Block B, which has a mass of 4t kg, is moving at a constant velocity across a flat surface. As shown in the diagram, it is being pulled forward by a force of 100 N. What is the magnitude of the force ?

Answer:

Shown by explanation;

Explanation:

The heat of the sample = mass ×specific heat capacity of the sample × temperature change(∆T)

Assumption;I assume the mass of the samples are : 109g and 192g

∆T= 30.1-21=8.9°c.

The heat of the samples are for 109g are:

0.109 × 4186 × 8.9 =4060.84J

For 0.192g are;

∆T= 67-30.1-=36.9°c

0.192 × 4186×36.9=29656.97J

Answer:

A) i) Dynamic error ≈ 3.1%

   ii) phase shift ≈ -12°

B) 79971.89 rad/s

Explanation:

Given data :

Damping ratio = 0.5

natural frequency = 18,000 Hz

a) Calculate the dynamic error and phase shift in accelerometer output at an impart vibration of 4500 Hz

i) Dynamic error

This can be calculated using magnitude ratio formula attached below is the solution

dynamic error ≈ 3.1%

ii)  phase shift

This phase shift can be calculated using frequency dependent phase shift formula

phase shift ≈ -12°

B) Determine resonance frequency

  Wr = 2\(\pi\) ( 18000 \(\sqrt{0.5}\) ) = 79971.89 rad/s

C) The maximum magnitude ratio that the system can achieve

Answer:

0.636 kJ

Explanation:

The charge on any capacity, q = CV, thus,

The initial charge on the 70 pF capacitor is

q = Cv

q = 70*10^-12 * 3.6*10^3

q = 2.52*10^-7 C

The charge on the 280 pF capacitor is q = C*v

q = 280*10^-12 * 3.6*10^3

q = 1.008x10^-6 C

When they are connected as stated, the net total charge remaining will be 1.008*10^-6 - 2.52*10^-7 = 7.56*10^-7 C

Since the capacitors are in parallel, the equivalent capacitance will be 70 + 280 pF = 350 pF

Remember, q = CV, then V = q/C

V = 7.56*10^-7 C / 350*10^12 F

V = 2160 V

b) The energy before is 1/2 C*v²

E = 1/2 * 70*10^-12 * 3600² + 1/2 * 280*10^-12 * 3600²

E = 4.536*10^-4 J + 1.814*10^-3 J

E = 2.268 kJ

The energy After is 1/2 Cv²

E = 1/2 * 70*10^-12 * 2160² + 1/2 * 280*10^-12 * 2160²

E = 3.266*10^-4 J + 1.306*10^-3 J

E = 1.632 kJ

so the loss is 2.268 - 1.632 = 0.636 kJ

1 The ball travel 58.29 m high

2. The time the ball spend in the air is 8.67 s

The maximum height reached by the ball can be obtained as follow:

v² = u² – 2gh (since the ball is going against gravity)

0² = 33.8² – (2 × 9.8 × h)

0 = 1142.44 – 19.6h

Collect like terms

0 – 1142.44 = –19.6h

–1142.44 = –19.6h

Divide both side by –19.6

h = –1142.44 / –19.6

h = 58.29 m

We'll begin by calculating the time to reach the maximum height . This can be obtained as follow:

v = u – gt (since the ball is going against gravity)

0 = 33.8 – (9.8 × t₁)

0 = 33.8 – 9.8t₁

Collect like terms

0 – 33.8 = –9.8t₁

–33.8 = –9.8t

Divide both side by –9.8

t₁ = –33.8 / –9.8

t₁ = 3.45 s

Next, we shall determine the time take to fall to the ground

h = ½gt²

133.29 = ½ × 9.8 × t₂²

133.29 = 4.9 × t₂²

Divide both side by 4.9

t₂² = 133.29 / 4.9

Take the square root of both side

t₂ = √(133.29 / 4.9)

t₂ = 5.22 s

Finally, we shall determine the time spend by the ball in the air. This is shown below:

T = t₁ + t₂

T = 3.45 + 5.22

T = 8.67 s

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Answer:

 x = v₀ cos θ t,  y = v₀ sin θ t - ½ g t² ,     y = ½ v² / g  

Explanation:

The formulas for launching projectiles is

as in the x axis there is no acceleration

          x = v₀ₓ t

         x = v₀ cos θ t

on the axis and the acceleration is the acceleration of gravity

         y = \(v_{oy}\) t - ½ g t²

         y = v₀ sin θ t - ½ g t²

the formulas for the position with energy metomentodos, we must see that since there is no friction the mechanical energy is conserved, we write the energy for two points

initial. Highest point

       \(Em_{o}\) = U = m g y

final . Lowest point

      Em_{f} = K = ½ m v²

      Em_{o} = Em_{f}

      mg y = ½ m v²

       y = ½ v² / g

The energy stored in the circuit at any time t is given by \(U = (1/2)L*I^{2} + (1/2)Q^{2} /C = (1/2)L*(V_{0} /R)^{2} *e^{(-2t/(R*C))} + (1/2)C*V_{0} ^{2} *(1 - e^{(-2t/(R*C)})).\)The units are in seconds.

The total energy stored in the circuit can be calculated using the formula: U = (1/2)L*I² + (1/2)Q²/C, where L is the inductance, I is the current, Q is the charge on the capacitor, and C is the capacitance.

Initially, the capacitor is uncharged, so the second term is zero.

Therefore, the initial energy stored in the circuit is U₀ = (1/2)L*I₀², where I₀ is the initial current, which is zero.

When the magnetic field is switched on, a current begins to flow in the solenoid.

This current increases until it reaches its maximum value, given by I = V/R, where V is the voltage across the solenoid and R is its resistance.

Since the solenoid is connected in series with the capacitor, the voltage across the solenoid is equal to the voltage across the capacitor, which is given by V = Q/C, where Q is the charge on the capacitor.

The charge on the capacitor is given by Q = C*V, where V is the voltage across the capacitor at any time t.

Therefore, we have I = V/R = Q/(R*C) = dQ/dt*(1/R*C), where dQ/dt is the rate of change of charge on the capacitor.

This is a first-order linear differential equation, which can be solved to give \(Q(t) = Q_{0} *(1 - e^{(-t/(R*C)}))\), where Q₀ is the maximum charge on the capacitor, given by Q₀ = C*V₀, where V₀ is the voltage across the capacitor at t=0.

The current in the solenoid is given by I(t) = \(dQ/dt*(1/R*C) = (V_{0} /R)*e^{(-t/(R*C)}).\)

The energy stored in the circuit at any time t is given by\(U = (1/2)L*I^{2} + (1/2)Q^{2} /C = (1/2)L*(V_{0} /R)^{2} *e^{(-2t/(R*C))} + (1/2)C*V_{0} ^{2} *(1 - e^{(-2t/(R*C)})).\)

The time t at which the energy stored in the circuit drops to 10% of its initial value can be found by solving the equation U(t) = U₀/10, or equivalently, \((1/2)L*(V_{0} /R)^{2} *e^{(-2t/(R*C)}) + (1/2)C*V_{0} /R)^{2}*(1 - e^{(-2t/(R*C)})) = (1/20)L*I_{0} /R)^{2}.\)

This equation can be solved numerically using a computer program, or graphically by plotting U(t) and U₀/10 versus t on the same axes and finding their intersection point.

The solution is t = 1.74 ms.

The units are in seconds.

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To better understand crash dynamics we have to look at "the laws of motion."

The laws of motion

The laws of motion were introduced by Sir Isaac Newton in 1687 in his book Philosophiæ Naturalis Principia Mathematica ("Mathematical Principles of Natural Philosophy"), which defined the laws of motion, or three fundamental laws that govern the movement of bodies. The laws of motion, according to Newton, govern the motion of an object or a system of objects that interact.

It defines the concepts of force and mass, and the fundamental dynamics of motion.The following are the laws of motion:Every 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 velocity of an object changes proportional to the force applied to it, and the acceleration of an object is proportional to both its force and its mass. For every action, there is an equal and opposite reaction.

Therefore, these laws are necessary to fully grasp crash dynamics because they explain how objects respond to outside forces that cause them to accelerate or decelerate.

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Answer:

If the mass of B is m and the temperature change is the same, the mass of B will be 2m.

Explanation:

Q = mcT

T = mc/Q

M = 4Q/2cT........... (1)

T = Q/mc

Plug this in equation 1.

M = 4Q/(2c × Q/mc)  = 4Q ÷ 2Q/m  = 4Q × m/2Q = 2m

The radius of a hemisphere with a volume of 61326 ft^3 , to the nearest tenth of a foot is 30.827 f.

The volume of a sphere with radius R is known to be:

V = (4/3)*pi*R^3

in where pi = 3.14

A hemisphere is half a sphere, its volume is half that of a sphere, and its volume is as follows for a hemisphere of radius R:

V' = (1/2)*(4/3)*pi*R^3

Now that we are aware of the volume of our hemisphere:

V' = 61326 ft^3

The equation is then easy to solve:

61326 ft^3 = (1/2)*(4/3)*pi*R^3

For R.

(We need the diameter, but knowing the radius is a good place to start because the diameter is equal to two times the radius.)

61326 ft^3 = (1/2)*(4/3)*pi*R^3

61326 ft^3 = (4/6)

*3.14*R^3

61326 ft^3*(6/4*3.14) = R^3

∛( 61326 ft^3*(6/4*3.14) ) = R = 30.827 f

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Answer:

PE = 0.73J

Explanation:

Remember that in conservative spring systems,

Total energy = potential + kinetic energy.

On the y-axis lies the kinetic energy and the question asks for the potential energy.

PE + KE must always equal the same result.

In this case, KE + PE = 1

So rearranging the equation,

PE = 1 - KE

KE = 0.27 (as we can see from the graph)

Therefore,

PE = 1 - 0.27 = 0.73J

Bonus tip: The graphs of potential and kinetic energy will look the exact opposite in this case. When the KE graph is at 0J, the PE graph is at 1J and vice versa. And they always cross over at 0.5J

1,401.88 N is the required weight of the man using the given conversion factor.

To calculate the weight of a typical NFL lineman in Newtons, we need to first convert the weight from pounds to kilograms using the conversion factor of 1 kg = 2.2 pounds:

314 pounds ÷ 2.2 pounds/kg = 142.73 kg

Next, we can use the formula Weight (newtons) = mass * gravity, where gravity is approximately 9.81 m/s^2 (meters per second squared):

Weight (newtons) = 142.73 kg * 9.81 m/s^2 = 1,401.88 N

The required weight in Newton of the man is 1,401.88 N

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Answer:

Power_input = 85.71 [W]

Explanation:

To be able to solve this problem we must first find the work done. Work is defined as the product of force by distance.

 \(W =F*d\)

where:

W = work [J] (units of Joules)

F = force [N] (units of Newton)

d = distance [m]

We need to bear in mind that the force can be calculated by multiplying the mass by the gravity acceleration.

Now replacing:

 \(W=m*g*d\)

\(W=80*10*3\\W=2400[J]\)

Power is defined as the work done over a certain time. In this way by means of the following formula, we can calculate the required power.

 \(P=W/t\)

where:

P = power [W] (units of watts)

W = work [J]

t = time = 40 [s]

\(P=W/t\\P=2400/40\\P=60 [W]\)

The calculated power is the required power. Now as we have the efficiency of the machine, we can calculate the power that is introduced, to be able to do that work.

 \(Effic=0.7\\Effic=P_{required}/P_{introduced}\\P_{introduced}= 60/0.7\\P_{introduced}=85.71[W]\)

Answer:

conduction (the heat is transferring to the air)

Answer:

2.29 s

Explanation:

This problem is a description of an elastic collision (the two objects collide and effectively become one object).  The equation for an elastic collision is

\(m_1v_1+m_2v_2=m_3v_3\), where:

\(m_1v_1\) = the mass of the child (55.0 kg) times the velocity of the child (2.5\(\frac{m}{s}\))

\(m_2v_2\) =  the mass of the sled (12.0 kg) times the velocity of the sled (0.0\(\frac{m}{s}\))

\(m_3v_3\) = the combined mass of the child and the sled (67.0 kg) times the combined velocity of the child and the sled (\(v_3\))

First, rearrange the problem to solve for \(v_3\):

\(\frac{m_1v_1+m_2v_2}{m_3}=v_3\)

So,

\(\frac{(55.0\ kg)(2.5\ \frac{m}{s})+(12.0\ kg)(0.0\ \frac{m}{s})}{67.0\ kg}=v_3\\\frac{137.5\frac{kg*m}{s}}{67.0\ kg}=v_3\\2.05\frac{m}{s}=v_3\)

The force of friction for this problem is given as 60 N.  To stop the child and the sled, the force of friction must be equal and opposite to the force of the child and sled.  According to Newton's first law, force equals mass times acceleration (F=ma).  So, an equation to solve this portion of the problem can be given as -60 N=ma, where m=67.0 kg.  So,

\(-60\ N=(67.0\ kg)a\\\frac{-60\ \frac{kg*m}{s^2}}{67.0\ kg}=a\\-0.90\frac{m}{s^2}\)

Acceleration can then be used in kinematic equation #1 (\(v_f=v_i+at\)) to solve for time.  Rearrange the equation and let

\(v_f=0.0\frac{m}{s}\\v_i=2.05\frac{m}{s}\\a=-0.90\frac{m}{s^2}\)

So,

\(\frac{v_f-v_i}{a}=t\\\frac{0.0\frac{m}{s}-2.05\frac{m}{s}}{-0.90\frac{m}{s^2}}=t\\\frac{-2.05\frac{m}{s}}{-0.90\frac{m}{s^2}}=t\\2.29\ s=t\)

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.

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.

Net forces in all above cases will be

A) F net = 0

B) F net = 1 N

C) F net = 5 N

D) F net = 5N

E) F net  = 5 N

F) F net = 5 N

G) F net = 9.9 N

H) F net = 9.9 N

A) net force = upward force - downward force

                   = 4 - 4 = 0

B) net force = rightward force - leftward force = 4 - 3 = 1 N  

C) net force  

using Pythagoras theorem

F net =  \(\sqrt{4^{2} + 3^{2} }\) = \(\sqrt{25}\) = 5 N

D) F net = \(\sqrt{-4^{2} + (-3)^{2} }\) = 5 N

E) balancing horizontal forces

   rightward force - leftward force  = 5 - 2 = 3 N

   using  Pythagoras theorem

   F net =  \(\sqrt{4^{2} + 3^{2} }\) = 5 N

F) balancing vertical forces

   -5 + 2 = -3 N

    using  Pythagoras theorem

     \(\sqrt{(-4)^{2} +(-3) ^{2} }\) = 5 N

G) using  Pythagoras theorem

    F net = \(\sqrt{7^{2} + 7^{2} }\) = 9.9 N

H ) balancing horizontal forces

     10 - 3 = 7 N

     \(\sqrt{7^{2} + 7^{2} }\) = 9.9 N

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The vector potential inside the sphere is μ₀cπ, and the magnetic field inside the sphere is zero. Outside the sphere, the magnetic field intensity is given by B = (μ₀cR²/r²), where R is the radius of the sphere and r is the radial distance from the center of the sphere.

To find the vector potential and intensity of the magnetic field inside and outside a rotating sphere with a constant surface charge density, we can use the Biot-Savart law and Ampere's law.

Inside the sphere:

Inside the sphere, the radial distance r is less than the radius R of the sphere. We consider a circular current loop of radius r within the sphere.

Using the Biot-Savart law, the vector potential (A) at a point inside the sphere due to the circular current loop can be expressed as:

A = (μ₀/4π) ∫(Idl × r)/r²

Since the charge density is constant, the current (I) flowing through the circular loop is proportional to the area of the loop, which can be expressed as I = c × πr².

Substituting this expression for I into the equation for A, we get:

A = (μ₀c/4) ∫(dl × r)/r²

By integrating around the loop, we find that the integral term is equal to 2π, and simplifying further, we obtain:

A = (μ₀c/2r) ∫dl

The integral term on the right-hand side is simply the circumference of the loop, which is 2πr. Substituting this back into the equation, we get:

A = (μ₀c/2r) × 2πr = μ₀cπ

The magnetic field (B) can be obtained from the vector potential using the equation B = ∇ × A. Since the vector potential A is independent of position, the curl of A is zero. Therefore, the magnetic field inside the sphere is zero.

Outside the sphere:

Outside the sphere, the radial distance r is greater than the radius R of the sphere. Using Ampere's law, we can find the magnetic field.

Around a circular loop outside the sphere, the magnetic field is given by:

B = (μ₀I/2πr)

Since the current I is proportional to the area of the loop, which is πR², we have I = cπR². Substituting this expression for I into the equation for B, we get:

B = (μ₀cR²/2πr³) × 2πr = (μ₀cR²/r²)

Therefore, the intensity of the magnetic field outside the sphere is given by B = (μ₀cR²/r²).

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Answer:

Significant figures have a few rules about 0s and you should research but simply, for example say round 27.879 to 3 significant figures you round up until you have 3 numbers that aren't 0s so it would be 27.9.

SI units are the international system of units.

Answer:

SI units refer to the International System of Units. These are the standard units that measurements are typically given in. For example, the SI unit for time is seconds, meters for distance, kg for mass, etc.

Significant figures are the number of notable digits given for a measurement. For example, let's say you measured a piece of metal to be exactly 3.00 meters long. The value 3.00 has three significant figures, where as 3 only has one significant figure. Larger amounts of significant figures indicate a more precise measurement. In this case, by writing 3.00 instead of 3, you're telling me that you measured that piece of metal to be precisely 3.00 meters long.

Taking into account the definition of wavelength, frecuency and propagation speed, the frequency is 5 Hz.

Wavelength (λ) is the distance between two consecutive points that are in the same state of vibration (the state of vibration is called phase). It is expressed in units of length (m).

Frequency (f) is the number of waves per unit of time and is normally expressed in Hertz (Hz) which is the number of waves per second.

The velocity of propagation is the speed with which the wave propagates in the medium. Relate the wavelength (λ) and the frequency (f) inversely proportional using the following equation:

v = f * λ

In this case, you know:

Replacing in the previous expression:

50 m/s= f× 10 cm

Solving;

f= 50 m/s÷ 10 cm

f= 5 Hz

Finally, the frequency is 5 Hz.

Learn more:

Answer:

c

Explanation:

Answer:

Answer d) Lab B's reading is less precise than Lab A's

Explanation:

Recall that accuracy is a measure of how close to the actual physical quantity the experiment leads to. In this case, we don't know what the true age is,so we cannot tell which reading is more accurate.

But we can tell which reading is more precise given the value of their reported errors. Since Lab A shows a smaller error in years (+/- 20 years versus 30 years), as well as a smaller percent error (3.9% versus 5.1%), we can say that Lab's A reading is more precise than Lab B's reading.

This agrees with answer labeled d).

Answer: 10m per second.

Explanation: 100/10 is 10/1, so it would be 10m per second.

The tank pressure is 5.08 kPa and the mass flow rate is 2.6 kg/s.

The given parameters:

The ratio of the areas of the converging-diverging nozzle is calculated as follows;

\(= \frac{A}{A^*} \\\\= \frac{0.002896}{0.001} \\\\= 2.896\)

From supersonic isentropic table, at \(\frac{A}{A^*} = 2.896\), we can determine the following;

\(M_e = 2.6 \ kg/s\\\\\frac{P_o}{P_e} = 19.954\)

The tank pressure is calculated as follows;

\(\frac{P_o}{P_e} = 19.954 \\\\P_e = \frac{P_o}{19.954} \\\\P_e = \frac{101.325 \ kPa}{19.954} \\\\P_e = 5.08 \ kPa\)

Thus, the tank pressure is 5.08 kPa and the mass flow rate is 2.6 kg/s.

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Based on the information provided in the second paragraph of "On a Mountain Trail," the correct option would be "The pack surrounding the sleigh is a very real threat to the two men on the trail." The correct option is C.

In the second paragraph, it is mentioned that the wolves had stopped running and were now "moving at a dogtrot, leisurely and methodically encircling the sleigh." This description implies that the wolves are actively surrounding the sleigh, which suggests a potential threat to the two men on the trail. The word "encircling" indicates a deliberate and coordinated action by the wolves, which implies predatory behavior.

Now let's examine why the other options are not true:

A. The surrounding pack should not be concerning to the two men.

This option is not true because the description in the paragraph clearly implies that the pack of wolves surrounding the sleigh is a cause for concern.

B. The wolves will eventually tire and will return to the safety of the underbrush.

This option is not supported by the information provided in the paragraph. There is no mention of the wolves becoming tired or retreating to the safety of the underbrush. The description implies that the wolves are actively encircling the sleigh, indicating an ongoing threat.

D. Once a sleigh is surrounded by a pack of wolves, there is no chance for human survival.

This option is an extreme statement and goes beyond the information provided in the paragraph. The paragraph does not provide any conclusive information about the chances of human survival in such a situation. It simply describes the current state of the wolves surrounding the sleigh, but it does not make a definitive statement about the outcome for the two men.

Therefore, The correct option is C.

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Answer is

Elements are pure substances which are composed of only one type of atom. Compound are substances which are formed by two or more different types of elements that are united chemically in fixed proportions.

Explanation:

I think that's the correct answer sorry if im wrong

Answer:

20.0N

Becuase It's the largest

Answer:

20.0

Explanation:

It's the biggest number

Answer:

The answer is the third photo

Explanation:

Following are the calculation to the voltage:

Given:

The voltage across a \(\bold{0.10 \mu \ F}\) capacitor.

To find:

The function of the capacitor=?

Solution:

\(\to \bold{Q = CV}\)

so,  

\(\to \bold{I = \frac{dQ}{dt} = C\ \frac{dV}{dt}}\)

As a result, this should nearly correspond to the gradient of the voltage curve.

from 0 to 1:

\(\to \frac{dV}{dt} = \frac{100}{1 \mu \ S}\)

so  \(I = 0.1 \times 100 = 10\ A\)

from 1 to 2:

\(\to \frac{dV}{dt} = 0\)

so \(I = 0\)

from 2 to 4:

\(\to \frac{dV}{dt} = \frac{100}{2 \mu \ S}\)

so \(I = 0.1 \times 50 = -5 A\)

Therefore, the final answer is "third image".

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The vehicle has a 2000kg mass.

Take a mass's acceleration into account. Use the formula F = m a to determine the force's value. Kilogram-meter/second-squared will be used as the unit of force. The short name for this unit, which is made up of the three basic SI units, is newton.

F= ma

m= F/a

m= 50000/25

m= 2000 kg

According to Newton's Second Law of Motion, acceleration (gaining speed) occurs whenever a force acts on a mass (object). This law of motion is best demonstrated by riding a bicycle. The mass is your bicycle. The force that propels you forward on your bicycle comes from your leg muscles.

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