How many times does a human heart beat during a person’s lifetime? How many gallons of blood does it pump? (Estimate that the heart pumps 50 cm3 of blood with each beat.)

Answer:

[tex]P= 60.5 \frac{psia ft^3}{s} *\frac{1 Btu}{5.404 psia ft^3} *\frac{1 hp}{0.7068 Btu/s}= 15.839 hp[/tex]

Explanation:

Notation

For this case we have the following pressures:

[tex] p_1 = 15 psia[/tex] initial pressure

[tex]p_2 = 70 psia[/tex] final pressure

[tex] V^{*} = 1.1 ft^3/s[/tex] represent the volumetric flow

[tex] rho[/tex] represent the density

[tex]m^{*}[/tex] represent the mass flow

Solution to the problem

From the definition of mass flow we have the following formula:

[tex] m^{*} = \rho V^{*}[/tex]

For this case we can calculate the total change is the sytem like this:

[tex] \Delta E= \frac{p_2 -p_1}{\rho}[/tex]

Since we just have a change of pressure and we assume that all the other energies are constant.

The power is defined as:

[tex] P = m^* \Delta E[/tex]

And replacing the formula for the change of energy we got:

[tex]P = m V^* \frac{p_2 -p_1}{\rho} = V^* (p_2 -p_1)[/tex]

And replacing we have this:

[tex] P= (70-15) psia * 1.1 \frac{ft^3}{s} =60.5 \frac{psia ft^3}{s}[/tex]

And we can convert this into horsepower like this:

[tex]P= 60.5 \frac{psia ft^3}{s} *\frac{1 Btu}{5.404 psia ft^3} *\frac{1 hp}{0.7068 Btu/s}= 15.839 hp[/tex]

Complete question:

When lithium iodide is dissolved in water, the solution becomes hotter.

What can you conclude about the relative magnitudes of the lattice energy of lithium iodide and its heat of hydration?

Answer:

The heat of hydration is greater in magnitude than the lattice energy  and lattice energy is smaller in magnitude that the heat of hydration.

Explanation:

When the solution becomes hotter on addition of lithium iodide, it shows exothermic reaction and it means that the heat of hydration is greater than the lattice energy  and lattice energy is smaller in magnitude that the heat of hydration.

This can also be observed in the formula below;

[tex]H_{solution} = H_{hydration} + H_{lattice. energy}[/tex]

Heat of the hydration is thus greater in magnitude than that of the lattice energy and the lattice energy is smaller in the magnitude than the heat of hydration.

The lattice energy is defined as the energy needed to separate the mole of the icon into a slid gaseous ion. It can be measured empirically and is calculated by use of electrostatics.

The heat of hydration is the great energy generated when the water reacts with the contact of cement powder. This leas to high temperatures and cause thermal cracking and the reduction of mechanical properties.

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Answer:

a.52.9 km/h

b.90 km

Explanation:

We are given that

[tex]v_1=89km/h[/tex]

[tex]t_1=30min[/tex]

[tex]v_2=100km/h[/tex]

[tex]t_2=12min[/tex]

[tex]v_3=40km/h[/tex]

[tex]t_3=45 min[/tex]

Time spend on eating lunch and buying ga=15 min.

a.Total time=30+12+45+15=102 minute=[tex]\frac{102}{60}=1.7 hour[/tex]

1 hour=60 minutes

Distance=[tex]speed\times time[/tex]

[tex]d_1=v_1\times t_1=80\times\frac{30}{60}=40km[/tex]

[tex]d_2=100\times \frac{12}{60}=20 km[/tex]

[tex]d_3=40\times \frac{45}{60}=30 km[/tex]

Total distance=[tex]d_1+d_2+d_3=40+20+30=90km[/tex]

Average speed=[tex]\frac{total\;speed}{total\;time}[/tex]

Using the formula

Average speed=[tex]\frac{90}{1.7}=52.9Km/h[/tex]

b.Total distance between the initial and final city lies along the route=90 km

Answer:

Electric field, E = 300.65 N/C

Explanation:

Given that,

Intensity of a beam of electromagnetic radiation, [tex]I=120\ W/m^2[/tex]

We need to find the maximum value of the electric field. The intensity of electromagnetic wave in terms of electric field is given by :

[tex]I=\dfrac{1}{2}\epsilon_oE^2c[/tex]

c is the speed of light

[tex]E=\sqrt{\dfrac{2I}{\epsilon_o c}}[/tex]

[tex]E=\sqrt{\dfrac{2\times 120}{8.85\times 10^{-12}\times 3\times 10^8}}[/tex]

E = 300.65 N/C

So, the maximum value of the electric field is 300.65 N/C. Hence, this is the required solution.

The maximum value of the electric field for the given beam of electromagnetic radiation.

the electric field of an electromagnetic radiation can be calculated by,

[tex]\bold {I = \dfrac 12 \epsilon_0 E^2C}[/tex]

[tex]\bold {E = \sqrt {\dfrac {2I}{\epsilon_0 C}}}[/tex]

Where,

I - intensity of the beam = 120 W/m2

C- speed of light = [tex]\bold { 3x10^8\ m/s}}[/tex]

E - electric field

Put the value of the formula

[tex]\bold {E = \sqrt {\dfrac {2\times 20 }{8.85x10^{-12} \times 3x10^8}}}\\\\\bold {E = 300.65\ N/C}[/tex]

Therefore, the maximum value of the electric field for the given beam of electromagnetic radiation.

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To calculate the approximate mass of the Milky Way Galaxy within the Sun's orbit, we use circular motion and gravity principles. The mass is approximately 5.8 trillion solar masses.

To calculate the approximate mass of the Milky Way Galaxy within the Sun's orbit, we can use the principles of circular motion and gravity. The mass of the Milky Way Galaxy can be determined using the formula gravitational force = centripetal force. By rearranging the equation and plugging in the given values, we can solve for the mass. The approximate mass of the Milky Way Galaxy within the Sun's orbit is approximately 5.8 trillion solar masses.

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The mass of the Milky Way Galaxy within the Sun's orbit is approximately 1.0 x 10⁴¹ kg or about 5 x 10¹¹ solar masses.

We know the Sun orbits the galactic center every 230 million years (2.3 x 10⁸ years) and is approximately 27,000 light-years (2.54 x 10¹⁷ meters) away from the center.

1. First, we convert the orbital period to seconds:

2. Next, we apply Newton's form of Kepler's third law, which states:

where

3. Rearranging for M gives us:

Substituting known values:

This mass is approximately 5 x 10¹¹ solar masses, considering one solar mass is about 2 x 10³⁰ kg.

Answer: The final volume of the gas is 1.12 L

Explanation:

W = work done on or by the system

w = work done by the system = [tex]P\Delta V[/tex]  

P = pressure = 783 torr = 1.03 atm     (1atm=760 torr)

w= 110.8 J = 1.094 J       (1Latm=101.3J)

[tex]V_1[/tex] = initial volume = 57.8 ml = 0.0578L   (1L=1000ml)

[tex]V_2[/tex] = final volume = ?

[tex]1.094Latm=1.03atm\times (V_2-0.0578)L[/tex]

[tex](V_2-0.0578)=1.06[/tex]

[tex]V_2=1.12L[/tex]

The final volume of the gas is 1.12 L

Answer:

0.00833542627085 Nm

Explanation:

[tex]\omega_f[/tex] = Final angular velocity = 700 rpm

[tex]\omega_i[/tex] = Initial angular velocity

[tex]\alpha[/tex] = Angular acceleration

m = Mass of stone = 1.3 kg

r = Radius = 8.5 cm

[tex]\omega_f=\omega_i+\alpha t\\\Rightarrow \alpha=\dfrac{\omega_f-\omega_i}{t}\\\Rightarrow \alpha=\dfrac{0-700\dfrac{2\pi}{60}}{41.3}\\\Rightarrow \alpha=-1.77491110372\ rad/s^2[/tex]

Torque is given by

[tex]\tau=-I\alpha\\\Rightarrow \tau=-\dfrac{1}{2}mr^2\alpha\\\Rightarrow \tau=-\dfrac{1}{2}1.3\times 0.085^2\times -1.77491110372\\\Rightarrow \tau=0.00833542627085\ Nm[/tex]

The frictional torque is 0.00833542627085 Nm

Answer:

62.6m

Explanation:

We are given that

Speed of Cheetah,v=20 m/s

Time=2.5 s

Top speed=[tex]v'=28m/s[/tex]

We have to express Cheetah's top speed in mi/h

1 mile=1609.34 m

1 m=[tex]\frac{1}{1609.34}miles[/tex]

1 hour=3600 s

By using these values

[tex]v'=\frac{\frac{28}{1609.34}}{\frac{1}{3600}}[/tex]mi/h

[tex]v'=\frac{28}{1609.34}\times 3600[/tex]mi/h

Top speed of Cheetah=62.6mph

Answer:

The acceleration of the laundry cart is 13.3 m/s²

Explanation:

Hi there!

According to Newton's second law, the sum of all forces acting on an object in a given direction is equal to the mass of the object times its acceleration in that direction:

∑F = m · a

Where:

∑F = net force acting on the cart.

m = mass of the cart.

a = acceleration.

Then, solving this equation for the acceleration:

∑F / m = a

60.0 N / 4.50 kg = a

a = 13.3 m/s²

The acceleration of the laundry cart is 13.3 m/s²

Using the formula of acceleration a = F/m, where F is the net external force and m is the mass, substituting the given values yields an acceleration of 13.33 m/s².

According to Newton's second law, the acceleration of an object as produced by a net force is directly proportional to the net force, in the same direction as the net force, and inversely proportional to the mass of the object. This can be expressed with the formula a = F/m, where F is the net external force and m is the object's mass.

Given the mass m of the laundry cart is 4.5 kg and the net external force F on the cart is 60.0 N, we can substitute these values into the formula.

Therefore, the acceleration a = F/m = 60.0 N / 4.50 kg = 13.33 m/s².

So, the magnitude of the cart's acceleration is 13.33 m/s².

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Answer:

24.3 degrees

Explanation:

A car traveling in circular motion at linear speed v = 12.8 m/s around a circle of radius r = 37 m is subjected to a centripetal acceleration:

[tex]a_c = \frac{v^2}{r} = \frac{12.8^2}{37} = 4.43 m/s^2[/tex]

Let α be the banked angle, as α > 0, the outward centripetal acceleration vector is split into 2 components, 1 parallel and the other perpendicular to the road. The one that is parallel has a magnitude of 4.43cosα and is the one that would make the car slip.

Similarly, gravitational acceleration g is split into 2 component, one parallel and the other perpendicular to the road surface. The one that is parallel has a magnitude of gsinα and is the one that keeps the car from slipping outward.

So [tex] gsin\alpha = 4.43cos\alpha[/tex]

[tex]\frac{sin\alpha}{cos\alpha} = \frac{4.43}{g} = \frac{4.43}{9.81} = 0.451[/tex]

[tex]tan\alpha = 0.451[/tex]

[tex]\alpha = tan^{-1}0.451 = 0.424 rad = 0.424*180/\pi \approx 24.3^0[/tex]

Using Newton's second law and free-body diagram the angle with which the curve is to be banked is obtained as [tex]24.31^\circ[/tex].

This problem can be analysed using a free-body diagram.

The acceleration in the horizontal direction (radial diretion) is the centripetal acceleration.

Applying Newton's second law of motion in the x-direction, we get;

[tex]\sum F = ma[/tex]

[tex]\implies N\,sin\, \theta =\frac{mv^2}{r}[/tex]

Now, applying Newton's second law of motion in the y-direction, we get;

[tex]\implies N\,cos \, \theta=mg[/tex]

Dividing both the equations, we get;

[tex]\frac{N\,sin\, \theta}{N\,cos\, \theta} =\frac{mv^2}{r\, mg}[/tex]

[tex]\implies tan\theta=\frac{v^2}{rg}=\frac{12.8^2}{37\times9.8} =0.4518[/tex]

[tex]\implies \theta=tan^{-1}(0.4518)=24.31^\circ[/tex]

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The question involves calculations using the principles of projectile motion and 2D kinematics to understand the trajectory of a baseball pitch. Values include horizontal and vertical velocity changes over time, the exact speed of the baseball and the angle at which baseball hits the ground.

The question involves the physics of projectile motion, specifically applied to the trajectory of a pitch in baseball. The parameters of this problem can be solved using the kinematic equations and principles that govern 2D motion.

(1) To solve part (a), one must understand that for such problems involving gravity, the x (horizontal) component of the object's velocity remains constant throughout the motion, in this case 142 ft/sec. This fact is obtained from the equation x(t) = v_xt, where v_x is the constant x-component (horizontal) of velocity.

(2) For part (b), similarly, the x-component of the velocity remains same at any point in trajectory, including when it passes over home plate, so it is again 142 ft/sec.

(3) For part (c), the derivative of y(t) -16t^2 + 5t + 5 needs to be found to get the y-component (vertical) of velocity which is -32t + 5. This is because as the object moves under the effect of gravity, vertical velocity changes with time.

(4) For part (d), the magnitude of the speed at any time can be found by taking the square root of the sum of squares of x and y-components of velocity. (5) Part (e), seeks the time when the baseball hits the ground. The equation of vertical motion -16t^2 + 5t + 5 = 0 should be used, as the height of the object from ground is 0 when it hits the ground. Solving for t would give that time.

End of the problem involves understanding some trigonometric relationships to calculate the angle (in radians).

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To solve this exercise we will define the units of conversion between each of the variables given to facilitate the calculation in each section.

[tex]1 mile = 5280ft[/tex]

[tex]1h = 3600s[/tex]

[tex]1 ft = 30.48cm[/tex]

[tex]1 m = 100cm[/tex]

[tex]1kg = 1000g[/tex]

PART A ) For this part we have 60mph to ft/s, then

[tex]60mph = 60\frac{miles}{hour} (\frac{5280ft}{1mile})(\frac{1h}{3600s})[/tex]

[tex]60mph = 88ft/s[/tex]

PART B) Convert from [tex]ft/s^2[/tex] to [tex]m/s^2[/tex]

[tex]32ft/s^2 = 32 \frac{ft}{s^2} (\frac{30.48cm}{1ft})(\frac{1m}{100cm})[/tex]

[tex]32ft/s^2 = 9.7536m/s^2[/tex]

PART C) Convert [tex]g/cm^3[/tex] to [tex]kg/m^3[/tex]

[tex]1 g/cm^3 = 1\frac{g}{cm^3}(\frac{1kg}{1000g})(\frac{100cm}{1m})^3[/tex]

[tex]1 g/cm^3 = 1000kg/m^3[/tex]

Based on the conversion factors,  the conversions are as follows:

Conversions are used when converting between different units measuring the same quantity.

a. To convert 60 mph to ft/s:

60 mph = 60 * 5280/3600

60 mph = 88 ft/s

b. To convert 32 ft/s² to m/s

1 ft = 30.48 cm = 0.3048 m

32 ft/s² = 32 * 0.3034

32 ft/s² = 9.75 m/s²

c. To convert g/cm³ to kg/m³

1 g = 0.001 kg

1 cm³ = 0.000001 m³

1.0 g/cm3 = 1.0 * 0.001 kg/0.000001 m³

1 g/cm³ = 1000 Kg/m³

Therefore, the conversions are as follows:

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Answer:

The minimum shear strain in the tube is [tex]4.162\times10^{-3}[/tex]

The shear strain at the median line of the tube section is [tex]9.15\times10^{-3}[/tex]

Explanation:

Given that,

Maximum shear strain = 0.005

We need to calculate the minimum shear strain

Using formula of maximum shear strain

[tex]\gamma_{max}=\dfrac{d_{2}}{2}\times\theta[/tex]

[tex]\theta=\dfrac{2\times\gamma_{max}}{d_{2}}[/tex]

Where, [tex]\gamma_{max}[/tex]=maximum shear strain

[tex]\theta[/tex]=angle of twist

[tex]d_{2}[/tex]= diameter

Put the value into the formula

[tex]\theta=\dfrac{2\times0.005}{3}[/tex]

[tex]\theta=0.00333\ rad[/tex]

[tex]\theta=3.33\times10^{-3}\ rad[/tex]

Now, Using formula of minimum shear strain

[tex]\gamma_{min}=\dfrac{d_{1}}{2}\times\theta[/tex]

Put the value into the formula

[tex]\gamma_{min}=\dfrac{2.5}{2}\times3.33\times10^{-3}[/tex]

[tex]\gamma_{min}=0.0041625[/tex]

[tex]\gamma_{min}=4.162\times10^{-3}[/tex]

We need to calculate the shear strain at the median line of the tube section

Using formula of shear strain at the median line

[tex]\gamma=\dfrac{d_{1}+d_{2}}{2}\times\theta[/tex]

Put the value into the formula

[tex]\gamma=\dfrac{2.5+3}{2}\times3.33\times10^{-3}[/tex]

[tex]\gamma=0.0091575[/tex]

[tex]\gamma=9.15\times10^{-3}[/tex]

Hence, The minimum shear strain in the tube is [tex]4.162\times10^{-3}[/tex]

The shear strain at the median line of the tube section is [tex]9.15\times10^{-3}[/tex]

Explanation of how to calculate the minimum shear strain and the shear strain at the median line in a circular tube subjected to torque.

Shear Strain Calculations:

a) Yes, if acceleration and velocity have opposite directions

b) Yes, if acceleration and velocity have same direction

Explanation:

a)

In order to answer this question, we have to keep in mind that both velocity and acceleration are vector quantities, so they have also a direction.

Acceleration is defined as the rate of change in velocity:

[tex]a=\frac{v-u}{t}[/tex]

where

u is the initial velocity

v is the final velocity

t is the time elapsed

In this problem, the object is slowing down: this means that the magnitude of its velocity is decreasing, so

[tex]|v|<|u|[/tex]

This means that the direction of the acceleration is opposite to the direction of the velocity. Then, the magnitude of the acceleration can be increasing (this will not affect the fact that the object will slow down, but it will affect only the rate at which the object is slowing down).

b)

In this case, the object is speeding up. This means that the magnitude of its velocity is increasing, so we have

[tex]|v|>|u|[/tex]

In order for this to happen, it must be that the direction of the acceleration is the same as the direction of the velocity: therefore, this way, the magnitude of the velocity  will be increasing (either in the positive or in the negative direction).

Then, the magnitude of the acceleration can be decreasing (this will not affect the fact that the object will speed up, but it will only affect the rate at which the object is speeding up).

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Answer:

404K

Explanation:

Data given, Kinetic Energy.K.E=8.37*10^-21J

Note: as the temperature of a is increase, the rate of random movement will increase, hence leading to more collision per unit time. Hence we can say that the relationship between the kinetic energy and the temperature is a direct variation.

This relationship can be expressed as

[tex]K.E=\frac{3}{2}KT[/tex]

where K is a constant of value 1.38*10^-23

Hence if we substitute the values, we arrive at

[tex]T=\frac{2/3(8.37*10^{-21})}{1.38*10^-23}\\ T=404K[/tex]

converting to degree we have [tex]131^{0}C[/tex]

Answer:

bicycle>soccer ball>cat>toy car

Explanation:

s = Distance

t = Time

Speed is given by

[tex]v=\dfrac{s}{t}[/tex]

For toy car

[tex]v=\dfrac{0.1}{2.5}=0.04\ m/s[/tex]

For soccer ball

[tex]v=\dfrac{2.5}{0.55}=4.54\ m/s[/tex]

For bicycle

[tex]v=\dfrac{0.6}{7.5\times 10^{-2}}=8\ m/s[/tex]

For cat

[tex]v=\dfrac{8}{2.5}=3.2\ m/s[/tex]

8>4.54>3.2>0.04

bicycle>soccer ball>cat>toy car

Answer:

A black body or blackbody is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. (It does not only absorb radiation, but can also emit radiation. The name "black body" is given because it absorbs radiation in all frequencies, not because it only absorbs.) A white body is one with a "rough surface that reflects all incident rays completely and uniformly in all directions."

Answer:

30 N

Explanation:

We are given that

Force,F =9 N

Charge,q=3 C

We have to find the exact magnitude of the force(in N) exerted by the system of charges on the 10.0 C.

We know that

[tex]E=\frac{F}{q}[/tex]

Using the formula

[tex]E=\frac{9}{3}=3 N/C[/tex]

Now, charge=10 C

The electric field remains same then

[tex]F=3\times 10=30 N[/tex]

Hence, the exact magnitude of the force exerted by the system of charges on the 10 C=30 N

The exact magnitude of the force exerted by the system of charges on the 10.0 C charge is 29.97 N.

The force exerted by a fixed system of charges on a charge is given by Coulomb's law, which states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. In this case, we are given that the force exerted on a 3.0 C charge is 9.0 N. When the 3.0 C charge is replaced with a 10.0 C charge, the force can be calculated using the proportionality of the charges. Since the charge is increased by a factor of (10.0 C)/(3.0 C) = 3.33, the force will also increase by the same factor. Therefore, the exact magnitude of the force exerted by the system of charges on the 10.0 C charge is 9.0 N * 3.33 = 29.97 N.

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To solve the problem, we analyze a block on an incline to determine its acceleration with and without friction, calculate the minimum spring constant to prevent motion, and find the required coefficient of static friction for a new block added to the system.

This problem involves concepts from Physics, specifically dynamics and statics, to understand the motion of a block on an incline and the effects of friction and spring force. To solve such problems, we use Newton's second law of motion, the equation for frictional force, and Hooke's law for the spring force. These principles help us calculate the acceleration of the block, the conditions required to prevent its motion, and the properties of friction between surfaces in contact.

For the first part, without friction, the acceleration can be found using the component of gravitational force along the incline. With friction, the net force includes both the component of gravitational force along the incline and the frictional force, affecting the acceleration. To find the minimum spring constant, Hooke's law is applied considering the balance of forces to prevent the block's motion. Lastly, calculating the minimum coefficient of static friction for a new block involves considering the combined system's weight and ensuring the frictional force is sufficient to prevent motion.

Answer:

 R=19 N

Explanation:

Given that forces are taking opposite to each other.

Take

F₁ = 86 N ( Towards right ,take positive)

F₂ = - 67 N ( Towards left)

Given that the angle between above two forces is 180° so the resultant can be given as

Lets take the resultant = R N

R= F₁ + F₂

Now by putting the values

R= 86 N - 67 N

R=19 N

Therefore the resultant force on the block box will be 19 N.

Final answer:

The magnitude of the net force on the box is 19 N, calculated by subtracting the smaller force from the larger force since they are directed oppositely.

Explanation:

When two brothers push on a box from opposite directions, one with a force of 86 N and the other with a force of 67 N, the net force on the box is determined by subtracting the smaller force from the larger force because they are applied in opposite directions. Therefore, the magnitude of the net force on the box can be calculated as follows:

Net Force = Larger Force - Smaller Force
Net Force = 86 N - 67 N
Net Force = 19 N

Hence, the magnitude of the net force acting on the box is 19 N.

Answer:

17.23 m/s²

Explanation:

Applying the equation of motion,

Δs = ut + 1/2at²..................... Equation 1

Where Δs  = change in height of the rocket, u = initial velocity of the rocket, a = acceleration of the rocket, t = time

making a the subject of the equation,

a = 2(Δs-ut)/t²..................... Equation 2

Given: Δs = (56-4) m = 52 m, u = 11.0 m/s, t = 1.90 s.

Substitute into equation 2

a = 2[52-(11×1.9)]/1.9²

a = 2(52-20.9)/1.9²

a = 2(31.1)/3.61

a = 62.2/3.61

a = 17.23 m/s².

Thus the acceleration = 17.23 m/s²

Final answer:

To find the magnitude of acceleration, we used the kinematic equation s = ut + ½at². We determined the displacement due to the initial velocity and the time interval, and then solved for acceleration to find that the rocket's magnitude of acceleration is 17.2 m/s².

Explanation:

To calculate the magnitude of its acceleration, we can use the kinematic equations for uniformly accelerated motion along with the information provided about the rocket's velocity and positions at different times. We have two positions, 4.00 m and 56.0 m, and a time interval of 1.90 s. The rocket's velocity at the lower height is 11.0 m/s.

Step 1: Use the second kinematic equation

We will use the kinematic equation:
s = ut + ½at², where 's' is the displacement, 'u' is the initial velocity, 'a' is the acceleration, and 't' is the time.

Step 2: Set up the equation with the known values

Let's calculate the displacement (Δs): Δs = 56.0 m - 4.00 m = 52.0 m
Now put the known values into the equation: 52.0 m = (11.0 m/s)(1.90 s) + ½a(1.90 s)²

Step 3: Solve for acceleration 'a'

First, we calculate the distance traveled due to the initial velocity: (11.0 m/s)(1.90 s) = 20.9 m
Subtract this value from the total displacement to find the displacement caused by acceleration: 52.0 m - 20.9 m = 31.1 m
Rewrite the equation with this new information: 31.1 m = ½a(1.90 s)²
Now solve for 'a': a = (2 × 31.1 m) / (1.90 s)² = 17.2 m/s²

The magnitude of acceleration of the rocket is therefore 17.2 m/s².

Answer:

11.245 m

Explanation:

The vertical component of the initial velocity v0 is

[tex]v_v = v_0sin58^0 = 0.848v_0[/tex]

This makes the ball reach a maximum height of 8m. If we apply the conservation law of mechanical energy, its kinetic energy is converted to potential energy when it travels to the maximum height

[tex]E_p = E_k[/tex]

[tex]mgh = mv_v^2/2[/tex]

where m is the mass and h = 8 m is the maximum vertical distance traveled, g = 9.81m/s2 is the gravitational acceleration

we can divide both sides by m

[tex]gh = v_v^2/2[/tex]

[tex](0.848v_0)^2 = 2gh = 2*9.81*8 = 156.96[/tex]

[tex]0.848v_0 = \sqrt{156.96} = 12.53[/tex]

[tex]v_0 = 12.53 / 0.848 = 14.77 m/s[/tex]

So if the ball is directed fully upward at v0 speed then we can apply the same equation to find the new H

[tex]E_p = E_k[/tex]

[tex]mgH = mv_0^2/2[/tex]

[tex]H = \frac{v_0^2}{2g} = \frac{14.77^2}{2*9.81} = \frac{218.3}{19.62} = 11.245m[/tex]

the ball would go approximately 0.454 times as high if it were thrown straight upward at speed v0 compared to when it was thrown at an angle of 58.0 degrees above the horizontal.

When a projectile is launched at an angle, its vertical motion is influenced by gravity, while its horizontal motion is independent of gravity. In this case, the ball is initially launched at an angle of 58.0 degrees above the horizontal and reaches a maximum height of 8.0 m.

If the ball were thrown straight upward at the same initial speed (v0), its vertical motion would still be influenced by gravity. In both cases, the initial vertical speed (in the upward direction) is v0. The time it takes to reach the maximum height in both scenarios would also be the same because only the vertical component of velocity affects the vertical motion.

To find how high the ball would go if thrown straight upward, you can use the following kinematic equation:

h = (v0² * sin²(θ)) / (2 * g)

Where:

h is the maximum height (which we want to find).

v0 is the initial speed (given as v0).

θ is the launch angle (58.0 degrees).

g is the acceleration due to gravity (approximately 9.81 m/s²).

First, convert the angle from degrees to radians:

θ (in radians) = 58.0 degrees * (π radians / 180 degrees) ≈ 1.01 radians

Now, plug in the values and solve for h:

h = (v0² * sin²(1.01)) / (2 * 9.81 m/s²)

h ≈ (v0² * 0.454) / 19.62 m/s²

Now, if we consider that the initial speed v0 remains the same and throw the ball straight upward (θ = 90 degrees), the equation becomes:

h_straight_up = (v0² * sin²(π/2)) / (2 * 9.81 m/s²)

h_straight_up ≈ (v0² * 1) / 19.62 m/s²

Now, compare the two expressions for h and h_straight_up:

h / h_straight_up ≈ ((v0² * 0.454) / 19.62 m/s²) / ((v0² * 1) / 19.62 m/s²)

The "v0²" terms cancel out, and you get:

h / h_straight_up ≈ 0.454 / 1

h / h_straight_up ≈ 0.454

So, the ball would go approximately 0.454 times as high if it were thrown straight upward at speed v0 compared to when it was thrown at an angle of 58.0 degrees above the horizontal.

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Answer:

f = 23.43 Hz for radio waves.

Explanation:

In this case, we need to find the frequency of an electromagnetic wave having a wavelength equal to Earth’s diameter i.e. 12,800 km. The relation between the frequency, wavelength and the speed is given by :

[tex]v=f\lambda[/tex]

Electromagnetic wave moves with a speed of light

[tex]c=f\lambda[/tex]

[tex]f=\dfrac{c}{\lambda}[/tex]

[tex]f=\dfrac{3\times 10^8}{12800\times 10^3}[/tex]

f = 23.43 Hz

So, the frequency of an electromagnetic wave is 23.43 Hz. It belongs to radio waves.

Final answer:

The frequency of an electromagnetic wave with a wavelength of Earth's diameter (12,800 km) would be approximately 23.4 Hz and would lie in the extremely low frequency (ELF) portion of the electromagnetic spectrum, typically used for submarine communication.

Explanation:

The frequency of an electromagnetic wave can be calculated using the formula c = λf, where c is the speed of light (approximately 3×108 m/s), λ is the wavelength, and f is the frequency. Given the Earth’s diameter as the wavelength (12,800 km, which is 12,800,000 meters), we can rearrange the formula to solve for frequency: f = c / λ.

Plugging in the values, we get:
f = 3×108 m/s / 12,800,000 m
This results in a frequency of approximately 23.4 Hz. Electromagnetic waves with this frequency would fall in the extremely low frequency (ELF) range of the electromagnetic spectrum, which is commonly used for submarine communication due to its ability to penetrate deep into the ocean.

Answer:

L > 0.08944 m or L > 8.9 cm

Explanation:

Given:

- Flux intercepted by antenna Ф = 0.04 N.m^2 / C

- The uniform electric field E = 5.0 N/C

Find:

- What is the minimum side length of the antenna L ?

Solution:

- We can apply Gauss Law on the antenna surface as follows:

                             Ф = [tex]\int\limits^S {E} \, dA[/tex]

- Since electric field is constant we can pull it out of integral. The surface at hand is a square. Hence,

                             Ф = E.(L)^2

                             L = sqrt (Ф / E)

                             L > sqrt (0.04 / 5.0)

                             L > 0.08944 m

The area of a square antenna needed to intercept a flux of 0.040 N⋅m2/C in a uniform electric field of magnitude 5.0 N/C is 0.008 m². Consequently, each side of the antenna must be about 0.089 meters (or 8.9 cm) long.

The question pertains to the relationship between electric field and flux. The electric flux through an area is defined as the electric field multiplied by the area through which it passes, oriented perpendicularly to the field.

We are given that the electric field (E) is 5.0 N/C and the flux Φ must be 0.040 N⋅m2/C.

Hence, to intercept this amount of flux, the antenna must have an area (A) such that A = Φ / E.

That is, A = 0.040 N⋅m2/C / 5.0 N/C = 0.008 m².

Since the antenna is square, each side will have a length of √(0.008) ≈ 0.089 meters (or 8.9 cm).

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Answer:

no additional information required.

Explanation:

given,

vertical height, h = 35 m

acceleration due to gravity, g = 9.8 m/s²

time taken by the bullet to fall in the water = ?

initial vertical velocity of the bullet = 0 m/s

using equation of motion for the time calculation

[tex]s = ut + \dfrac{1}{2}gt^2[/tex]

[tex]h= 0\times t + \dfrac{1}{2}\times g \times t^2[/tex]

[tex]t = \sqrt{\dfrac{2h}{g}}[/tex]

[tex]t= \sqrt{\dfrac{2\times 35}{9.8}}[/tex]

      t = 2.67 s

The time taken by the bullet to fall in the ocean is equal to 2.67 s.

Hence, there is no additional information required.

Answer:

  α = 5 10⁻³ rad / s²

Explanation:

For this exercise we can use Newton's second law for rotational movement, where the force is electric

             τ = I α

Where the torque is

             τ = F x r = F r sin θ

Strength is

              F = q E

The moment of inertia of a small ball, which we approximate to a point is

             I = m r²

We replace

            2 (q E) r sin θ   = 2m r² α

The number 2 is because the two forces create the same torque

             α = q E sin θ / m r

Let's reduce the magnitudes to the SI system

           m = 1.0g = 1.0 10⁻³ kg

           L = 2.0 cm = 2.0 10⁻² m

           q = 10 nc = 10 10⁻⁹ C

           E = 1.0 10 N / C

           r = L / 2

           r = 1.0 10⁻² m

Let's calculate

           α = 10 10⁻⁹ 1.0 10 sin 30 / 1.0 10⁻³ 1.0 10⁻²

           α = 5 10⁻³ rad / s²

The initial angular acceleration of the system is 0.25 radians per second squared.

To find the initial angular acceleration of the system when the charged balls are released in the uniform electric field, we can use the concept of torque. The torque experienced by the system will cause it to rotate, resulting in angular acceleration.

The torque (τ) experienced by an electric dipole in an electric field is given by the formula:

τ = p * E * sin(θ)

Where:

- τ is the torque.

- p is the electric dipole moment, which is the product of the charge (q) and the separation (d) between the charges on the dipole: p = q * d.

- E is the electric field strength.

- θ is the angle between the electric field direction and the dipole moment direction.

In this case, we have:

- q1 = +10 nC (positive charge)

- q2 = -10 nC (negative charge)

- d = 2.0 cm = 0.02 m

- E = 1.0 * 10^3 N/C (1.0 * 10^3 N/C = 1.0 * 10^3 V/m, as 1 N/C = 1 V/m)

- θ = 30°

First, calculate the electric dipole moment (p):

p = q * d = (+10 * 10^-9 C) * (0.02 m) = 2 * 10^-10 C·m

Now, calculate the torque (τ):

τ = p * E * sin(θ) = (2 * 10^-10 C·m) * (1.0 * 10^3 V/m) * sin(30°)

To calculate sin(30°), we can use its exact value: sin(30°) = 1/2.

τ = (2 * 10^-10 C·m) * (1.0 * 10^3 V/m) * (1/2) = 1 * 10^-7 N·m

Now, we can find the moment of inertia (I) of the system. Since we have two balls rotating at a fixed distance (d), we can use the formula for a simple pendulum's moment of inertia:

I = 2 * m * d^2

Where:

- m is the mass of each ball (1.0 g = 0.001 kg)

- d is the separation (0.02 m)

I = 2 * (0.001 kg) * (0.02 m)^2 = 4 * 10^-7 kg·m^2

Now, we can calculate the initial angular acceleration (α) using the equation:

τ = I * α

α = τ / I = (1 * 10^-7 N·m) / (4 * 10^-7 kg·m^2) = 0.25 rad/s^2

So, the initial angular acceleration of the system is 0.25 radians per second squared.

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a: The eccentricity is 1.086.

b: The altitude at closest approach is 5088 km

c: The velocity at perigee is 8.516 km/s

d: The turn angle is 134.08 while the aiming radius is 5641.28 km

Part a

Specific energy is given by

[tex]\epsilon=(v^2)/(2)-(\mu)/(r)[/tex]

Here

ε is the specific energy

v is the velocity which is given as 2.23 km/s

μ is the gravitational constant whose value is 398600

r is the distance between earth and the meteorite which is 402,000 km

[tex]\epsilon=(v^2)/(2)-(\mu)/(r)\n\epsilon=(2.2^2)/(2)-(398600)/(402,000)\n\epsilon=1.495 km^2/s^2[/tex]                        

Value of specific energy is also given as

[tex]\epsilon=(\mu)/(2a)\na=(\mu)/(2\epsilon)\na=(398600)/(2* 1.495)\na=13319 km[/tex]

Orbit formula is given as

[tex]r=a((e^2-1)/(1+ecos \theta))\nae^2-recos\theta-(a+r)=0[/tex]

Putting values in this equation and solving for e via the quadratic formula gives

[tex]ae^2-recos\theta-(a+r)=0\n(133319)e^2-(402000)(cos 150) e-(133319+402000)[/tex]

[tex]=0\n133319e^2+348142.21 e-535319=0\n\ne[/tex]

[tex]=(-348142.21 \pm \sqrt{(348142.21^2-4(133319)(535319)))}/(2 (133319))\n\ne[/tex]

=1.086 , or , -3.69

As the value of eccentricity cannot be negative so the eccentricity is 1.086.

Part b

The radius of trajectory at perigee is given as

[tex]r_p=a(e-1)\n[/tex]

Substituting values gives

[tex]r_p=133319 (1.086-1)\nr_p=11465.4 km[/tex]

Now for estimation of altitude z above earth is given as

[tex]z=r_p-R_E\nz=11465.4-6378\nz=5087.434\nz\approx 5088 km[/tex]

So the altitude at closest approach is 5088 km

Part c

radius of perigee is also given as

[tex]r_p=(h^2)/(\mu)(1)/(1+e)[/tex]

Rearranging this equation gives

[tex]h=√(r_p\mu(1+e))\nh=√(11465.4 * 3986000 * (1+1.086))\nh=97638.489 km^2/s[/tex]

Now the velocity at perigee is given as

[tex]v_p=(h)/(r_p)\nv_p=(97638.489)/(11465.4)\nv_p=8.516 km/s\n[/tex]

So the velocity at perigee is 8.516 km/s

Part d

Turn angle is given as

[tex]\delta =2 sin^{(-1)} ((1)/(e))[/tex]

Substituting value in the equation gives

[tex]\delta =2 sin^{(-1)} ((1)/(e))\n\delta =2 sin^{(-1)} ((1)/(1.086))\n\delta =134.08[/tex]

Aiming radius is given as

[tex]\Delta =a \sqrt{(e^2-1)[/tex]

Substituting value in the equation gives

[tex]\Delta =a \sqrt{(e^2-1)\n\Delta} =13319 \sqrt{(1.086^2-1)\n\Delta}=5641.28 km[/tex]

So the turn angle is 134.08 while the aiming radius is 5641.28 km

Therefore, a: The eccentricity is 1.086.

b: The altitude at closest approach is 5088 km

c: The velocity at perigee is 8.516 km/s

d: The turn angle is 134.08 while the aiming radius is 5641.28 km

Answer:

1590 N.

Explanation:

Force: This can be defined as the product of mass and the acceleration of a body. The S.I unit of Force is Newton (N).

The formula of force is given as

F = ma ........................ Equation 1

Where F = Force, m = mass of the astronaut, a = takeoff acceleration if the astronaut.

Given: m = 53.0 kg, a = 30 m/s²

Substitute into equation 1

F = 53(30)

F = 1590 N.

Hence the force exerted on the astronaut = 1590 N.

To calculate force, use the equation F=ma. Given an astronaut's mass of 53.0 kg and acceleration of 30.0 m/s² during a spaceship's takeoff, the exerted force totals around 1071 Newtons, subtracting the force of gravity.

To calculate the force exerted on the astronaut, you would use the equation F=ma, where F is force, m is mass and a is acceleration. Given that the mass (m) is 53.0 kg and the acceleration (a) is 30.0 m/s², the force (F) can be calculated as follows: F = ma = (53.0 kg)(30.0 m/s²) = 1590 Newtons.

This force is a result of combining gravity and the spaceship's upward propulsion (i.e. the astronaut's weight and the force of the spaceship accelerating). The force of gravity can be calculated simply by Fgravity = mg = (53.0 kg)(9.8 m/s²) = 519.4 Newtons. Therefore, the net force exerted by the spaceship on the astronaut during takeoff is F - Fgravity = 1590N - 519.4N = 1070.6 N, rounded off to 1071 N.

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Answer:

The other frequency is either 253Hz (the altered tuning frequency vibrates lower) or 259Hz(if the altered tuning frequency vibrates higher):

Explanation:

We have two frequencies: the tuning fork frequency  and  the altered tuning fork frequency  

F1 -----tuning fork frequency

F2-----Altered tuning fork frequency

Fbeat=3

F1=256Hz

To find the alterd tuning fork frequency:

The beat frequency of any two waves is:

Fbeat =|f1 – f2|

i.e  we have two choices

for  frequency tied to length increase (wavelength increases as length increases, therefore frequency decrease (the altered tuning frequency vibrates lower):   Fbeat = f2-f1

       F2=F1-Fbeat

     F2= 256-3

         =253Hz

For  frequency tied to length decrease wavelength increases as length increases, therefore frequency also increases(the altered tuning frequency vibrates higher) :    Fbeat = -(f2-f1)

F2= Fbeat+F1

   = 256+3

   = 259Hz

Note that a wavelength increase means a decrease of frequency because v = fλ

Answer:

If we increase the temperature in a reactor by 54 degrees Fahrenheit​ [54°F], the temperature will increase by 12.22 degrees Celsius [12.22 ⁰C]

Explanation:

To determine the number of degrees Celsius the temperature will be increased, we convert from Fahrenheit to Celsius.

Converting from Fahrenheit to degree Celsius

54°F -----> °C

54 = 1.8°C + 32

54-32 = 1.8°C

22 = 1.8°C

°C = 22/1.8

    = 12.22 °C

Thus, 54°F -----> 12.22 °C

Therefore, If we increase the temperature in a reactor by 54degrees Fahrenheit​ [54°F], the temperature will increase by 12.22 degrees Celsius [12.22 ⁰C]

12.22°C

The temperature increase in the reactor is 54°F

Now let's convert this to °C using the following relation;

(x − 32) × 5/9 = y         -------------------(i)

Where;

x is the value of the degree Fahrenheit = 54

y is the value of its corresponding degree Celsius.

Substitute x = 54 into equation (i)

(54 − 32) × 5/9 = y

(22) × 5/9 = y

Solve for y;

y = 22 x 5/9

y = 12.22°C

Therefore, the increase in temperature of the reactor in °C is 12.22