While you push a box you begin to decrease the force you are exerting on the box. When will the box reach equilibrium?

A. When the force you are exerting on the box is equal to 0.

B. When Fyou on box = -Fbox on you.

C. When the force of the box becomes Fyou on box < Fbox on you

D. The box will never reach equilibrium.

While You Push A Box You Begin To Decrease The Force You Are Exerting On The Box. When Will The Box Reach

Answers

Answer 1

The application of a force on the box overcomes the friction and causes the box to accelerate

While the force is decreasing, the box will stabilize;

B. When \(\underline{F_{you \, on \, box} = -F_{box \, on \, you}}\)

Reason:

Newton's third Law of Motion states that action and reaction are equal in magnitude and opposite in direction

When the box is pushed with a force, \(F_{you \, on \, box}\), the reaction of the box of mass, m,  is as follows;

\(F_{you \, on \, box}\) = \(F_{friction}\) + m × acceleration

Where;

\(F_{friction}\) = \(-F_{box}\) for example

The negative sign is due to the direction of the friction force, or \(F_{box}\) is opposite to the direction of the applied force

When the force is decreased to F₂ = \(F_{you \, on \, box}\), such that we have;

\(F_{you \, on \, box}\) = \(-F_{box \, on \, you}\) , which is the condition for equilibrium, and the net

force is zero and according to Newton's first law of motion,  the box moves

at constant speed no acceleration

Therefore the box will reach equilibrium when;

\(\mathbf{\underline{F_{you \, on \, box} = -F_{box \, on \, you}}}\)

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Answer 2

Answer:

When the force you are exerting on the box is equal to 0

Explanation:

Once again expert verifiers are sabotaging people here is the actual answer.


Related Questions

Peak expiratory flow readings are Higher in the morning; lower in the evening Lower when patients are well; higher when patient's airway is constricted Lower in the morning; higher in the evening Higher when patients are well; lower when patient's airway is constricted

Answers

Peak expiratory flow readings are higher when patients are well, but lower when a  patient's airway is constricted.

What is the peak expiratory flow?

This term is used in medicine to refer to the maximum rate of a person's exhalation or to how fast and how long can they exhale.

This rate is measured by using the peak expiratory flow test that requires you to deeply inhale and then exhale as fast as hard as possible.

What does the peak expiratory flow indicate?

This rate is closely related to the amount of air flowing out of the lungs. This implies the peak expiratory flow is lower if there is a disease such as asthma that can constrict the airways.

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An object is thrown into the air going 80m/s. How high does it go?

Answers

From 3rd equation of motion:
2as= vf2-vi2
By rearranging
S= vf2-vi2/2g
H= 0 - 6400/19.6
H = 326.5m
Hence the object will goes high about 326.5 m

which element has more than 5 valency​

Answers

Answer:

Sulfur (Has six valence electrons). It has maximum valency due to belonging to VI groups of the Periodic Table.

Explanation:

The electrons found in an element's outermost atomic shell are known as valence electrons.

Sulfur, which has an atomic number of 16, has an electrical configuration of 2, 8, 6, meaning it has six electrons in its outermost shell. As a result, its valence electrons will also be six.

However, in its natural condition, sulfur exists as the S8 molecule, which has the classic chair structure where each sulfur atom is covalently connected to two other sulfur atoms. In that sense, there will be 8 valence electrons.

Consequently, the answer will be 6 if you're asking about the "sulphur atom," but 8 if you're talking about sulfur in general.

Thank you ,

Eddie

The force that holds planets, stars, and other heavenly bodies in space is called _____.


inertia
universal force
gravity
cosmic force

Answers

Answer:

Gravity

Explanation:

The answer is Cosmic Force

Spacecraft is traveling in inner planetary space at a constant velocity was it estimated distance traveled by the spacecraft in 9.50 seconds

Answers

The distance traveled by the Spacecraft is  2.3 x 10² m.

What is constant velocity?

To have a constant velocity, the change in velocity or speed of the object must be zero.

Constant speed will elapse equal distance in an identical period of time as a result is an example of steady speed.

For a Spacecraft is traveling in inner planetary space at a constant velocity and a given time of motion, the distance traveled by the Spacecraft is calculated as follows;

Distance = speed x time

the speed is given as 24.21 m/s

the time of motion is given as 9.5 seconds

distance = 24.21 m/s  x 9.5 s

distance = 2.3 x 10² m

Thus, the distance traveled by the Spacecraft is  2.3 x 10² m.

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The complete question is below;

Spacecraft is traveling in inner planetary space at a constant velocity of 24.1 m/s. What it estimated distance traveled by the spacecraft in 9.50 seconds?

You place a box weighing 276 N on an inclined plane that makes a 44.5° angle with the horizontal.
Compute the component of the gravitational force acting down the inclined plane.
Answer in units of N.

Answers

Answer:

this is the answer

Explanation:

hope it helps

You place a box weighing 276 N on an inclined plane that makes a 44.5 angle with the horizontal.Compute

What is every type of compound

Answers

Answer:

There are four types of compounds, depending on how the constituent atoms are held together: molecules held together by covalent bonds. ionic compounds held together by ionic bonds. intermetallic compounds held together by metallic bonds.

Explanation:

Great Company manufactures and sells a product whose peak sales occur in the third quarter. Management is now preparing detailed budgets for 20x4- the coming year and has assembled the following information to assist in the budget preparation: The company’s product selling price is Br. 20 per unit. The marketing department has estimated sales in units as follows for the next six quarters.

Answers

Answer:

Explanation:

Quarter 1 - 10,000 units

Quarter 2 - 12,000 units

Quarter 3 - 16,000 units

Quarter 4 - 14,000 units

Quarter 5 - 10,000 units

Quarter 6 - 8,000 units

Based on this information, the total estimated sales revenue for the next six quarters is Br. 480,000.

A bicyclist started from rest along a straight path. After 2.0 s, his speed was 2.0 m/s. After 5.0 s, his speed was 8.0 m/s. What was his acceleration during the time 2.0 s to 5.0 s?

Answers

Acceleration is the change in velocity over time. We can calculate the acceleration of the bicyclist during the time 2.0 s to 5.0 s using the formula acceleration = (final velocity - initial velocity) / time.

The initial velocity of the bicyclist at 2.0 s is 2.0 m/s and the final velocity at 5.0 s is 8.0 m/s. The time interval between 2.0 s and 5.0 s is 3.0 s.

Substituting these values into the formula, we get acceleration = (8.0 m/s - 2.0 m/s) / 3.0 s = 6.0 m/s / 3.0 s = 2.0 m/s^2.

So, the acceleration of the bicyclist during the time 2.0 s to 5.0 s was 2.0 m/s^2.

statics and strength of materials

statics and strength of materials

Answers

The magnitude of the force P provided that the stress in the part AB is two times that of BC part is 0.8 kN.

What is the force P?

The magnitude of the force P provided that the stress in the part AB is two times that of BC part is calculated as follows;

Take moment about the joint to determine the magnitude of the force along part BC.

120 kN x 750 mm  =  F x 1000 mm

F = ( 120 kN x 750 mm ) / ( 1000 mm )

F = 90 kN

Stress is given as force divided by area. The following equation can be used to determine the magnitude of force P.

Stress in AB = 2 times stress in BC

P/A₁  = 2F/A₂

where;

A₁ is the area of segment ABA₂ is the area of segment BC

A₁ =  πd²/4  =  π(50 x 10⁻³)²/4

A₁ = 1.96 x 10⁻⁵ m²

A₂ = πd²/4  =  π(75 x 10⁻³)²/4

A₂ = 4.42 x 10⁻³ m²

P/A₁ = 2F/A₂

P = (2F x A₁) / (A₂)

P = (2 x 90 kN x 1.96 x 10⁻⁵ m² ) / ( 4.42 x 10⁻³ m² )

P = (2 x 90,000 N x 1.96 x 10⁻⁵ m² ) / ( 4.42 x 10⁻³ m² )

P = 798.2 N

P = 0.798 kN

P ≈ 0.8 kN

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An air puck of mass m1 = 0.21 kg is tied to a string and allowed to revolve in a circle of radius R = 0.9 m on a frictionless horizontal table. The other end of the string passes through a hole in the center of the table, and a mass of m2 = 1.0 kg is tied to it (see the figure below). The suspended mass remains in equilibrium while the puck on the tabletop revolves.

Answers

The speed of the puck is 3.67 m/s.

To find the speed of the puck, we can use the concept of centripetal force. The tension in the string provides the necessary centripetal force to keep the puck moving in a circle. At the same time, the tension in the string also supports the weight of the suspended mass.

Using Newton's second law, we can write two equations of motion: one for the puck and one for the suspended mass. For the puck, the net force acting on it is the tension in the string, which is equal to the centripetal force required to keep it moving in a circle. Thus, we can write:

= m1 * v^2 / R

where T is the tension in the string, v is the speed of the puck, and R is the radius of the circle.

For the suspended mass, the net force acting on it is its weight minus the tension in the string, which must be zero since the mass is in equilibrium. Thus, we can write:

T = m2 * g

where g is the acceleration due to gravity.

Combining these two equations, we can solve for the speed of the puck:

v = sqrt(T * R / m1) = sqrt(m2 * g * R / m1)

Substituting the given values, we get:

v = sqrt(1.0 kg * 9.81 m/s^2 * 0.9 m / 0.21 kg) = 3.67 m/s

Therefore, the speed of the puck is 3.67 m/s.

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ONE sound wave travels through two containers of different gasses. Wave through container 1 has a wavelength of 1.2 m. Wave through container 2 has a wavelength of 3.6 m. The frequency of wave through container 2 must be __________ the frequency of wave through container 1.


a. one-ninth


b. one-third


c. the same as


d. three times larger than

Answers

I’m not 100% but the answer is b

The first law of motion describes the principle of __________

Answers

Answer:

The first law of motion describes the principle of law of inertia.

How are work and power different

Answers

Work is defined as the process of energy transfer to the motion of an object through the application of force. Power is defined as the amount of energy transferred in unit time.

Model a hydrogen atom as a three-dimensional potential well with Uo = 0 in the region 0 < x a. 283 eV
b. 339 eV
c. 113 eV
d. 226 eV

Answers

This question is incomplete, the complete question is;

Model a hydrogen atom as a three-dimensional potential well with U₀ = 0 in the region 0 < x < L, 0 < y < L and 0 < z < L, and infinite otherwise, with L = 1.0 × 10⁻¹⁰ m.

Which of the following is NOT one of the lowest three energy levels of an electron in this model?

a. 283 eV

b. 339 eV

c. 113   eV  

d. 226 eV        

Answer:

the lowest three energy are; 113 eV, 225 eV, and 339 eV.

Hence Option a) 283 eV is not among the three lowest energy

Explanation:

Given the data in the question;

Three dimension cube or particle in a cubic box

the energy value is given by;

\(E_{nx,ny,nz\) = \(( n_x^2 + n_y^2 + n_z^2 )\) × π²h"² / 2ml²

where h" = h/2π and h is Planck's constant ( 6.626 × 10⁻³⁴ m² kg / s )

m is mass of electron ( 9.1 × 10⁻³¹ kg )

l is length of side of box ( 1.0 × 10⁻¹⁰ m )

for ground level ( \(n_x = n_y = n_z = 1\) )

so

\(( n_x^2 + n_y^2 + n_z^2 )\) ×  π²h"² / 2ml²

since h" = h/2π

\(( n_x^2 + n_y^2 + n_z^2 )\) × π²h² / (2π)²2ml²

so we substitute

\(E_{111\) = ( 1² + 1² + 1² ) × [ π²( 6.626 × 10⁻³⁴ )² ] / [ (2π)² × 2 × 9.1 × 10⁻³¹ kg × ( 1.0 × 10⁻¹⁰)² ]

\(E_{111\) = 3 × [ (4.333188779 × 10⁻⁶⁶) / ( 7.185072 × 10⁻⁴⁹ ) ]    

\(E_{111\) = 3 × [ 6.03082165 × 10⁻¹⁸ ]

Now, we know that electric charge = 1.602 x 10⁻¹⁹

so

\(E_{111\) = 3 × [ (6.03082165 × 10⁻¹⁸) / (1.602 x 10⁻¹⁹) ]

\(E_{111\) = 3 × [ 37.645578 ]

\(E_{111\) = 112.9 ≈ 113 eV

\(E_{211\) = \(( n_x^2 + n_y^2 + n_z^2 )\)  × π²h² / (2π)²2ml²

we substitute

\(E_{211\) = ( 1² + 1² + 2² ) × [ 37.645578 ]

\(E_{211\) = 6 × [ 37.645578 ]

\(E_{211\) = 225.87 ≈ 226 eV

\(E_{221\) = \(( n_x^2 + n_y^2 + n_z^2 )\)  × π²h² / (2π)²2ml²

we substitute

\(E_{221\) = ( 2² + 2² + 1² ) × [ 37.645578 ]

\(E_{211\) = 9 × [ 37.645578 ]

\(E_{211\) = 338.8 ≈ 339 eV

Therefore, the lowest three energy are; 113 eV, 225 eV, and 339 eV.

Hence Option a) 283 eV is not among the three lowest energy

Which individual or group had perhaps the most profound effect on establishing social work as a specialized practice

Answers

Answer:

Which individual or group had perhaps the most profound effect on establishing social work as a specialized practice

Explanation:

proof(how this formula comes )
vector
u.v=|u||v|cosβ

Answers

The formula you mentioned is known as the dot product formula or the scalar product formula. It is used to find the angle between two vectors u and v.

Let's start by defining the vectors u and v. Suppose we have two vectors u and v in a two-dimensional space.

u = (u1, u2)

v = (v1, v2)

The dot product of these vectors is defined as:

u . v = |u| |v| cos(β)

where |u| and |v| are the magnitudes of the vectors u and v respectively, and β is the angle between the vectors u and v.

Now, let's derive this formula. The dot product of two vectors u and v is given by:

u . v = (u1 × v1) + (u2 × v2)

The magnitude of a vector is given by:

|u| = sqrt(u1² + u2²)

|v| = sqrt(v1² + v2²)

We can use the dot product and magnitude equations to obtain:

cos(β) = (u . v) / (|u| × |v|)

Multiplying both sides by |u| × |v| gives us:

|u| × |v| × cos(β) = u . v

Therefore, we have derived the dot product formula:

u . v = |u| × |v| × cos(β)

This formula can be used to find the angle between two vectors u and v in any two-dimensional or three-dimensional space.

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The complete question is-

Write the proof of the formula

u.v=|u||v|cosβ

what is the full distance when an object is thrown at 35 m/s at an angle of 45 degrees

what is the full distance when an object is thrown at 35 m/s at an angle of 45 degrees

Answers

Okay, here are the steps to calculate the full distance traveled when an object is thrown at a certain speed and angle:

You have the initial velocity (v): 35 m/s

You have the launch angle (θ): 45 degrees

We need to split the initial velocity into its horizontal (vx) and vertical (vy) components.

To calculate vx (horizontal component):

vx = v * cosθ

vx = 35 * cos(45) = 24.7 m/s

To calculate vy (vertical component):

vy = v * sinθ

vy = 35 * sin(45) = 24.7 m/s

We can calculate the horizontal distance (d) traveled using:

d = vx * t (where t is time)

Since there is no air resistance, the vertical velocity (vy) will remain constant. This means the time the object is in the air is:

t = vy / g (where g is acceleration due to gravity, 9.8 m/s^2)

t = 24.7 / 9.8 = 2.52 seconds

Now we can calculate the full horizontal distance traveled:

d = vx * t

d = 24.7 * 2.52

= 62.3 meters

So the full distance the object will travel when thrown at 35 m/s at a 45 degree angle is approximately 62 meters.

Let me know if you have any other questions!

Answer:

To calculate the full distance traveled by an object thrown at a velocity of 35 m/s at an angle of 45 degrees, we need to consider the horizontal and vertical components of the motion separately.

The horizontal component of the motion remains constant throughout the trajectory and is given by:

Horizontal distance = (Initial velocity) * (Time of flight) * cos(angle)

In this case, the initial velocity is 35 m/s, the angle is 45 degrees, and we need to find the time of flight.

The time of flight can be calculated using the vertical component of the motion. The vertical motion can be described using the equation:

Vertical displacement = (Initial velocity * sin(angle))^2 / (2 * acceleration)

Where the initial velocity is 35 m/s, the angle is 45 degrees, and the acceleration is the acceleration due to gravity, approximately 9.8 m/s^2.

The vertical displacement is zero at the highest point of the trajectory since the object comes back down to the same height it was launched from. So we can solve the equation for the time of flight.

Using these calculations, we can find the horizontal distance traveled by the object.

Let's calculate step by step:

Step 1: Calculate the time of flight

Vertical displacement = 0 (at the highest point)

0 = (35 * sin(45))^2 / (2 * 9.8)

0 = (24.75^2) / 19.6

0 = 616.0125 / 19.6

0 = 31.43

Step 2: Calculate the time of flight

Vertical displacement = (Initial velocity * sin(angle)) * time - (1/2) * acceleration * time^2

0 = (35 * sin(45)) * time - (1/2) * 9.8 * time^2

0 = 24.75 * time - 4.9 * time^2

4.9 * time^2 - 24.75 * time = 0

time * (4.9 * time - 24.75) = 0

time = 0 (initial point) or 24.75 / 4.9

time = 5.05 seconds

Step 3: Calculate the horizontal distance

Horizontal distance = (Initial velocity) * (Time of flight) * cos(angle)

Horizontal distance = 35 * 5.05 * cos(45)

Horizontal distance = 35 * 5.05 * (sqrt(2)/2)

Horizontal distance = 88.96 meters

Therefore, when an object is thrown at 35 m/s at an angle of 45 degrees, the full distance traveled is approximately 88.96 meters.

WHAT IS THE MASS OF A PURE PLATINUM DISK

Answers

The mass of a pure platinum disc can be gotten by multiplying the density with the volume.

Therefore the mass is 2418.2 grams or 2.4182 kilograms.

What is mass?

A body's mass is an inherent quality. Prior to the discovery of the atom and particle physics, it was widely considered to be tied to the amount of matter in a physical body.

The kilogram is the primary mass unit in the SI.

The resistance of the body to acceleration in the presence of a net force can be measured as mass.

Due to the lower gravity on the Moon, an object would weigh less than it does on Earth while maintaining the same mass. This is due to the fact that mass, coupled with gravity, determines the strength of weight, which is a force.

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What is the mass of a pure platinum disk with a volume of 113 cm3? The density of platinum is 21.4 g/cm3.

Give your answer in grams and kilograms.

One mole of magnesium (6 × 1023 atoms) has a mass of 24 grams, as shown in the periodic table on the inside front cover of the textbook. The density of magnesium is 1.7 grams/cm3. What is the approximate diameter of a magnesium atom (length of a bond) in a solid block of the material? Make the simplifying assumption that the atoms are arranged in a "cubic" array, as shown in the figure. Remember to convert to SI units.

Answers

This question involves the concepts of density, volume, and mass.

The approximate diameter of a magnesium atom is "3.55 x 10⁻¹⁰ m".

STEP 1 (FINDING MASS OF INDIVIDUAL ATOM)

It is given that:

Mass of one mole = 24 grams

Mass of 6 x 10²³ atoms = 24 grams

Mass of 1 atom = \(\frac{24\ grams}{6\ x\ 10^{23}\ atoms}\) = 4 x 10⁻²³ grams

STEP 2 (FINDING VOLUME OF A SINGLE ATOM)

\(\rho = \frac{m}{V}\\\\V=\frac{m}{\rho}\)

where,

\(\rho\) = density = 1.7 grams/cm³m = mass of single atom = 4 x 10⁻²³ gramsV = volume of single atom = ?

Therefore,

\(V=\frac{4\ x\ 10^{-23}\ grams}{1.7\ grams/cm^3}\)

V = 2.35 x 10⁻²³ cm³

STEP 3 (FINDING DIAMETER OF ATOM)

The atom is in a spherical shape. Hence, its Volume can be given as follows:

\(V =\frac{\pi d^3}{6}\\\\d=\sqrt[3]{ \frac{6V}{\pi}}\\\\d=\sqrt[3]{ \frac{6(2.35\ x\ 10^{-23}\ cm^3)}{\pi}}\)

d = 0.355 x 10⁻⁷ cm = 3.55 x 10⁻¹⁰ m

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If you are sitting in the back seat of a car that makes a hard left turn, you will feel pushed toward the right side of the car. Why does your body move to the right

Answers

Answer:

Inertia

Explanation:

Your body is naturally resisting turning left, as it wants to continue straight. So if feels like you are going right.

Answer:

Because my body tries to continue in the rectilinear motion it was experiencing before the turn.

Explanation:

The body tries to continue in the rectilinear motion it was having before the hard left turn, in which a centripetal force is experienced. This is in agreement with Newton's first Law of motion:

"An object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force."

The half-life of a radioactive kind of cerium is 32 days. If you start with 84,288 grams of it, how much will be left after 160 days?

Answers

ANSWER

\(2,634g\)

EXPLANATION

To find the amount left after 160 days, we have to apply the formula for the amount of a substance remaining using its half-life:

\(N=N_0(\frac{1}{2})^{\frac{t}{T_{}}}\)

where N0 = initial amount of the substance

t = time elapsed

T = half-life

Therefore, we have that the amount of Cerium left after 160 days is:

\(\begin{gathered} N=84,288\cdot(\frac{1}{2})^{\frac{160}{32}} \\ N=84,288\cdot(\frac{1}{2})^5=84,288\cdot0.03125 \\ N=2,634g \end{gathered}\)

Hence, 2,634 grams of Cerium will be left.

What amount of force is required to accelerate a 20 gram toy car at 5 m/s²?
O 150 N
O 100 N
O 50 N
Ο ΟΝ

Answers

Answer:

100

Explanation:

F = m * a

Given that the mass (m) of the toy car is 20 grams (or 0.02 kilograms, since 1 kilogram = 1000 grams) and the acceleration (a) is 5 m/s^2, we can plug these values into the formula to calculate the force (F):

F = 0.02 kg * 5 m/s^2 = 0.1 N

So, the amount of force required to accelerate the 20 gram toy car at 5 m/s^2 is 0.1 N, which is equivalent to 100 N when rounded to the nearest whole number. Therefore, the correct answer is 100 N.

The evaporation of water is an example of a change in ______

Answers

Answer:

The evaporation of water is an example of a change in Pysical Change .

A 1.2 kg basketball is thrown upwards. What is the potential energy of the basketball at the top of its path if it reaches a height of 15.6 m?

Answers

Answer:

Answer is 183.6 J

Explanation:

Using the Physics reference sheet the formula for Potential energy is

(mass) x (gravity) x (height)

Mass= 1.2

Gravity I used is 9.81 (use 10 to get the answer most schools use)

Height= 15.6

Which wave has the longest wavelength?
A. A
B. B
C. C
D.D

Which wave has the longest wavelength?A. AB. BC. CD.D

Answers

Answer:

In my opinion, ''A" would be the longest wavelength.

1. A ball is at rest on the top of a hill (see the figure).
At the top of the hill, the ball will have [the maximum value of its, no, the minimum value of its] gravitational potential energy and [no, the maximum value of its] kinetic energy. If the ball rolls down the hill then, its [gravitational potential energy, kinetic energy] is converted to [gravitational potential energy, kinetic energy] when it gets to the ground.

2. Get your stopwatch ready and prepare to drop the object from the height h you selected in the previous step. You should drop the object so its [bottom, top, middle] part is initially at the height h. The initial speed of the ball [zero, 9.8 m/s, 9.8 m/s^2, depends on the height h] You'll need to measure the time from when the ball leaves your hand to exactly when it hits the ground [ for the first time it bounces, after it bounces and then comes to rest, both the first time and then after it bounces; then average the two times]
.

1. A ball is at rest on the top of a hill (see the figure).At the top of the hill, the ball will have

Answers

1. At the top of the hill, the ball will have the maximum value of its gravitational potential energy and the minimum value of its kinetic energy. As the ball rolls down the hill, its gravitational potential energy is converted to kinetic energy when it gets to the ground.

2. When dropping the object, you should drop it so its top part is initially at the height h. The initial speed of the ball will be zero since it starts from rest. To measure the time it takes for the ball to hit the ground, you should start the stopwatch when the ball leaves your hand and stop it when the ball hits the ground for the first time. It is recommended to perform multiple trials and calculate the average time to minimize errors.

A marble rolls off of a table that is 0.97 meters tall with a velocity of 1.87 m/s. How long
does it take the marble to hit the floor?
O 0.44 seconds
O 0.98 seconds
O 0.39 seconds
O 0.52 seconds

Answers

It’s the last one
Good luck
God bless you

at the temperature at which we live, earth's core is solid or liquid?

Answers

Explanation:

The Earth has a solid inner core

A liquid x at 25 degree Celsius is poured to a height of 40cm in a capillary tube of length 70cm and the diameter is 1cm .Assume that volume does not change with temperature. A find the initial volume of the liquid in cm^3. B. The temperature is reduced by 10°C causing the liquid to reduce in height to 37cm.Find the volume coefficient of the thermal expansion of the liquid. C. At the initial height of 40cm and temperature of 25°C , what change in temperature is needed for liquid to rise to a height of 49cm.

Answers

The initial volume of the liquid is 31.4 cm³. The volume coefficient of thermal expansion of the liquid is 0.002 per degree Celsius. A temperature increase of 109.5°C is needed for the liquid to rise to a height of 49cm.

The initial volume of the liquid can be found using the formula for the volume of a cylinder:

V = πr²h

where r is the radius (half the diameter), h is the height, and π is approximately 3.14. Plugging in the given values, we get:

V = π(0.5 cm)²(40 cm)

V = 31.4 cm³

The volume coefficient of thermal expansion (β) is defined as the fractional change in volume per degree Celsius change in temperature. It can be calculated using the formula:

β = ΔV/(VΔT)

where ΔV is the change in volume, V is the initial volume, and ΔT is the change in temperature. We can rearrange this formula to solve for ΔV:

ΔV = βVΔT

We know that ΔT = -10°C (a decrease of 10°C) and that the height decreased from 40cm to 37cm, or by 3cm. The change in volume can be found using the formula for the volume of a cylinder again, with the new height of 37cm:

ΔV = π(0.5 cm)²(40 cm - 37 cm)

ΔV = 0.59 cm³

Plugging in all the values, we get:

0.59 cm³ = β(31.4 cm³)(-10°C)

β = 0.002

To find the change in temperature needed for the liquid to rise to a height of 49cm, we can use the same formula as before, but solve for ΔT:

ΔT = ΔV/(βV)

We know that ΔV is the difference between the initial volume and the volume at the new height, which is:

ΔV = π(0.5 cm)²(49 cm - 40 cm)

ΔV = 6.86 cm³

Plugging in all the values, we get:

ΔT = 6.86 cm³/(0.002)(31.4 cm³)

ΔT = 109.5°C

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