Water flows through a pipe diameter of 8.000 cm at 49.0 m/min. Find the flow rate in m3/min

Answers

Answer 1

We are asked to determine the volumetric flow rate through a pipe of diameter 8.000 cm. To do that we will use the following formula:

[tex]R=Av[/tex]

Where:

[tex]\begin{gathered} R=\text{ volumetric flow rate} \\ A=\text{ cross-area of the pipe} \\ v=\text{ velocity of the flow} \end{gathered}[/tex]

The cross-area of the pipe is the area of a circle and is given by:

[tex]A=\frac{\pi D^2}{4}[/tex]

Where:

[tex]\begin{gathered} A=\text{ cross-area} \\ D=\text{ diameter} \end{gathered}[/tex]

Before we determine the area we will convert the diameter from cm to meters using the following conversion factor:

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

Multiplying by the conversion factor we get:

[tex]8.000cm\times\frac{1m}{100cm}=0.080m[/tex]

Now, we plug in the value in the formula for the area:

[tex]A=\frac{\pi(0.080m)^2}{4}[/tex]

Solving the operations:

[tex]A=0.005m^2[/tex]

Now, we plug in the values of area and velocity in the formula or the volumetric flow rate:

[tex]R=(0.005m^2)(49.0\frac{m}{\min })[/tex]

Solving the operations:

[tex]R=0.246\frac{m^3}{min}[/tex]

Therefore, the flow rate is 0.246 cubic meters per minute.


Related Questions

Pascal's principle states that:all liquids exert pressure downward.pressure will move toward areas where pressure is lowest.applied pressure will be transmitted throughout a fluid.None of the choices are correct.

Answers

According to Pascal's principle states that applied pressure will be transmitted throughout a fluid.

Thus, third one is the correct option.

One way to create more fissionable fuel in the form of plutonium-239 is in which of the following?Select one:a.a coal-fire power station b.radioactive wastec.a meltdown of the cored.a breeder reactor

Answers

The correct answer is radioactive waste.

The Plutonium-239 is waste material of fuel road used in a nuclear power plant for the electricity production. The use of nuclear power plant will increase the radioactive waste and the production of Plutonum-239 will be more.

Thus, option b is

An object moving with uniform acceleration has a velocity of 13.0 cm/s in the positive x-direction when its x-coordinate is 2.76 cm. If its x-coordinate 3.05 s later is −5.00 cm, what is its acceleration?______ cm/s2

Answers

Since the object is moving with uniform acceleration we have an uniformly accelerated motion which means that we can use the following equations:

[tex]\begin{gathered} a=\frac{v_f-v_0}{t} \\ x=x_0+v_0t+\frac{1}{2}at^2 \\ v_f^2-v_0^2=2a(x-x_0) \end{gathered}[/tex]

Now, in this case we know:

• The initial position 2.76 cm.

,

• The initial velocity 13 cm/s

,

• The final position -5 cm

,

• The time it takes 3.05 s.

And we want to determine the acceleration; from what we know and what we want we determine that we can use the second equation. Plugging the values in that equation we have that:

[tex]\begin{gathered} -5=2.76+(13)(3.05)+\frac{1}{2}(3.05)^2a \\ \frac{3.05^2}{2}a=-5-2.76-(13)(3.05) \\ \frac{3.05^2}{2}a=-47.41 \\ 3.05^2a=-94.82 \\ a=-\frac{94.82}{3.05^2} \\ a=-10.19 \end{gathered}[/tex]

Therefore, the acceleration is -10.19 cm/s²

i need help please. i tried different answers but i cant get it.

Answers

Let's make a diagram to visualize the angle.

As you can observe, the angle is closer to the South orientation.

Therefore, the new angle is 42 degrees from South.

The fundamental frequency of a pipe is the lowest resonant frequency. Is this true or false?

Answers

By definition, the fundamental frequency of an object is the lowest frequency such that the object resonates.

Then, the answer is:

[tex]\text{True}[/tex]

Answer:

By definition, the fundamental frequency of an object is the lowest frequency such that the object resonates.

Then, the answer is: true

Explanation:

Part C and D please, part A=291.2 and part B=33.8

Answers

Given,

The mass of the skater, m=63 kg

The coefficient of static friction, μs=0.4

The coefficient of the kinetic friction, μk=0.02

F₁=242 N

F₂=162 N

(c) The static friction is given by,

[tex]f_s=N\mu_s[/tex]

Where N is the normal force.

The normal force acting on the skater is

[tex]N=mg[/tex]

Where g is the acceleration due to gravity.

Therefore the static friction is given by,

[tex]f_s=mg\mu_s[/tex]

On substituting the known values,

[tex]\begin{gathered} f_s=63\times9.8\times0.4 \\ =246.96\text{ N} \end{gathered}[/tex]

Therefore the static friction on the skater is 246.96 N

d)The net force acting on the skater is

[tex]\begin{gathered} F_{\text{net}}=ma_{} \\ =F_{\text{tot}}-f \\ =F_{\text{tot}}-N\mu_k \\ =F_{\text{tot}}-mg\mu_k \end{gathered}[/tex]

On substituting the known values,

[tex]\begin{gathered} 63a=291.2-63\times9.8\times0.02 \\ a=\frac{278.85}{63} \\ =4.43m/s^2 \end{gathered}[/tex]

Thus the acceleration of the skater is 4.43 m/s²

According to Coulomb's law, the electrical force between two charged objects:A.is zero if they are opposite charges.B.increases with increasing charge.C.does not depend on the amount of charge.D.increases with increasing distance.

Answers

Answer and explanation:

A correct option is an option (B).

The electrical force between two charges is given as,

[tex]F=\frac{1}{4\pi\epsilon_0}\frac{q_1q_1}{r^2}[/tex]

The electrical force is directly proportional to the product of two charges. Thus Force will depend on two charges irrespective of their signs.

Option (A) is incorrect because if charges are opposite, the value of force will not be zero. It will be -ve.

Option (C) is incorrect because the force is directly proportional to the product of charges, it depends on the amount of charge.

Option (D) is also incorrect because the force in inversly proportional to the distance between two charges. Thus, if the distance between two charges is increased, the force between two charges will decrease.

Concllusion:

The correct option is option (B).

what happens to F 1. m is doubled2. m is tripled3. m an m are both doubled4. m is halved5. r is doubled6. r is tripled7. r is increased 10 times8. r is halved

Answers

The expression for the gravitational force is given as:

[tex]F_g=\frac{GMm}{r^2}[/tex]

1. When M is doubled, then force will also be doubled as Force is directly proportional to the mass.

[tex]\begin{gathered} F\alpha M \\ F\alpha m \\ F\alpha\frac{1}{r^2} \end{gathered}[/tex]

2. When the m is tripled, then force will be tripled.

[tex]\begin{gathered} F^{\prime}\alpha\frac{M\times3m}{r^2} \\ F^{\prime}\alpha\frac{3Mm}{r^2} \\ F^{\prime}\alpha3F \end{gathered}[/tex]

3. When both M and m are doubled then, the force will become four times.

[tex]\begin{gathered} F^{\prime}\alpha\frac{2M\times2m}{r^2} \\ F^{\prime}\alpha4F \end{gathered}[/tex]

4.When m is halved, then Force will be halved, as force is directly proportional to the mass.

[tex]\begin{gathered} F^{\prime}\alpha\frac{M\times\frac{m}{3}}{r^2} \\ F^{\prime}\alpha\frac{Mm}{3r^2} \\ F^{\prime}\alpha\frac{F}{3} \end{gathered}[/tex]

5. When distance is doubled, then force will become one-fouth.

[tex]\begin{gathered} F^{\prime}\alpha\frac{Mm}{(2r)^2} \\ F^{\prime}\alpha\frac{Mm}{r^2}\times\frac{1}{4} \\ F^{\prime}\alpha\frac{F}{4} \end{gathered}[/tex]

6.When the distance is tripled, the force will become one-ninth.

[tex]\begin{gathered} F^{\prime}\alpha\frac{Mm}{(3r)^2} \\ F^{\prime}\alpha\frac{Mm}{r^2}\times\frac{1}{9} \\ F^{\prime}\alpha\frac{F}{9} \end{gathered}[/tex]

7. When the distance is increased to ten times, the force will become one-hundredth.

[tex]\begin{gathered} F^{\prime}\alpha\frac{Mm}{(10r)^2} \\ F^{\prime}\alpha\frac{Mm}{r^2}\times\frac{1}{100} \\ F^{\prime}\alpha\frac{F}{100} \\ 8.\text{ When the distance in halved, the force will be four time.} \\ F^{\prime}\alpha\frac{Mm}{(\frac{r}{2})^2} \\ F^{\prime}\alpha4\frac{Mm}{r^2} \\ F^{\prime}\alpha4F \end{gathered}[/tex]

John is at the park playing fetch with his cat. He throws the ball 1m south, and his cat retrieves the ball and returns it to John. John then throws the ball 3 meters, and the cat again collects the ball and returns it to John. When the cat returns for the second time, what distance has the cat traveled?6m8m2m4m

Answers

As John throws the ball 3 meters and the cat collects the ball and returns to John. Then. the distance traveled by the cat when it returns from the second time is calculated as

[tex]\begin{gathered} d=3+3 \\ =6\text{ m} \end{gathered}[/tex]

A guitar player tunes her strings so thatthere is a beat frequency of 1.0 Hzbetween them. If one string has afrequency of 220 Hz, what is thefrequency of the other string? (Thereare two possible answers; give one.) -(Unit = Hz)

Answers

Fb = beat frequency = 1 Hz

F1 = frequency 1 = 220 Hz

Fb = l F1 - F2 l or

Fb= l F2 - F1 l

Replacing:

1 = 220 - F2

f2 = 220 - 1

f2 = 219 HZ

A ballistic pendulum consists of a 1.25-kg block of wood that is hanging from the ceiling in such a way that when a bullet enters it, the block’s change in height can be recorded as it swings. A bullet having a mass of 6.25-grams and unknown velocity strikes the block and becomes imbedded in it. The impulse imparted to the block causes it to swing in such a way that its height increases by 7.15 cm.1. What was the change in potential energy of the block/bullet combo after the collision?2. What was the speed of the block/bullet combo immediately after the collision (and before it beganto swing)?3. What was the speed of the bullet before entering the block of wood?

Answers

1.

The potential energy is defined as:

[tex]U=mgh[/tex]

The change in potential energy is:

[tex]\Delta U=U_f-U_i[/tex]

the initial height of the block/bullet is zero, then we have that:

[tex]\begin{gathered} \Delta U=(1.25+0.00625)(9.8)(0.0715)-0 \\ \Delta U=0.8802 \end{gathered}[/tex]

Therefore, the change in potential energy is 0.8802 J

2.

We know that the energy is conserved, this means that the kinetic energy inmediately after collision has to be equal to the potential energy at the 7.15 cm heigh, then we have:

[tex]\begin{gathered} \frac{1}{2}mv^2=0.8802 \\ \frac{1}{2}(1.25625)v^2=0.8802 \\ v=\sqrt[]{\frac{2\cdot0.8802}{1.25625}} \\ v=1.184 \end{gathered}[/tex]

Therefore, the velocity at this moment is 1.184 m/s

3.

From conservation of momentum we know that:

[tex]m_bv_b=mv[/tex]

then:

[tex]\begin{gathered} (0.00625)v_b=(1.25625)(1.184) \\ v_b=\frac{(1.25625)(1.184)}{0.00625} \\ v_b=237.98 \end{gathered}[/tex]

Therefore the speed of the bullet is 237.98 m/s

Two figure skaters, one weighing 625 N and the other 725 N, push off against each other onfrictionless ice. If the heavier skater travels at 1.5 m/s, how fast will the lighter one travel?A 1.7 m/sB 2.8 m/sC -1.7 m/sD -2.8 m/s

Answers

We are given the following information:

Weight of skater 1 = 625 N

Weight of skater 2 = 725 N

Final velocity of skater 2 = 1.5 m/s

Final velocity of skater 1 = ?

Recall from the law of conservation of momentum, the total momentum before the collision and after the collision must be equal.

[tex]\begin{gathered} p_{before}=p_{after} \\ m_1u_1+m_2u_2=m_1v_1+m_2v_2 \end{gathered}[/tex]

The initial velocities of both skaters are 0 m/s

[tex]m_1\cdot0_{}+m_2\cdot0=m_1v_1+m_2v_2[/tex]

Also, m = W/g

[tex]\begin{gathered} 0=m_1v_1+m_2v_2 \\ 0=(\frac{625}{9.8})\cdot_{}v_1+(\frac{725}{9.8})\cdot1.5 \\ (\frac{625}{9.8})\cdot_{}v_1=-(\frac{725}{9.8})\cdot1.5 \\ (63.78)\cdot_{}v_1=-110.97 \\ _{}v_1=-\frac{110.97}{63.78} \\ _{}v_1=-1.7\: \frac{m}{s} \end{gathered}[/tex]

So, the lighter skater will travel with a velocity of 1.7 m/s

The negative sign means that the lighter skater will be traveling oppositely to the heavier skater.

Find the y-component of thisvector:12.0 m73.3°Remember, angles are measured fromthe +X axis.y-component (m)

Answers

Given data:

The magnitude of the given vector is,

[tex]A=12.0\text{ m}[/tex]

An angle between the given vector and +x axis is,

[tex]\theta=73.3^o[/tex]

The formula of y-component is as follows:

[tex]A_y=A\sin \theta[/tex]

Here,

[tex]A\text{ is the magnitude of the given vector-A}[/tex]

Now, substitute known values in above equation;

[tex]\begin{gathered} A_y=12\text{ m}\times\sin 73.3^o \\ A_y=11.49\text{ m} \end{gathered}[/tex]

Therefore, the y-component of the given vector is 11.49 m

Calculate the torque experienced by the door due to this force using torque is equal to force times lever armLength of the lever arm = 1 mForce = 5 N

Answers

Given:

The applied force on the door is F = 5 N

The length of the lever arm is l = 1 m

Required: Torque experienced by the torque.

Explanation:

Torque is the product of force and the distance between the force applied and the rotational axis.

The force is applied on one side of the lever arm while the rotational axis will be at the other end of the lever arm.

So, the distance between the rotational axis and the force applied is the length of the arm.

Torque can be calculated by the formula

[tex]\tau=F\times l[/tex]

On substituting the values, the torque will be

[tex]\begin{gathered} \tau=5\times1 \\ =5\text{ N m } \end{gathered}[/tex]

Final Answer: The torque experienced by the door is 5 N m.

The mass of a satellite orbiting Earth is 15000 kg.

Answers

Newton's universal law of gravity

[tex]F=G\frac{m1\cdot m2}{r^2^{}}[/tex]

Where:

F= force between objects

m1= mass 1 = 15,000 kg

m2= mass 2 = 6x10^24

r = distance = 34,000,000 m

G= universal contant of gravitation = 6.67 x10^-11

Replacing:

[tex]F=6.67\cdot10^{-11}\cdot\frac{15,000\cdot6x10^{24}}{(34,000,000)^2}[/tex]

F= 5,193 N

Which of the following phenomena provide evidence for the wave theory of light?a) Wavelength theoryb) Color Theoryc) The photoelectric effectd) Diffraction

Answers

The double slip experiement shows that light can display properties of particles and waves. The wave part of this experiment is due to the phenomenon of diffraction that appears in the behaviour of light whe it passes through a slit. This means that light has wave propeties. Therefore, the right asnwer is d) diffraction.

The ejection of electrons from metals illuminated with different frequencies of light provides evidence for the particle theory of light.

What is the photoelectric effect?

The effect is often defined as the ejection of electrons from a metal plate when light falls on it.

In a broader definition, the radiant energy may be infrared, visible, or ultraviolet light, X-rays, or gamma rays; the material may be a solid, liquid, or gas; and the released particles may be ions (electrically charged atoms or molecules) as well as electrons. The phenomenon was fundamentally significant in the development of modern physics because of the puzzling questions it raised about the nature of light—particle versus wavelike behavior—that was finally resolved by Albert Einstein in 1905. The effect remains important for research in areas from materials science to astrophysics, as well as forming the basis for a variety of useful devices.

Discovery: The photoelectric effect was discovered in 1887 by the German physicist Heinrich Rudolf Hertz. In connection with work on radio waves, Hertz observed that, when ultraviolet light shines on two metal electrodes with a voltage applied across them, the light changes the voltage at which sparking takes place.

Applications: Devices based on the photoelectric effect have several desirable properties, including producing a current that is directly proportional to light intensity and a very fast response time. One basic device is the photoelectric cell or photodiode. Originally, this was a phototube, a vacuum tube containing a cathode made of metal with a small work function so that electrons would be easily emitted

To learn more about the photoelectric effect visit,

https://brainly.com/question/22054853

which choice are equivalent to the expression below? check all that apply. 4 square root 5answer choices: square root of 16*6, square root of 32*3, square root of 96, square of 24, 96, square root of 4*36

Answers

Given

4 square root 6

[tex]4\sqrt[]{6}[/tex]

Wich choices are equivalent to the expression below

[tex]\begin{gathered} \sqrt[]{16}\sqrt[]{6} \\ \sqrt[]{32}\sqrt[]{3} \\ \sqrt[]{96} \end{gathered}[/tex]

The first three options are the correct answers.

in four hours, a hiker in a canyon goes from 892ft to 256 ft above the canyon floor. Find the hikers vertical speed.

Answers

From the given question, we can deduce the following information:

• Time, t = 4 hours

,

• The hiker goes from 892 ft to 256 ft above the canyon floor.

Let's find the vertical speed of the hiker.

To find the speed, apply the formula:

[tex]speed=\frac{dis\tan ce}{time}[/tex]

To find the distance, we have:

Distance covered = 256 ft - 892 ft = -636 ft.

Hence, to find the vertical speed, we have:

[tex]\begin{gathered} speed=\frac{dis\tan ce}{time} \\ \\ \text{speed}=\frac{-636}{4}=-159\text{ ft/h} \\ \end{gathered}[/tex]

Therefore, the vertical speed of the hiker is -159 feet per hour.

ANSWER:

What are electromagnetic radiations?​

Answers

Radiations associated with electric and magnetic field is called Electromagnetic radiations.

electric and magnetic field radiations = electromagnetic radiations.

URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!!

Answers

Answer:

b heated gas will have decreased kinetic energy and decreased density

Explanation:

gas loses weight

how do I convert fractions into percentages like 14 over 20

Answers

Given data

*The given fraction is

[tex]x=\frac{14}{20}[/tex]

Convert the given fraction into percentage as

[tex]\begin{gathered} x=\frac{14}{20}\times100\text{\%} \\ =0.7\times100\text{\%} \\ =70\text{\%} \end{gathered}[/tex]

What is the maximum speed at which a cyclist can move on a bend and at an angle from the vertical, he should deviate to the side of the bend, so as not to fall, if the coefficient of friction of the wheel from the road is 0.4 and the radius of curvature of the road is 100m

Answers

Given,

The coefficient of friction between the wheel and the road, μ=0.4

The radius of curvature of the road, r=100 m

The centripetal force for the cyclist to move in the curved path is provided by the friction between the road and the wheel.

Thus,

[tex]\begin{gathered} \frac{mv^2}{r}=\mu mg \\ \Rightarrow v^2=r\mu g \\ v=\sqrt[]{r\mu g} \end{gathered}[/tex]

Where m is the mass of the cyclist and the cycle and g is the acceleration due to gravity.

I have some problems applying the formulas to solve physics problems. I understand all the concepts needed, but just freeze when I see questions, especially when it comes to trying to combine linear and rotational conceptsA uniform, 255 N rod that is 1.90 m long carries a 225 N weight at its right end and an unknown weight W toward the left end (Figure 1). When W is placed 60.0 cm from the left end of the rod, the system just balances horizontally when the fulcrum is located 75.0 cm from the right end.1) Find W.2) If W is now moved 30.0 cm to the right, how far must the fulcrum be moved to restore balance?

Answers

ANSWER

[tex]\begin{gathered} 1)\text{ }214.90\text{ }N \\ \\ 2)\text{ }0.09\text{ }m \end{gathered}[/tex]

EXPLANATION

First, let us make a sketch of the diagram showing the distances on the rod:

1) Since the fulcrum is balanced, the center of gravity of the system will be at the fulcrum.

The center of gravity (in the horizontal is given by:

[tex]x=\frac{W_1x_1+W_2x_2+W_3x_3}{W_1+W_2+W_3}[/tex]

where W1 = the weight on the right end = 225 N

W2 = the weight of the rod = 255 N

W3 = the weight place on the left = W

x1 = the position of W1 (taking the left as the origin) = 1.90 m

x2 = the position of the center of mass of the rod = x1/2 = 0.95 m

x3 = the position of W from the left end = 0.60 m

x = position of center of gravity of the rod from the left end i.e. at the fulcrum = 1.90 - 0.75 = 1.15 m

Now, substitute the values given in the question and solve for W:

[tex]\begin{gathered} 1.15=\frac{(225*1.90)+(255*0.95)+(W*0.60)}{225+255+W} \\ \\ 1.15=\frac{427.5+242.25+0.60W}{480+W} \\ \\ 1.15(480+W)=669.75+0.60W \\ \\ 552+1.15W=669.75+0.60W \\ \\ 1.15W-0.60W=669.75-552 \\ \\ 0.55W=117.75 \\ \\ W=\frac{117.75}{0.55} \\ \\ W=214.09\text{ }N \end{gathered}[/tex]

That is the value of W.

2) Now, W is moved 30.0 cm (0.30 m) to the right.

This implies that:

[tex]x_3=0.60+0.30=0.90\text{ }m[/tex]

Since the other values (including W) do not change, we can now solve for x, which is the new center of gravity:

[tex]\begin{gathered} x=\frac{(225\times1.90)+(255\times0.95)+(214.09\times0.90)}{225+255+214.09} \\ \\ x=\frac{427.5+242.25+192.681}{694.09}=\frac{862.431}{694.09} \\ \\ x=1.24\text{ }m \end{gathered}[/tex]

Therefore, the fulcrum must be moved:

[tex]\begin{gathered} 1.24\text{ }m-1.15\text{ }m \\ \\ 0.09\text{ }m \end{gathered}[/tex]

The fulcrum should be moved 0.09 m to the right (since the W is moved to the right).

General relativity is combines special relativity with the equivalence principle.Why and why not?

Answers

The equivalence principle is a fundamental law of physics that states that inertial forces and gravitational forces are similar in nature and are often indistinguishable from each other.

The application of the equivalence principle to in combination with the general theory of relativity allowed the refinement of the equations of the theory helping give birth to the theory of general relativity.

For example, in special relativity objects are considered to be moving with a constant velocity. When the principle of equivalence is introduced this allows considering inertial frames or accelerated frames of reference and the gravitational forces in a system thus completing the special theory of relativity.

When the acceleration in the general theory of relativity is considered to be zero then it reduces to the special theory of relativity.

Dispersion occurs forGroup of answer choicesmonochromatic light in reflectionmonochromatic light in refractionpolychromatic light in reflectionpolychromatic light in refraction

Answers

Given:

Dispersion

Required: To choose the correct option.

Explanation:

Reflection is the process when a light ray strikes a surface and returns back in the same medium.

Refraction is the process of bending light when light travels from one medium to another.

Monochromatic light is light that has only one color.

Polychromatic light is the light that constitutes multiple colors in the same source.

When dispersion occurs light travels from one medium to another, and it bends after entering the second medium.

As polychromatic has multiple colors and each color corresponds to a particular wavelength.

The bending of light also differs by wavelength, so each color will bend at different angles.

Final Answer: The dispersion occurs for polychromatic light in refraction.

What happens to the strength of an electromagnet if the current in the wire is increased?

Answers

We will have the following:

What will happen is that the magnetic field will increase; since the magnetic field increases when the current in the wire of the electromagnet increases.

The solar system formed about 4.5 billion years ago. This expressed asA. 4.5x10^6 yearsB. 4.5x10^7 yearsC. 4.5x10^8 yearsD. 4.5 x10^9 years

Answers

Given,

The age of the solar system is 4.5 billion years.

One billion is 1,000,000,000.

In scientific notation, we can write one billion as 1×10⁹.

Therefore to express any number in billions we need to multiply it with the above number.

Therefore, we can write 4.5 billion years as,

[tex]4.5\times1\times10^9=4.5\times10^9\text{ years}[/tex]

Therefore we can express 4.5 billion years as 4.5

Where does electricity come from I.n Your own words

Answers

Electricity is electrons moving through a conductor.

Voltage pushes electrons through the conductor to create an electric current.

Electricity comes from Power stations , that have generators that produce electricity.

Generators use different sources of energy such as water flow, fossil fuel, etc.

A car traveling at 11.6 meters per second crashes into a barrier and stops in 0.287 meters. What force must be exerted on a child of mass 21.2 kilograms to stop him or her in the same time as the car? Include units in your answer. Answer must be in 3 significant digits. Hint: This is an impulse-momentum theorem problem.

Answers

[tex]\begin{gathered} \text{For car} \\ v_1=11.6\text{ m/s} \\ \Delta x=0.287m \\ v_2=\text{ 0 m/s} \\ t=\text{?} \\ To\text{ find t} \\ v^2_2=v^2_1+2a\Delta x \\ \text{Solving a} \\ v^2_2-v^2_1=2a\Delta x \\ a=\frac{v^2_2-v^2_1}{2\Delta x} \\ a=\frac{(0m/s)^2-(11.6m/s)^2}{2(0.287m)} \\ a=\frac{0m^2/s^2-134.56m^2/s^2}{0.574m} \\ a=\frac{-134.56m^2/s^2}{0.574m} \\ a=-234.42m/s^2 \\ \text{Then} \\ t=\frac{v_2-v_1}{a} \\ t=\frac{0\text{ m/s-11.6m/s}}{-234.42m/s^2} \\ t=\frac{\text{-11.6m/s}}{-234.42m/s^2} \\ t=0.0495\text{ s} \\ \text{For child} \\ m=21.2\text{ kg} \\ v_1=11.6\text{ m/s} \\ v_2=\text{ 0 m/s} \\ t=0.0495\text{ s} \\ F=\text{?} \\ F=\frac{P_2-P_1}{t} \\ P_2-P_1=mv_2-mv_1=m(v_2-v_1),\text{ then} \\ F=\frac{m(v_2-v_1)}{t} \\ F=\frac{(21.2kg)(0\text{ m/s-11.6m/s})}{0.0495\text{ s}} \\ F=\frac{(21.2kg)(-11.6\text{ m/s})}{0.0495\text{ s}} \\ F=\frac{-245.92\operatorname{kg}\text{ m/s}}{0.0495\text{ s}} \\ F=-4968\text{ N} \\ \text{The force to stop the child is 4968 N. The negative means } \\ \text{the force is opposite to the movement} \end{gathered}[/tex]

A car with a mass of 1200kg is driving in circular path with radius of 65m at a constant speed of 5.5 m/s. What is the magnitude of the net force on the car? a) 102N b) 14182 N c) 6600 N d) 78000 N e) 558 N

Answers

Take into account that due to the speed of the car is constant, the net force on the car is the force due to the centrifugal force, which is given by the following formula:

[tex]F=ma_c=m\cdot\frac{v^2}{r}[/tex]

where:

m: mass of the car = 1200 kg

v: speed = 5.5 m/s

r: radius of the circular trajectory = 65 m

replace the previous values of the parameters into the formula for F:

[tex]F=1200kg\cdot\frac{(5.5m/s)^2}{65m}=558.46N\approx558N[/tex]

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