How much of a 500 g sample of potassium-42 is left after 62.0 hours if its half-life is 12.4hours?

The electrostatic force of attraction between the proton and electron is 4.2 x 10⁻⁸N.

The gravitational force between the proton and electron is 1.9 x 10⁻⁴⁷N.

a) Charge on proton = charge on electron = q = 1.6 x 10⁻¹⁹C

Distance between the proton and electron, r = 7.4 x 10⁻¹¹m

The electrostatic force of attraction between the proton and electron is given by,

F = 1/4πε₀(q²/r²)

F = 9 x 10⁹ x (1.6 x 10⁻¹⁹)²/(7.4 x 10⁻¹¹)²

F = 9 x 10⁹ x 2.56 x 10⁻³⁸/54.76 x 10⁻²²

F = 4.2 x 10⁻⁸N

b) Mass of the electron, m₁ = 9.1 x 10⁻³¹kg

Mass of the proton, m₂ = 1.67 x 10⁻²⁷kg

Distance between the proton and electron, r = 7.4 x 10⁻¹¹m

The gravitational force between the proton and electron is given by,

F = Gm₁m₂/r²

F = 6.67 x 10⁻¹¹x 9.1 x 10⁻³¹x 1.67 x 10⁻²⁷/(7.4 x 10⁻¹¹)²

F = 1.9 x 10⁻⁴⁷N

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Answer:

A basketball sitting still in a players hands

Explanation:

The other 3 answers have the ball in motion (going towards the basket, bouncing, and rolling) so that would be kinetic energy.

When the basketball is sitting in the player's hands, it has the potential to be in motion.

Answer:

it is D not B it D

Explanation:

Answer:

same and unique

Explanation:

scientist use same laws eg newton law everywhere in the world.

As per the given data, the centripetal force acting on the stone is 18 N.

A force that causes a body to follow a curved path is known as a centripetal force.

The centripetal force always points in a direction that is opposite to the motion of the body and in the general direction of the instantaneous center of curvature of the route.

To calculate the centripetal force acting on the stone, we can use the following formula:

F = (m * \(v^2\)) / r

Where F is the centripetal force, m is the mass of the stone, v is the tangential velocity of the stone, and r is the radius of the circular path.

In this case, we are given the mass of the stone (m = 500g = 0.5kg), the radius of the circular path (r = 50cm = 0.5m), and the angular velocity of the stone (ω = 12 rad/s).

To find the tangential velocity of the stone, we can use the formula:

v = r * ω

Substituting the given values, we get:

v = 0.5m * 12 rad/s = 6 m/s

Now we can substitute the values for m, v, and r in the formula for centripetal force:

F = (m * \(v^2\)) / r = (0.5kg * \((6 m/s)^2\)) / 0.5m = 18 N

Therefore, the centripetal force acting on the stone is 18 N.

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To solve this problem, we will use Newton's second law of motion.

Newton's second law states that the force is equal to mass times acceleration.

Hence, the formula is as follows:Force = mass x acceleration

To calculate the force, we need to know the mass of the cart and the acceleration at which it is being towed.

As per the question, the cart's mass is 400 kg, and it is being accelerated at a rate of 3 m/s^2.

Hence, the force required to accelerate the cart can be calculated as follows:

Force = mass x acceleration \(Force = 400 kg\times3 m/s^2\)

\(Force = 1200 N\)

Therefore, the tension in the rope is 1200 N.

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Each of the five friends needs to pay £12 to cover the cost of their own meals and contribute towards the birthday person's meal. Using mean allows us to distribute the cost equally among the friends, ensuring a fair division of expenses for the meal.

To determine how much each of the five friends needs to pay, we can use the concept of averages (mean) and divide the total cost by the number of people paying.

In this scenario, the total cost of the meal for 6 people is £12 per person. Since the other 5 friends have decided to pay for the birthday person's meal, they will collectively cover the cost of their own meals plus the birthday person's meal.

To calculate the total cost covered by the five friends, we can subtract the cost of one person's meal (since the birthday person's meal is being paid by the group) from the total cost. The cost of one person's meal is £12.

Total cost covered by the five friends = Total cost - Cost of one person's meal

= (£12 x 6) - £12

= £72 - £12

= £60

Now, to find out how much each of the five friends needs to pay, we divide the total cost covered by the five friends (£60) by the number of friends (5).

Amount each friend needs to pay = Total cost covered by the five friends / Number of friends

= £60 / 5

= £12

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The Sun’s effect on Earth change if the Sun was half its mass, the pull of gravity from the Sun would only be half as strong and is denoted as option A.

This is referred to as the universal force of attraction which acts on all matters and is dependent on some parameters such as mass etc.

The increase in mass denotes a corresponding increase in gravity and vice versa which is therefore the reason why if the Sun was half its mass, then the pull of gravity from the Sun would only be half as strong.

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Answer:(vi^2+d)^2=vf+a^2+2t

Explanation:

ANSWER

4) The illuminance will be quartered.

EXPLANATION

According to the inverse square law of light, the illuminance of a light source is inversely proportional to the square of the distance from the source.

Mathematically:

where E = illuminance; r = distance from the light source

If the distance is doubled, then we have that:

As we can see, the illuminance on the object will be quartered if the distance from the light source is doubled.

In order to calculate the power used, we can use the formula:

Where V is the voltage and I is the current.

So, using V = 10 and I = 5.5, we have:

So the power used by the flashlight is 55 W.

The kinetic energy of the brick equal the elastic potential energy at the top of the hill. Using this, the speed of the brick is 14 m/s.

The elastic potential of a spring is directly proportional to the squire of the displacement.

Then,

p = 1/2 k x²

Given that, spring constant k = 500 N/m

height of the hill x = 2 m

weight of the load = 100 N

then mass = 100N/9.8 m/s² =10.20 Kg.

At the top of the hill, kinetic energy of the hill is equal to the elastic potential.

then, 1/2 mv² =  1/2 k x²

speed v of the brick  = √kx²/m

v = √(500 N/m × 2 m²/10.20 kg)

  = 14 m/s.

Therefore, the speed of the brick at the top of the hill is 14 m/s.

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Answer:

True

Explanation:

I had the same question.

(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 vectors addition permits locating the perfect result for the sum of the two vectors in option B).  See attached and the vector is directed to the right and up.

Vector addition is the operation of adding or extra vectors together into a vector sum. The so-known as parallelogram regulation gives the rule for vector addition of or greater vectors. for two vectors and, the vector sum is received via placing them head to tail and drawing the vector from the loose tail to the unfastened head.

A vector is an amount or phenomenon that has impartial residences: importance and direction. The time period also denotes the mathematical or geometrical representation of the sort of quantity. Examples of vectors in nature are velocity, momentum, force, electromagnetic fields, and weight.

Vectors are used in technological know-how to describe something that has a direction and a magnitude. they're commonly drawn as pointed arrows, the length of which represents the vector's importance

Disclaimer: your question is incomplete, please see below for the complete question.

The image shows the complete question.

Which vector is the sum of vectors à and b?

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Answer:

spring D stretches the weakest

#1

The kinetic energy decreases

#2

This is because of law of conservation of linear momentum .

The momentum is conserved

So the velocity of ball decreases than before .

So kinetic energy also decreases

#3 and #4

Kinetic energy of the can increases as after the collision the velocity of the can increases so the kinetic energy also increases

Using the formula for the Doppler effect:

f' = (v + vr) / (v + vs) * f

Given:

Source frequency (horn): f = 625 Hz

Speed of sound: v = 343 m/s (approximate value at room temperature)

The velocity of the receiver, vr, is zero because the person waiting at the crosswalk is stationary.

The velocity of the source, vs, is the speed of the car, which is given as 9.0 m/s.

Thus:

f' = (v + vr) / (v + vs) * f

= (343 m/s + 0) / (343 m/s + 9.0 m/s) * 625 Hz

= (343 m/s) / (352 m/s) * 625 Hz

≈ 609 Hz

Therefore, the person waiting at the crosswalk hears a frequency of approximately 609 Hz.

(2)Using the same Doppler effect formula:

f' = (v - vr) / (v - vs) * f

In this case, the velocity of the receiver, vr, is still zero because the person remains stationary.

The velocity of the source, vs, is now negative, indicating that the car is moving away from the person.

Thus:

f' = (v - vr) / (v - vs) * f

= (343 m/s + 0) / (343 m/s - (-9.0 m/s)) * 625 Hz

= (343 m/s) / (352 m/s) * 625 Hz

≈ 609 Hz

In other words, as the car moves away from the person, they would still hear a frequency of approximately 609 Hz.

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Answer: put them in the microwave

Explanation:

Answer: Should the sabre tooth curriculum really exist at the moment? As far as I am concerned, the sabre tooth program should remain, because our school system needs to help people know how to do complex activities on their own and we let them do activities that will help them develop their brains as well as their skills.

Great schools promote better teaching because they have the most experience of teaching practice and are accountable for executing the instruction in the classroom. Teacher engagement is also vital for the effective and substantive implementation of the curriculum.

Sources: files.eric.ed.gov and James Kennedy Monash

We are given two points on the distance-time graph: (1, 40) and (3,130)

This means that:

At time 1 hour, the distance traveled was 40 km

At time 3 hours, the distance traveled was 130 km

We want to find the average speed during this 2 hour interval (from 1 hour to 3 hours).

Average speed is defined as:

Average Speed = Change in Distance / Change in Time

The change in distance is the distance traveled from 1 hour to 3 hours, which is 130 km - 40 km = 90 km

The change in time is 3 hours - 1 hour = 2 hours

Average Speed = 90 km / 2 hours

= 45 km/hr

Therefore, the average speed during this interval of time is 45 km/hr.

Answer:

Having the inside dimensions (ID) and the outside dimensions (OD) will allow you to figure out the wall thickness on tubing. You would need to subtract the ID from the OD and then divide by two. This number is the wall thickness.

Explanation:

Answer:

equator

Explanation:

in south & north pole you could have 20+ hours daylight or night, everyday!

In general, option c - warming it up on the stove - is often an effective method to increase the reaction rate.

Increasing the temperature of a reaction generally leads to faster reaction rates. This is because higher temperatures provide more thermal energy to the reactant particles, causing them to move faster and collide more frequently. The increased collision frequency and energy lead to more successful collisions and a higher likelihood of effective molecular interactions, which speeds up the reaction. On the other hand, options a and b - putting it in the fridge where it is cold or covering it with a blanket to make it dark - are unlikely to have a significant effect on the reaction rate. While temperature can influence reaction rates, cooling the reaction or making it dark typically reduces the kinetic energy of the particles, resulting in slower reaction rates. Option d - there is nothing you can do to change the speed of the reaction - is not accurate. The reaction rate can be influenced by various factors such as temperature, concentration, catalysts, and surface area, among others. By manipulating these factors, it is often possible to control and change the speed of a reaction. Hence option c, is correct

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Answer:

c. Total energy

Explanation:

An "orbit" is a path for an object to follow. An example of an object is the "satellite."

At certain points in the orbit, the satellite increases its speed and decreases its speed in relation to the gravity caused by the Earth. As it moves farther away from the Earth, its speed slows down. So, this means that the kinetic energy changes. It also gains and loses height which is responsible for the changes occurring regarding potential energy. This is true for elliptical motion of satellites.

However, the total mechanical energy (TME) of the satellite remains the same or is unchanged (elliptical/circular).

Answer:

the initial speed of the arrow before joining the block is 89.85 m/s

Explanation:

Given;

mass of the arrow, m₁ = 49 g = 0.049 kg

mass of block, m₂ = 1.45 kg

height reached by the arrow and the block, h = 0.44 m

The gravitational potential energy of the block and arrow system;

P.E = mgh

P.E = (1.45 + 0.049) x 9.8 x 0.44

P.E = 6.464 J

The final velocity of the system after collision is calculated as;

K.E = ¹/₂mv²

6.464 = ¹/₂(1.45 + 0.049)v²

6.464 = 0.7495v²

v² = 6.464 / 0.7495

v² = 8.6244

v = √8.6244

v = 2.937 m/s

Apply principle of conservation of linear momentum to determine the initial speed of the arrow;

\(P_{initial} = P_{final}\\\\mv_{arrow} + mv_{block} = (m_1 + m_2)V\\\\0.049(v) + 1.45(0) = (0.049 + 1.45)2.937\\\\0.049v = 4.4026\\\\v = \frac{4.4026}{0.049} \\\\v = 89.85 \ m/s\)

Therefore, the initial speed of the arrow before joining the block is 89.85 m/s

The arrow moving as the speed of "76.36 m/s".

According to the question,

By using the conservation of energy, we have

→                \(K.E=P.E\)

→ \(\frac{1}{2} (m_1+m_2)v_2^2= (m_1+m_2)gh\)

or,

→                    \(v_2 = \sqrt{2mgh}\)

By substituting the values, we have

→                         \(= \sqrt{2\times 9.8\times 0.44}\)

→                         \(=2.469 \ m/s\)

Now,

By using the conservation of momentum, we get

→ \(m_1 v_1 = (m_1+m_2) v_2\)

or,

→      \(v_1 = \frac{(m_1+m_2)v_2}{m_1}\)

            \(= \frac{1.45+0.049}{0.049}\times 2.469\)

            \(= 30.6\times 2.496\)

            \(= 76.36 \ m/s\)

Thus the above approach is correct.  

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C) a bicyclist riding up a steep hill

The metaphor for a system with rising gravitational potential energy is "a bicyclist riding up a steep hill." Let's get into greater detail:

A cyclist faces resistance from gravity as they ride up a steep slope. The cyclist's elevation, or height above the ground, rises as they cycle and climb uphill. Gravity is pulling the cyclist down the hill by exerting downward force. The cyclist must apply force to the pedals in order to move forward and overcome the pull of gravity. In order to do this, the bicyclist must transform chemical energy from their body into mechanical energy. The distance of the cyclist from the centre of the Earth grows as they ride up the hill. The height and mass of an object affect its gravitational potential energy. In this scenario, as the bicyclist's height rises, their gravitational potential energy also rises.

     Due to the higher elevation, the energy input from the biker is stored as increased potential energy. When the bicycle descends the hill or does work, this potential energy can be transformed back into kinetic energy or other types of energy.

Answer:

its the number of something repeating,

For example, a human heart may beat at a frequency of 68 beats per minute

In order to determine which of the two solutions of salt water is more concentrated, we need to first understand what concentration means and how it is measured. Concentration refers to the amount of solute dissolved in a given amount of solvent. It is typically measured in units of mass per volume, such as grams per liter (g/L) or milligrams per milliliter (mg/mL). so The second solution is more concentrated

When comparing the concentration of two solutions, the one with a higher concentration has more solute dissolved in the same amount of solvent. Therefore, in the picture provided, we can determine which solution is more concentrated by looking at the relative amounts of solute in each solution.If the solutions have the same concentration, then they must have the same amount of solute dissolved in the same amount of solvent. From the picture, we can see that both solutions are in the same size container and have the same amount of solvent (water) in them. Therefore, we can conclude that they have the same concentration of salt.The amount of solute dissolved in a solution can be increased by either adding more solute or by reducing the amount of solvent. If we were to add more salt to one of the solutions, we would increase the concentration of that solution. Alternatively, if we were to evaporate some of the water from one of the solutions, we would reduce the amount of solvent and increase the concentration of that solution.

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The time interval between 3 successive dots on the tape timer is 0.045 seconds. This is calculated by dividing 1 second by the frequency of the tape timer (22 Hz), which gives 0.045 seconds.

Frequency is the rate at which something occurs over a given period of time, usually measured in cycles per second (Hertz). It is an important concept in physics, engineering, and mathematics and is used to describe the behavior of waves, such as sound and light, and other periodic phenomena. Frequency can also be used to describe the rate at which events occur, such as the number of times a given event takes place within a given period of time. Frequency is often used in communication systems to measure the rate at which data is transmitted. Frequency can also refer to the number of occurrences of a given event within a given timeframe. Frequency is also used to measure the power of a signal, such as an electrical signal, or electromagnetic radiation.

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