns with the zero mark on the vernier scale. In this case, the main scale reading will be 45mm.

6. Locate the vernier scale reading: Examine the vernier scale and identify the division on the vernier scale that lines up perfectly with a division on the main scale. This will give you the additional measurement beyond the main scale reading.

7. Determine the vernier scale reading: Find the division on the vernier scale that aligns with a division on the main scale. The value of this vernier division corresponds to the additional measurement. In this case, the vernier scale reading will be 0.75mm.

8. Add the main scale and vernier scale readings: Combine the main scale reading and the vernier scale reading to get the final measurement. In this case, the final reading will be 45.75mm.

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The hammer must be moving at a speed of 12.0 m/s in order to just barely ring the bell.

When the hammer strikes the target, it transfers its kinetic energy to the metal piece, causing it to move upwards. This means that the kinetic energy of the hammer is converted into potential energy (PE) of the metal piece, given by:

PE = mgh

where m is the mass of the metal piece, g is the acceleration due to gravity, and h is the height of the bell above the metal piece. Substituting the given values, we get:

PE = (0.400 kg)(9.81 m/s²)(5.00 m) = 19.62 J

Since 25.0% of the hammer's kinetic energy is used to do this work, we can write:

0.25KE_hammer = PE

where KE_hammer is the kinetic energy of the hammer before the collision. Solving for KE_hammer, we get:

KE_hammer = 4PE = 4(19.62 J) = 78.48 J

Finally, we can use the formula for kinetic energy to find the velocity (v) of the hammer:

KE_hammer = (1/2)mv²

where m is the mass of the hammer. Rearranging and substituting the given values, we get:

v = sqrt(2KE_hammer/m) = sqrt(2(78.48 J)/(9.00 kg)) = 12.0 m/s

The hammer must be moving at a speed of 12.0 m/s in order to just barely ring the bell.

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Answer:

Explanation:

The bullet travels for a time of

180 m/800 m/s = 0.225 s

Assuming the original velocity was horizontal

h = ½(-9.8)0.225² = 0.25 m

The bullet will accelerate as it descends at the same rate  that it slowed down as it rose, since gravity is constant (i.e., it doesn't vary). It will therefore be travelling at the same speed as when it was first fired from the gun when it reaches the bottom.

As soon as the gun is discharged, the propellant in the barrel expands, speeding up the bullet. The bullet is no longer propelled once it exits the muzzle since the gasses can now escape outside and the bullet is now encountering air resistance. Therefore, the muzzle velocity at the barrel's exit is the highest it can be.

A bullet thrown straight up on Earth would be able to reach a maximum height of around three kilometres (about 10,000 feet (ca. 3 km)), assuming there is no wind, before falling back to Earth.

Therefore, The bullet travels for a time of 180 m/800 m/s = 0.225 s assuming the original velocity was horizontal h = ½(-9.8)0.225² = 0.25 m.

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Answer:

The  wavelength is  \(\lambda = 1029 nm\)

Explanation:

From the question we are told that

    The  wavelength of the left light is  \(\lambda_o = 500 nm = 500 *10^{-9} \ m\)

      The  voltage across A  and  B is  \(V_{AB } = 1.2775 \ V\)

Let the stopping potential  at A  be \(V_A\) and the electric potential at B  be  \(V_B\)

The voltage across A and B is mathematically represented as

      \(V_{AB} = V_A - V_B\)

Now  According to Einstein's photoelectric equation the stopping potential at A for the ejected electron from the left side  in terms of electron volt is mathematically represented as

        \(eV_A = \frac{h * c}{\lambda_o } - W\)

Where  W is the work function of the metal

             h is the Planck constant with values  \(h = 6.626 *10^{-34} \ J \cdot s\)

             c  is the speed of light with value \(c = 3.0 *10^{8} \ m/s\)

And  the stopping potential at B for the ejected electron from the right side  in terms of electron volt is mathematically represented as

          \(eV_B = \frac{h * c}{\lambda } - W\)

So  

      \(eV_{AB} = eV_A - eV_B\)

=>    \(eV_{AB} = \frac{h * c}{\lambda_o } - W - [\frac{h * c}{\lambda } - W]\)

=>   \(eV_{AB} = \frac{h * c}{\lambda_o } - \frac{h * c}{\lambda }\)

=>   \(\frac{h * c}{\lambda } = \frac{h * c}{\lambda_o } -eV_{AB}\)

=>  \(\frac{1}{\lambda } =\frac{1}{\lambda_o } - \frac{ eV_{AB}}{hc}\)

Where e is the charge on an electron with the value  \(e = 1.60 *10^{-19} \ C\)

=>   \(\frac{1}{\lambda } = \frac{1}{500 *10^{-9} } - \frac{1.60 *10^{-19} * 1.2775}{6.626 *10^{-34} * 3.0 *10^{8}}\)      

=>  \(\frac{1}{\lambda } = 9.717*10^{5} m^{-1}\)  

=>   \(\lambda = 1.029 *10^{-6} \ m\)

=>   \(\lambda = 1029 nm\)

The force of gravity acting on the 23 Kg object in the diagram is 225.4 N

The force of gravity is defined as follow:

Force of gravity (F) = mass (m) × acceleration due to gravity (g)

Using the above formula, we can easily obtain the force gravity acting on the 23 Kg object. This is shown below:

Force of gravity (F) = mass (m) × acceleration due to gravity (g)

Force of gravity = 23 Kg × 9.8 m/s²

Force of gravity = 225.4 N

Thus, from the calculation made above, we can conclude that the gravitaional force is 225.4 N

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Answer:

Friction is the resistive force. when a driver applies brakes, the wheels stop rotating and there is friction between the tyres and the rough surface of the road. (but if you ask why it moves 3.5 m after braking, that is due to the intertia of the moving car)

Answer:

The angular momentum of a cylinder, when it is rotating with constant angular velocity is Lini =Iωi

. When two cylinders are added to the rotating cylinder, which are identical in their dimensions, the moment of inertia of the entire system increases (since mass increases). The final moment of inertia will be 3I

Since friction exist, all the cylinders start rotating with same angular velocity, the new angular velocity can be calculated using conservation of angular momentum

Thus, Iωi =3Iωf ⟹ωf =ωi/3 = 0.33ωi

The resultant of the displacement is 336.5m

The process of splitting a vector into its components is called resolution of the vector. The vectors are splitted into vertical and horizontal component.

For the first displacement;

The vertical component = - 150 sin45 = -106.1 m

The horizontal component = - 150 cos 45° = -106.1 m

For the second displacement;

The vertical displacement = - 85sin90 = -85

The horizontal component = 0

For the third displacement;

The vertical displacement = 550 sin55 = 450.5

The horizontal displacement = 550 cos 55 = 315.5

Sum of vertical component = 450.5-85-106.1 = 263.4

sum of horizontal component = 315.5 -106.1 = 209.4

Using Pythagorean theorem

R = √ 263.4² + 209.4²

R = √113227.92

R = 336.5m

The resultant angle = tan^-1( 263.4/209.4)

= tan^-1(1.26)

= 51.56°

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