A 15.0 kg stone slides down a snow-covered hill (the figure (Figure 1)), leaving point A with a speed of 10.0 m/s . There is no friction on the hill between points A and B, but there is friction on the level ground at the bottom of the hill, between B and the wall. After entering the rough horizontal region, the stone travels 100 m and then runs into a very long, light spring with force constant 2.30 N/m . The coefficients of kinetic and static friction between the stone and the horizontal ground are 0.20 and 0.80, respectively.
a) What is the speed of the stone when it reaches point B?
b) How far will the stone compress the spring?
c) Will the stone move again after it has been stopped by the spring?

Answer:

2342.7 J

Explanation:

The work can be calculated as

W = Fd

Where F is the force and d is the distance.

Replacing F = 427.5 N and d = 5.48 m, we get

W = (427.5 N)(5.48 m)

W = 2342.7 J

Therefore, the answer is 2342.7 J

Answer:

B. Cart B

Explanation:

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The time required for half of the oil droplets to coalesce is 34.65 minutes.b) Calculation to find how long it takes for practically all of the oil droplets to coalesce:To find the time it would take for practically all of the oil droplets to coalesce, we need to use the following formula and solve for time when n is equal to 0.0 = e^(-0.02t)-infinity = -0.02tNo oil droplets remain after an infinite amount of time. Therefore, it takes an infinite amount of time for all the oil droplets to coalesce.Answer: It takes an infinite amount of time for all the oil droplets to coalesce.

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The tension in the strings are 31.47 and 19.25 N respectively.

Mass of the block, m = 3 kg

From the figure, consider the vertical components,

T₁ sin45° + T₂ sin30° = mg

(T₁/√2) + (T₂/2) = 3 x 9.8 = 29.4

Also, consider the horizontal components,

T₁ cos45° = T₂ cos30°

T₁/√2 = T₂ x√3/2

T₁ = T₂ x √3/2 x √2

So,

T₁ = 0.612T₂

Applying in the first equation,

(T₁/√2) + (T₂/2) = 29.4

(0.612T₂/1.414) + 0.5T₂ = 29.4

0.434 T₂ + 0.5 T₂ = 29.4

0.934 T₂ = 29.4

Therefore, the tension,

T₂ = 29.4/0.934

T₂ = 31.47 N

So, the tension,

T₁ = 0.612 T₂

T₁ = 0.612 x 31.47

T₁ = 19.25 N

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Given data:

*The given mass of the Superball is m = 5.0 g

*The initial speed of the Superball is u = -28.5 m/s

*The ball rebounds at a final speed is v = +18.0 m/s

*The given time is

Considering the rebound direction is positive

The formula for the magnitude of the average acceleration of the ball during this time interval is given as

Substitute the known values in the above expression as

Answer:

a)  3.265 kg-m^2

b)  - 4.96  rad/s^2

c) 16.1944 N-m

d) 35.625

e)  - 1.488 m/s^2

f)  67.1175 m.

Explanation:

Given data:

Diameter of grindstone ( D ) = 0.650 m ,  Radius ( R ) = 0.325 m

mass of grindstone ( M ) = 55 kg

Radius of shaft ( r ) = 0.300 m

mass of shaft ( m ) = 4 kg

Initial Angular velocity = 450 rev/min = f = 7.5 rev/s = w  =15π rad/s

time ( t ) = 9.50 secs

a) Determine the moment of inertia of the grindstone including the shaft

moment of inertia of grindstone = MR^2 / 2 = 55* (0.325)^2 / 2 = 2.905

moment of inertia of shaft = mr^2 = 4 *0.3^2 = 0.36

∴ moment of inertia including shaft = 2.905 + 0.36 = 3.265 kg-m^2

b) Determine the angular acceleration of the grindstone

∝ = - 15π / 9.5 ( i.e.  angular velocity / time )

   = - 4.96  rad/s^2 ( deceleration value )

c) Determine average torque done by friction to bring the grindstone to rest

Torque ( I * ∝ )  = 3.265 x 4.96 = 16.1944 N-m (magnitude)

d) Determine the number of revolutions before grindstone comes to rest

Total revolutions N before grindstone comes to rest

= ( f1 + f2)* t /2 = 7.5 * 9.5 / 2 = 35.625

Note : f2 = 0 as it comes to rest

          f1 = 7.5 rev/s

e) Determine the Linear acceleration of the shaft in this process

This can be calculated using this relation

r * ∝ = 0.3 x (- 4.96 ) = - 1.488 m/s^2

f) Determine the linear distance travelled by the shaft

This can be calculated with the relation below

r * 2 * π * N = 0.3 * 2π * 35.625 = 67.1175 m.

(C)

Explanation:

The circle has a radius r = 0.5 m, which means that its circumference C is

\(C = 2\pi r = 2\pi(0.5\:\text{m}) = 3.14\:\text{m}\)

One revolution means that the stopper travels a distance equal to the circumference of the circle so the velocity of the stopper is

\(v = \dfrac{C}{t} =\dfrac{3.14\:\text{m}}{0.2\:\text{s}} = 15.7\:\text{m/s} \approx 16\:\text{m/s}\)

The resistance of the electric device using a power of 650 watts is approximately 27.7 ohms.

Ohm’s law states that the potential difference between two points is directly proportional to the current flowing through the resistance.

Hence

V = IR

R = V/I

Where V is the voltage or potential difference, potential difference, I is the current and R is the resistance.

We need to first find the electric current I.

Note:

Power = Voltage × Current.

Hence:

Current I = Power/Votage

Plug in the values

I = 650 / 120

I = 13/3 A

Substituting the values of voltage and current intio the above formula, we can calculate the resistance:

R = V/I

R = 120 / (13/3)

R = 27.7 ohms

Therefore, the resistance is approximately 27.7 ohms.

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a. When the force = 12 N, mass = 6 kg, the acceleration is a = 2 m/s²

b. When the force = 48 N, mass = 6 kg, the acceleration is a = 8 m/s².

The acceleration of the body is calculated by applying Newton's second law of motion as follows;

F = ma

where;

a = F / m

when the force = 12 N, mass = 6 kg, the acceleration is calculated as;

a = 12 N / 6 kg

a = 2 m/s²

when the force = 48 N, mass = 6 kg, the acceleration is calculated as;

a = 48 N / 6 kg

a = 8 m/s²

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Answer:

\(\boxed {\boxed {\sf 126 \ Newtons}}\)

Explanation:

According to Newton's 2nd Law of Motion, force is the product of mass and acceleration.

\(F=ma\)

The mass is 42 kilograms and the acceleration is 3 meters per square second.

\(m= 42 \ kg \\a= 3 \ m/s^2\)

Substitute the values into the formula.

\(F= 42 \ kg * 3 \ m.s^2\)

Multiply.

\(F= 126 \ kg*m/s^2\)

\(F= 126 \ N\)

The object's force is 126 Newtons.

First-order analysis of a seismogram record enables seismologists to do all except to develop a Modified Mercalli Intensity map.

First-order analysis of a seismogram record identifies the different kinds of seismic waves reaching to the earth's surface by the fault movement. This analysis records P waves.

The P wave will be the first wave to reach the surface. P waves are the fastest seismic waves. So, they will usually be the first ones that are recorded by a seismograph. The next seismic waves to record on a seismogram are the S waves.

A seismograph is the main instrument used to measure earthquakes. The seismograph produces a digital graphic recording of the ground motion caused by the reaching seismic waves on the earth surface. The digital recording is known as a seismogram.

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Explanation:

It is given that,

Distance covered by the cart to the right is 2 m

Distance covered by the cart to the left is 1 m

We need to find the total distance rolled by the cart. Total distance is equal to the sum of the distances covered by an object. It does depend on the direction.

Total distance = 2 m + 1 m

D = 3 m

The cart rolled to a total distance of 3 m.

Answer:Magnetic fields from two sources add up as vectors at each point, so the strength of the field is not necessarily the sum of the strengths1. Magnetic fields are vectors, which means they have direction as well as size. Therefore, the sum of two magnetic fields is not simply the sum of their magnitudes2.

Explanation:

Answer:

Potential Energy = x = m g h

Kinetic energy = 1/2 m v^2

Assuming the mass fall from rest

1/2 m v^2 = m g h

v^2 = 2 g h

So the speed attained is independent of the mass

Also, x / v   does not have the units of mass

So the solution is none of the above.

Answer:

the frequency of the wave is 13mm

Explanation:

15mm divided by 3 = 5 x 2= 10+3= 13mm so the answer is 13

by ohm's law V= IR

HERE V is given and I is given

Calculate R

Now, the resistance is the same in the

second part

V= IR AGAIN

SO, V = 0.46 * 75 = 34.50 Volts

So, the correct option is C

The frictional force of an object is the product of the normal force and coefficient of kinetic friction. Here the frictional force acting on the object  is 16.4 N.

Frictional force is a kind of force acting on a body to resist it from motion. Thus, the direction of the force will be in negative with the magnitude. Frictional force is the product of coefficient of friction and the normal force.

The normal  force acting on the object of mass 4.2 Kg is N = mg

N = 4.2 Kg × 9.8 m/s² = 41.16 N

Frictional force = ц N

                         = 0.40 × 41.16 N

                         = 16.4 N.

Therefore, the frictional force acting between the surface of the object and the floor is 16.4 N

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Your question is incomplete. But your complete question probably was:

The coefficient of kinetic friction between an object and the surface upon which it is sliding is 0.40 the weight of the object is 4.2 kg. What is the frictional force of the object?

Answer:

44M 64M

Explanation:

Answer:

P = 14700 J

Explanation:

Given that,

Mass of a piano, m = 75 kg

It is delivered throughout the window of a 6th story apartment which is 20 m above the ground.

We need to find the potential energy of the piano. It is given by :

P = mgh

Putting all the values,

P = 75 kg × 9.8 m/s² × 20 m

P = 14700 J

So, the potential energy of the piano is 14700 J.

The Big Bang theory is the most widely accepted explanation for the origins of the universe, but it does not necessarily imply that the universe emerged from nothing.

It is possible that new discoveries or insights may shed light on this fundamental question in the future. The universe may have arisen from a pre-existing state or through some other natural process that we do not yet understand.

Instead, the theory describes how the universe underwent a rapid expansion from a very dense and hot state. The conditions and laws of physics that applied during the earliest moments of the universe may not necessarily be the same as those we observe today, and there are many unknowns and uncertainties in our understanding of these early stages.

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Answer:

a) ΔS = 14.46 J/k

b) ΔS = 70.76 J/k

Explanation:

The general formula to calculate the entropy change accompanied with a process is:

ΔS = ΔQ/T

where,

ΔS = entropy change for the process

ΔQ = Heat Transfer during the process

T = Absolute Temperature during the process

a)

In this case the heat transfer will be given as:

ΔQ = (ΔHfus)(N)

where,

ΔHfus = Molar Heat of Fusion of Tin = 7.029 KJ/mol

N = No. of moles of tin = 1 mol

Therefore,

ΔQ = (7.029 KJ/mol)(1 mol)

ΔQ = 7.029 KJ = 7029 J

and the absolute temperature is:

T = 213°C +273 = 486 k

using these values in the entropy formula, we get:

ΔS = 7029 J/486 k

ΔS = 14.46 J/k

b)

In this case the heat transfer will be given as:

ΔQ = (ΔHvap)(N)

where,

ΔHvap = Molar Heat of Vaporization of Carbon Dioxide = 15.326 KJ/mol

N = No. of moles of Carbon Dioxide = 1 mol

Therefore,

ΔQ = (15.326 KJ/mol)(1 mol)

ΔQ = 15.326 KJ = 15326 J

and the absolute temperature is:

T = 216.6 k

using these values in the entropy formula, we get:

ΔS = 15326 J/216.6 k

ΔS = 70.76 J/k

A test specimen in a tensile test has a gage length of 2.0 inches for this problem, fracture occurs at a gage length of 2.92 in. determine the percent elongation.

Percent elongation is a measure of the deformation or stretching of a material before it fractures. Calculated as percentage increase in length of a material sample after it has been subjected to a tensile test .The formula for percent elongation is:

Percent Elongation = (Final Gauge Length - Original Gauge Length) / Original Gauge Length x 100%

% Elongation = (2.92 in - 2.0 in) / 2.0 in x 100

% Elongation = 46%

Therefore, the percent elongation is 46%.

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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

It is not recommended to fire a gun straight up into the air.

When a bullet is fired into the air, it will eventually come down and can pose a danger to people and property below. The bullet can still be lethal when it reaches the ground, especially if it lands on a hard surface or hits someone directly.

Additionally, firing a gun in a residential area can be illegal and can result in legal consequences. In general, guns should only be fired in designated shooting ranges or in self-defense situations where there is an immediate threat to life. It is important to handle firearms responsibly and follow all safety guidelines to prevent accidents and injuries.

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Answer:

Here is the answer!! :) I put it as a pic so you wouldn't plagiarize.

Explanation:

Hope this helps you!

Answer:

It makes work require less force perform.

Explanation:

Answer:

The mass of the second ball is \(m_2 = 2.175m \ kg\)

Explanation:

From the question we are told that  

     The mass of the first  ball is  m

Let assume

    The original speed of the first ball is  \(u_1\)

     The rebound speed is  \(v_1 = 0.370u_1 \ m/s\)

According to the law of momentum conservation

       \(m_1 u_1 + m_2 u_2 = -m_1 v_1 + m_2 v_2\)

The  second ball is at rest so  

      \(u_2 = 0\)

And the negative sign shows that it is a rebound velocity

        \(mu_1 + = -m v_1 + m_2 v_2\)

=>   \(mu_1 + = -0.370 mu_1 + m_2 v_2\)

Now  we are told that the collision is  elastic, this means that the velocity of approach will be equal to the velocity of separation

  So  

          \(u_1 = v_1 + v_2\)

=>       \(u_1 = 0.370u_1 + v_2\)

=>       \(v_2 = 0.63 \ u_1\)

substituting this into equation above

\(mu_1 + = -0.370 mu_1 + m_2 (0.63 u_1)\)

\(1.370 mu_1 = m_2 (0.63 u_1)\)

=>    \(m_2 = 2.175m \ kg\)

The mass of the second ball in terms of the first ball, m, is 2.175 m.

The given parameters;

Apply the principle of conservation of linear momentum to determine the mass of the second ball as shown below;

\(m_1 u_1 + m_2 u_2 = m_1v_1 + m_2 v_2\\\\mu_1 + m_2(0) = m(-0.37u_1) + m_2v_2\\\\mu_1 = -0.37u_1m + m_2v_2\\\\mu_1 + 0.37mu_1 = m_2v_2\\\\1.37 mu_1 = m_2 v_2 \ --(1)\)

Apply one-dimensional velocity equation for elastic collision;

\(u_1 + v_1 = u_2 + v_2\\\\u_1 + (-0.37u_1) = 0 + v_2\\\\u_1 -0.37u_1 = v_2\\\\v_2 = 0.63 u_1\)

substitute the value of v₂ into the above equation;

\(1.37mu_1 = m_2(0.63u_1)\\\\1.37mu_1 = 0.63m_2u_1\\\\m_2 = \frac{1.37mu_1}{0.63u_1} \\\\m_2 = 2.175 \ m\)

Thus, the mass of the second ball in terms of the first ball, m, is 2.175 m.

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