Suppose your friend claims to have discovered a mysterious force in nature that acts on all particles in some region of space. He tells you that the force is always pointed away a definite point in space, which we can call the force center. The magnitude of the force turns out to be proportional to B/r3, where r is the distance from the force center to any other point. Your friend says that it has been determined that the constant of proportionality has been determined to be B= 2 (in units to be determined later), so that the magnitude of the force on a particle (in newtons) can be written as 2r^3, when the particle is at a distance r from the force center.

Required:
Write an expression of potential energy.

Answers

Answer 1

Answer:

             U = 1 / r²

Explanation:

In this exercise they do not ask for potential energy giving the expression of force, since these two quantities are related

             

         F = - dU / dr

this derivative is a gradient, that is, a directional derivative, so we must have

          dU = - F. dr

the esxresion for strength is

         F = B / r³

let's replace

          ∫ dU = - ∫ B / r³  dr

in this case the force and the displacement are parallel, therefore the scalar product is reduced to the algebraic product

let's evaluate the integrals

            U - Uo = -B (- / 2r² + 1 / 2r₀²)

To complete the calculation we must fix the energy at a point, in general the most common choice is to make the potential energy zero (Uo = 0) for when the distance is infinite (r = ∞)

             U = B / 2r²

we substitute the value of B = 2

             U = 1 / r²


Related Questions

A coil has resistance of 20 W and inductance of 0.35 H. Compute its reactance and its impedance to an alternating current of 25 cycles/s.

Answers

Answer:

Reactance of the coil is 55 WImpedance of the coil is 59 W

Explanation:

Given;

Resistance of the coil, R = 20 W

Inductance of the coil, L = 0.35 H

Frequency of the alternating current, F = 25 cycle/s

Reactance of the coil is calculated as;

[tex]X_L=[/tex] 2πFL

Substitute in the given values and calculate the reactance [tex](X_L)[/tex]

[tex]X_L =[/tex] 2π(25)(0.35)

[tex]X_L[/tex] = 55 W

Impedance of the coil is calculated as;

[tex]Z = \sqrt{R^2 + X_L^2} \\\\Z = \sqrt{20^2 + 55^2} \\\\Z = 59 \ W[/tex]

Therefore, the reactance of the coil is 55 W and Impedance of the coil is 59 W

How can global warming lead to changes to the Earth’s surface? a. Global warming can lead to an increased number of earthquakes, which change the Earth’s surface. b. Global warming can lead to glaciers melting, causing flooding to areas and the decrease of glacial land masses. c. Global warming leads to a decrease in water levels of coastal wetlands. d. Global warming cannot lead to changes to the Earth’s surface.

Answers

Answer:

Option:  b. Global warming can lead to glaciers melting, causing flooding to areas and the decrease of glacial land masses.

Explanation:

Global warming is the reason for the changes in environment and climate on earth. Melting of glaciers leads to an increase in water level and a decrease in landmass. One of the most climactic consequences is the decrease in Arctic sea ice. Melting polar ice along with ice sheets and glaciers across Greenland, North America, Europe, Asia, and South America suspected to increase sea levels slowly. There is an increase in the glacial retreat due to global warming, which leaves rock piles that covered with ice.  

Answer:

B: Global warming can lead to glaciers melting, causing flooding to areas and the decrease of glacial land masses.

Explanation:

Global warming is primarily caused by the increase in greenhouse gases, such as carbon dioxide, in the Earth's atmosphere. This leads to a rise in global temperatures, which has various impacts on the Earth's surface. One significant effect is the melting of glaciers and ice caps in polar regions and mountainous areas.

As temperatures increase, glaciers and ice sheets start to melt at a faster rate. This melting results in the release of massive amounts of water into rivers, lakes, and oceans. Consequently, there can be an increase in the frequency and intensity of flooding events in regions downstream from these melting glaciers.

Moreover, the melting of glaciers and ice caps contributes to a rise in sea levels. As the melted ice enters the oceans, it adds to the overall volume of water, leading to a gradual increase in sea levels worldwide. This rise in sea levels poses a threat to coastal areas, as they become more vulnerable to coastal erosion, storm surges, and saltwater intrusion into freshwater sources.

Additionally, the loss of glacial land masses due to melting can have long-term effects on ecosystems. Glaciers act as freshwater reservoirs, releasing water gradually throughout the year. With their decline, the availability of freshwater for agriculture, drinking water, and other human needs can be significantly affected.

Therefore, global warming can indeed lead to changes in the Earth's surface, particularly through the melting of glaciers and subsequent impacts on sea levels, flooding, and glacial land masses.

E23 verified.

A proton with an initial speed of 400000 m/s is brought to rest by an electric field.
Part A- Did the proton move into a region of higher potential or lower potential?
Part B - What was the potential difference that stopped the proton?
?U = ________V
Part C - What was the initial kinetic energy of the proton, in electron volts?
Ki =_________eV

Answers

Answer:

moves into a region of higher potential

Potential difference = 835   V

Ki = 835 eV

Explanation:

given data

initial speed = 400000 m/s

solution

when proton moves against a electric field  so that it will move into higher potential  region

and

we know Work done by electricfield  W is express as

W = KE of proton   K

so

q × V   =  0.5 × m × v²     ......................1

put here va lue

1.6 × [tex]10^{-19}[/tex] × V   =   0.5 × 1.67 × [tex]10^{-27}[/tex] × 400000²

Potential difference V = 1.336 × 10-16 / 1.6  × 10-19      

Potential difference = 835   V

and

KE of proton in eV is express as

Ki  =   V numerical

Ki = 835 eV

We observe that a small sample of material placed in a non-uniform magnetic field accelerates toward a region of stronger field. What can we say about the material?

Answers

Answer:

C) It is either ferromagnetic or paramagnetic

Explanation:

The complete question is given below

We observe that a small sample of material placed in a non-uniform magnetic field accelerates toward a region of stronger field. What can we say about the material?

A) It must be ferromagnetic.

B) It must be paramagnetic.

C) It is either ferromagnetic or paramagnetic.

D) It must be diamagnetic.

A ferromagnetic material will respond towards a magnetic field. They are those materials that are attracted to a magnet. Ferromagnetism is associated with our everyday magnets and is the strongest form of magnetism in nature. Iron and its alloys is very good example of a material that readily demonstrate ferromagnetism.

Paramagnetic materials are weakly attracted to an externally applied magnetic field. They usually accelerate towards an electric field, and form internal induced magnetic field in the direction of the external magnetic field.

The difference is that ferromagnetic materials can retain their magnetization when the externally applied magnetic field is removed, unlike paramagnetic materials that do not retain their magnetization.

In contrast, a diamagnetic material is repelled away from an externally applied magnetic field.

A loop of wire with cross-sectional area 1 m2 is inserted into a uniform magnetic field with initial strength 1 T. The field is parallel to the axis of the loop. The field begins to grow with time at a rate of 2 Teslas per hour. What is the magnitude of the induced EMF in the loop of wire

Answers

Answer:

The magnitude of the EMF is 0.00055  volts

Explanation:

The induced EMF is proportional to the change in magnetic flux based on Faraday's law:

[tex]emf\,=-\,N\, \frac{d\Phi}{dt}[/tex]

Since in our case there is only one loop of wire, then N=1 and we get:

[tex]emf\,=-\,N\, \frac{d\Phi}{dt}[/tex]

We need to express the magnetic flux given the geometry of the problem;

[tex]\Phi=B\,\,A[/tex]where A is the area of the coil that remains unchanged with time, and B is the magnetic field that does change with time. Therefore the equation for the EMF becomes:

[tex]emf\,=-\,N\, \frac{d\Phi}{dt} = \frac{d\Phi}{dt} =-\frac{d\,(B\,A)}{dt} =-\,A\,\frac{d\,(B)}{dt}=- 1\,m^2(2\,\,T/h})= -2\,\,m^2\,T/(3600\,\,s)= -0.00055\,Volts[/tex]

2. A 2.0-kg block slides down an incline surface from point A to point B. Points A and B are 2.0 m apart. If the coefficient of kinetic friction is 0.26 and the block is starting at rest from point A. What is the work done by friction force

Answers

Answer:a

Explanation:

Which statement describes one feature of a mineral's definite chemical composition?
It always occurs in pure form.
It always contains certain elements.
It cannot form from living or once-living materials.
It cannot contain atoms from more than one element.
N

Answers

Answer:

It always contains certain elements

Explanation:

Minerals can be defined as natural inorganic substances which possess an orderly internal structural arrangement as well as a particular, well known chemical composition, crystal structures and physical properties. Minerals include; quartz, dolomite, basalt, etc. Minerals may occur in isolation or in rock formations.

Minerals contain specific, well known chemical elements in certain ratios that can only vary within narrow limits. This is what we mean by a mineral's definite chemical composition. The structure of these minerals are all well known as well as their atom to atom connectivity.

The statement describes one feature of a mineral's definite chemical composition - It always contains certain elements.

A mineral is a naturally occurring chemical compound, usually of a crystalline form.

A mineral has one specific chemical composition.chemical composition that varies within a specific limited range and the atoms that make up the mineral must occur in specific ratiosthe proportions of the different elements and groups of elements in the mineral.

Thus, The statement describes one feature of a mineral's definite chemical composition - It always contains certain elements.

Learn more:

https://brainly.com/question/690965

your washer has a power of 350 watts and your dryer has a power of 1800 watts how much energy do you use to clean a load of clothes in 1 hour of washing and 1 hour of drying?
A. 1.29 x 10^3 J
B. 2.58 x 10^3 J
C. 1.55 x 10^7 J
D. 7.74 x 10^6 J

Answers

Answer:

7.74 x 10⁶ Joules

Explanation:

recall that "Watts" is the SI unit used for "energy per unit time"

Hence "Watts" may also be expressed as Joules / Second (or J/s)

We are given that the washer is rated at 350W (i.e. 350 Joules / s) and the dryer is rated at 1800W (i.e. 1800 Joules / s).

We are also given that the appliances are each run for 1 hour

1 hour = 60 min = (60 x 60) seconds = 3600 seconds

Hence the total energy used,

= Energy used by Washer in 1 hour + Energy used by dryer in 1 hour

= (350 J/s x 3600 s)  + (1800 J/s x 3600 s)

= 3600 ( 350 + 1800)

= 3600 (2150)

= 7,740,000 Joules

= 7.74 x 10⁶ Joules

A trough is filled with a liquid of density 810 kg/m3. The ends of the trough are equilateral triangles with sides 8 m long and vertex at the bottom. Find the hydrostatic force on one end of the trough. (Use 9.8 m/s2 for the acceleration due to gravity.)

Answers

Answer:

The hydrostatic force on one end of the trough is 54994.464 N

Explanation:

Given;

liquid density, ρ = 810 kg/m³

side of the equilateral triangle, L = 8m

acceleration due to gravity, g =  9.8 m/s²

Hydrostatic force is given as;

H = ρgh

where;

h is the vertical height of the equilateral triangle

Draw a line to bisect upper end of the trough, to the vertex at the bottom, this line is the height of the equilateral triangle.

let the half side of the triangle = x

x = ⁸/₂ = 4m

The half section of the triangle forms a right angled triangle

h² = 8² - 4²

h² = 48

h = √48

h = 6.928m

F = ρgh

F = 810 x 9.8 x 6.928

F = 54994.464 N

Therefore, the hydrostatic force on one end of the trough is 54994.464 N

define limitations in the operation conditions of a pn junction

Answers

Answer:

Such limitations are given below.

Explanation:

Each pn junction provides limited measurements of maximum forwarding current, highest possible inversion voltage as well as the maximum output level.If controlled within certain adsorption conditions, the pn junction could very well offer satisfying performance. In connector operation, the maximum inversion voltage seems to be of significant importance.

An arrow is launched vertically upward at a speed of 50 m/s. What is the arrow’s speed at the highest point? Ignore air resistance

Answers

Answer:

depending on how high it goes at 100m it has taken 2 secondes

Explanation:

At the highest point, the arrow is changing from moving up to moving down. At that exact point, its speed AND its velocity are both ZERO.

And air resistance actually makes no difference.

A typical arteriole has a diameter of 0.080 mm and carries blood at the rate of 9.6 x10-5 cm3/s. What is the speed of the blood in (cm/s) the arteriole

Answers

Answer:

v= 4.823 × 10⁻⁹ cm/s

Explanation:

given

flow rate = 9.6 x10-5 cm³/s, d = 0.080mm

r = d/2= 0.080/2= 0.0040 cm

speed = rate of blood flow × area

v = (9.6 x 10⁻⁵ cm³/s) × (πr²)

v = (9.6 x 10⁻⁵ cm³/s) × π(0.0040 × cm)²

v= 1.536 × 10⁻⁹π cm/s

v= 4.823 × 10⁻⁹ cm/s

what is mean by the terminal velocity​

Answers

Terminal Velocity is the constant speed that a falling thing reaches when the resistence of a medium prevents the thing to reach any further speed.

Best of Luck!

Q 6.30: What is the underlying physical reason for the difference between the static and kinetic coefficients of friction of ordinary surfaces

Answers

Answer:

the coefficient of static friction is larger than kinetic coefficients of friction

Explanation:

The coefficient of static friction is usually larger than the kinetic coefficients of friction because an object at rest has increasingly settled agreements with the surface it's resting on at the molecular level, so it takes more force to break these agreement.

Until this force is been overcome, kinetic coefficient of friction is not going to surface.

Note: coefficient of static friction is the friction between two bodies when the bodies aren't moving. Meanwhile, kinetic coefficient is the ratio of frictional force of a moving body to the normal reaction.

[tex]F_{s}[/tex] ≤μ[tex]_{s}[/tex]N(coefficient of static friction)

where [tex]F_{s}[/tex]  is the static friction, μ[tex]_{s}[/tex] is the coefficient of static friction and N is the normal reaction

μ = [tex]\frac{F}{N}[/tex](kinetic coefficient of friction)

attached is diagram illustrating the explanation

A proud new Jaguar owner drives her car at a speed of 25 m/s into a corner. The coefficients of friction between the road and the tires are 0.70 (static) and 0.40 (kinetic) assuming the car is not skidding while traveling along the curve, what is the magnitude of the centripetal acceleration of the car

Answers

Answer:

ac = 3.92 m/s²

Explanation:

In this case the frictional force must balance the centripetal force for the car not to skid. Therefore,

Frictional Force = Centripetal Force

where,

Frictional Force = μ(Normal Force) = μ(weight) = μmg

Centripetal Force = (m)(ac)

Therefore,

μmg = (m)(ac)

ac = μg

where,

ac = magnitude of centripetal acceleration of car = ?

μ = coefficient of friction of tires (kinetic) = 0.4

g = 9.8 m/s²

Therefore,

ac = (0.4)(9.8 m/s²)

ac = 3.92 m/s²

Based on the data provided, the centripetal acceleration is 3.92 m/s²

What is centripetal acceleration?

Centripetal acceleration is the acceleration of a body moving in a circular path which is directed toward the center of the circle.

In the given question, the frictional force must balance the centripetal force for the car not to skid.

Frictional Force = Centripetal Force

where,

Frictional Force = μR

R = mg

F = μmg

Centripetal Force = m

Then

μmg = ma

a = μg

ac = 0.4 * 9.8 m/s²

ac = 3.92 m/s²

Therefore, the centripetal acceleration is 3.92 m/s².

Learn more about centripetal acceleration at: https://brainly.com/question/25243603

Find the terminal velocity (in m/s) of a spherical bacterium (diameter 1.81 µm) falling in water. You will first need to note that the drag force is equal to the weight at terminal velocity. Take the density of the bacterium to be 1.10 ✕ 103 kg/m3. (Assume the viscosity of water is 1.002 ✕ 10−3 kg/(m · s).)

Answers

Answer:

The terminal velocity of a spherical bacterium falling in the water is 1.96x10⁻⁶ m/s.

Explanation:

The terminal velocity of the bacterium can be calculated using the following equation:

[tex] F = 6\pi*\eta*rv [/tex]    (1)

Where:

F: is drag force equal to the weight

η: is the viscosity = 1.002x10⁻³ kg/(m*s)

r: is the radium of the bacterium = d/2 = 1.81 μm/2 = 0.905 μm

v: is the terminal velocity

Since that F = mg and by solving equation (1) for v we have:

[tex] v = \frac{mg}{6\pi*\eta*r} [/tex]  

We can find the mass as follows:

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

Where:

ρ: is the density of the bacterium = 1.10x10³ kg/m³

V: is the volume of the spherical bacterium

[tex] m = \rho*V = \rho*\frac{4}{3}\pi*r^{3} = 1.10 \cdot 10^{3} kg/m^{3}*\frac{4}{3}\pi*(0.905 \cdot 10^{-6} m)^{3} = 3.42 \cdot 10^{-15} kg [/tex]

Now, the terminal velocity of the bacterium is:

[tex] v = \frac{mg}{6\pi*\eta*r} = \frac{3.42 \cdot 10^{-15} kg*9.81 m/s^{2}}{6\pi*1.002 \cdot 10^{-3} kg/(m*s)*0.905 \cdot 10^{-6} m} = 1.96 \cdot 10^{-6} m/s [/tex]

Therefore, the terminal velocity of a spherical bacterium falling in the water is 1.96x10⁻⁶ m/s.

I hope it helps you!

The spectral lines of two stars in a particular eclipsing binary system shift back and forth with a period of 3 months. The lines of both stars shift by equal amounts, and the amount of the Doppler shift indicates that each star has an orbital speed of 88,000 m/s. What are the masses of the two stars

Answers

Answer:

Explanation:

given

T = 3months = 7.9 × 10⁶s

orbital speed = 88 × 10³m/s

V= 2πr÷T

∴ r = (V×T) ÷ 2π

r = (88km × 7.9 × 10⁶s) ÷ 2π

r = 1.10 × 10⁸km

using kepler's 3rd law

mass of both stars = (seperation diatance)³/(orbital speed)²

M₁ + M₂ = (2r)³/([tex]\frac{1}{4}[/tex]year)²

= (1.06 × 10²⁵)/(6.2×10¹³)

1.71×10¹²kg

since M₁ = M₂ =1.71×10¹²kg ÷ 2

M₁ = M₂ = 8.55×10¹¹kg

What direct current will produce the same amount of thermal energy, in a particular resistor, as an alternating current that has a maximum value of 2.59 A?

Answers

Answer:

The direct current that will produce the same amount of thermal energy is 1.83 A

Explanation:

Given;

maximum current, I₀ = 2.59 A

The average power dissipated in a resistor connected in an AC source is given as;

[tex]P_{avg} = I_{rms} ^2R[/tex]

Where;

[tex]I_{rms} = \frac{I_o}{\sqrt{2} }[/tex]

[tex]P_{avg} = (\frac{I_o}{\sqrt{2} } )^2R\\\\P_{avg} = \frac{I_o^2R}{2} ----equation(1)[/tex]

The average power dissipated in a resistor connected in a DC source is given as;

[tex]P_{avg} = I_d^2R --------equation(2)[/tex]

where;

[tex]I_d[/tex] is direct current

Solve equation (1) and (2) together;

[tex]I_d^2R = \frac{I_o^2R}{2} \\\\I_d^2 = \frac{I_o^2}{2} \\\\I_d=\sqrt{\frac{I_o^2}{2} } \\\\I_d = \frac{I_o}{\sqrt{2}} \\\\I_d = \frac{2.59}{\sqrt{2} } \\\\I_d = 1.83 \ A[/tex]

Therefore, the direct current that will produce the same amount of thermal energy is 1.83 A

1. A ski-plane with a total mass of 1200 kg lands towards the west on a frozen lake at 30.0
m/s. The coefficient of kinetic friction between the skis and the ice is 0.200. How far does
the plane slide before coming to a stop?

Answers

Answer:

d = 229.5 m

Explanation:

It is given that,

Total mass of a ski-plane is 1200 kg

It lands towards the west on a frozen lake at 30.0  m/s.

The coefficient of kinetic friction between the skis and the ice is 0.200.

We need to find the distance covered by the plane before coming to rest. In this case,

[tex]\mu mg=ma\\\\a=\mu g\\\\a=0.2\times 9.8\\\\a=1.96\ m/s^2[/tex]

It is decelerating, a = -1.96 m/s²

Now using the third equation of motion to find the distance covered by the plane such that :

[tex]v^2-u^2=2ad\\\\d=\dfrac{-u^2}{2a}\\\\d=\dfrac{-(30)^2}{2\times -1.96}\\\\d=229.59\ m[/tex]

So, the plane slide a distance of 229.5 m.  

Complete the following statement:

Bimetallic strips used as adjustable switches in electric appliances consist of metallic strips that must have different:_____

a. volume.
b. specific heat capacities.
c. expansion coefficients.
d. mass.
e. length.

Answers

Answer: c. expansion coefficients.

Explanation: Bimetallic strips used as adjustable switches in electric appliances consist of metallic strips that must have different expansion coefficients.

I found the answer on Quizlet. :)

Bimetallic strips used as adjustable switches in electric appliances consist of metallic strips that must have different expansion coefficients. The correct option is c.

What is the expansion coefficient?

The coefficient of thermal expansion (CTE) is the rate at which a material expands as its temperature rises. This coefficient is determined at constant pressure and without a phase change, i.e. the material is expected to remain solid or fluid.

Bimetallic strips, which are utilized as adjustable switches in electric appliances, are made up of metallic strips with differing expansion coefficients. The coefficient of thermal expansion indicates how the size of an object varies as temperature changes.

Therefore, the correct option is c. expansion coefficients.

To learn more about the expansion coefficient, refer to the link:

https://brainly.com/question/14780533

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Find the average power Pavg created by the force F in terms of the average speed vavg of the sled.

Answers

Complete Question

The complete question is shown on the first and second uploaded image

Answer:

The power created  is  [tex]P_{avg} = F * v_{avg}[/tex]

Explanation:

From the question we are told that

    The that the average power is  mathematically represented as

            [tex]P_{avg} = \frac{W }{\Delta t }[/tex]

Where W is  is the Workdone which is  mathematically represented as

         [tex]W = F * s[/tex]

      Where F is  the applies force and  s  is the displacement  due to the force  

        So  

                [tex]P_{avg} = \frac{F *s }{\Delta t }[/tex]

Now this  displacement can be represented mathematically as  

            [tex]s = v_{avg} * \Delta t[/tex]

Where [tex]v_{avg }[/tex] is the average  velocity and [tex]\Delta t[/tex] is the time  taken  

So  

            [tex]P_{avg} = \frac{F *v_{avg} * \Delta t }{\Delta t }[/tex]

=>         [tex]P_{avg} = F * v_{avg}[/tex]

Answer:

Pavg =  Fvavg

Explanation:

Since the P (power) done by the F (force) is:

P = Fs/t

and we are looking for the velocity, so then it would be:

P = Fv

with the average velocity the answer is:

Pavg =  Favg

If an object is moving at a constant speed, and the force F is also constant, this formula can be used to find the average power. If v  is changing, the formula can be used to find the instantaneous power at any given moment (with the quantity v in this case meaning the instantaneous velocity, of course).

Blue light (λ = 475 nm) is sent through a single slit with a width of 2.1 µm. What is the maximum possible number of bright fringes, including the central maximum, produced on the screen? (Hint: What is the largest angle that can be used?)

Answers

Answer:

  m = 4

Explanation:

The expression that explains the constructive interference of a diffraction pattern is

         a sin θ = m λ

where a  is the width of the slit and λ the wavelength

         sin θ = m λ / a

The maximum value is for when the sine is 1, let's substitute

         1 = m λ/a  

         m = a /λ

let's reduce the magnitudes to the SI system

        a = 2.1 um = 2.1 10⁻⁶

        lam = 475 nm = 475 10⁻⁹ m

let's calculate

        m = 2.1  10⁻⁶ / 475 10⁻⁹

        m = 4.42

with m must be an integer the highest value is

         m = 4

Which of the following gives the magnitude of the average velocity (over the entire run) of an athlete running on a circular track with a circumference of 0.5 km, if that athlete runs a total length of 1.0 km in a time interval of 4 minutes?
a. O m/s
b. 2 m/s
c. 4.2 m/s
d. 16.8 m/s

Answers

Answer:

c. 4.2 m/s

Explanation:

The definition of the average velocity, measured in meters per second, is given by the following expression:

[tex]\bar v = \frac{x_{f}-x_{o}}{t_{f}-t_{o}}[/tex]

Where:

[tex]x_{o}[/tex], [tex]x_{f}[/tex] - Initial and final positions, measured in meters.

[tex]t_{o}[/tex], [tex]t_{f}[/tex] - Initial and final instants, measured in seconds.

Positions and instants must be written in meters and seconds, respectively:

[tex]x_{o} = 0\,m[/tex], [tex]x_{f} = 1000\,m[/tex].

[tex]t_{o} = 0\,s[/tex], [tex]t_{f} = 240\,s[/tex].

Finally, the average velocity of the athlete that runs a total length of 1.0 kilometer in a time interval of 4 minutes is:

[tex]\bar v = \frac{1000\,m-0\,m}{240\,s-0\,s}[/tex]

[tex]\bar v = 4.167\,\frac{m}{s}[/tex]

Hence, the best option is C.

A 1.20 kg water balloon will break if it experiences more than 530 N of force. Your 'friend' whips the water balloon toward you at 13.0 m/s. The maximum force you apply in catching the water balloon is twice the average force. How long must the interaction time of your catch be to make sure the water balloon doesn't soak you

Answers

Answer:

t = 0.029s

Explanation:

In order to calculate the interaction time at the moment of catching the ball, you take into account that the force exerted on an object is also given by the change, on time, of its linear momentum:

[tex]F=\frac{\Delta p}{\Delta t}=m\frac{\Delta v}{\Delta t}[/tex]       (1)

m: mass of the water balloon = 1.20kg

Δv: change in the speed of the balloon = v2 - v1

v2: final speed = 0m/s (the balloon stops in my hands)

v1: initial speed = 13.0m/s

Δt: interaction time = ?

The water balloon brakes if the force is more than 530N. You solve the equation (1) for Δt and replace the values of the other parameters:

[tex]|F|=|530N|= |m\frac{v_2-v_1}{\Delta t}|\\\\|530N|=| (1.20kg)\frac{0m/s-13.0m/s}{\Delta t}|\\\\\Delta t=0.029s[/tex]

The interaction time to avoid that the water balloon breaks is 0.029s

When a hydrometer (see Fig. 2) having a stem diameter of 0.30 in. is placed in water, the stem protrudes 3.15 in. above the water surface. If the water is replaced with a liquid having a specific gravity of 1.10, how much of the stem would protrude above the liquid surface

Answers

Answer:

5.79 in

Explanation:

We are given that

Diameter,d=0.30 in

Radius,r=[tex]\frac{d}{2}=\frac{0.30}{2}=0.15 in[/tex]

Weight of hydrometer,W=0.042 lb

Specific gravity(SG)=1.10

Height of stem from the water surface=3.15 in

Density of water=[tex]62.4lb/ft^3[/tex]

In water

Volume  of water displaced [tex]V=\frac{mass}{density}=\frac{0.042}{62.4}=6.73\times 10^{-4} ft^3[/tex]

Volume of another liquid displaced=[tex]V'=\frac{V}{SG}=\frac{6.73\times 10^{-4}}{1.19}=5.66\times 10^{-4}ft^3[/tex]

Change in volume=V-V'

[tex]V-V'=\pi r^2 l[/tex]

Substitute the values

[tex]6.73\times 10^{-4}-5.66\times 10^{-4}=3.14\times (\frac{0.15}{12})^2l[/tex]

By using

1 ft=12 in

[tex]\pi=3.14[/tex]

[tex]l=\frac{6.73\times 10^{-4}-5.66\times 10^{-4}}{3.14\times (\frac{0.15}{12})^2}[/tex]

l=2.64 in

Total height=h+l=3.15+2.64= 5.79 in

Hence, the height of the stem protrude above the liquid surface=5.79 in

Two identical pendulums have the same period when measured in the factory. While one pendulum swings on earth, the other is taken on a spaceship traveling at 95%% the speed of light. Assume that both pendulums operate under the influence of the same net force and swing through the same angle.
When observed from earth, how many oscillations does the pendulum on the spaceship undergo compared to the pendulum on earth in a given time interval?
a. more oscillations
b. fewer oscillations
c. the same number of oscillations

Answers

Answer:

Explanation:

As a result of impact of time widening, a clock moving as for an observer seems to run all the more gradually than a clock that is very still in the observer's casing.  

At the point when observed from earth, the pendulum on the spaceship takes more time to finish one oscillation.  

Hence, the clock related with that pendulum will run more slow (gives fewer oscillations as observed from the earth)  than the clock related with the pendulum on earth.

Ans => B fewer oscillations

A water-balloon launcher with mass 5 kg fires a 1 kg balloon with a velocity of
8 m/s to the east. What is the recoil velocity of the launcher?

Answers

Answer:

1.6 m/s west

Explanation:

The recoil velocity of the launcher is 1.6 m/s west.

What is conservation of momentum principle?

When two bodies of different masses move together each other and have head on collision, they travel to same or different direction after collision.

A water-balloon launcher with mass 5 kg fires a 1 kg balloon with a velocity of 8 m/s to the east.

Final momentum will be zero, so

m₁u₁ +m₂u₂ =0

Substitute the values for m₁ = 5kg, m₂ =1kg and u₂ =8 m/s, then the recoil velocity will be

5 x v +1x8 = 0

v = - 1.6 m/s

Thus, the recoil velocity of the launcher is  1.6 m/s (West)

Learn more about conservation of momentum principle

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What is the work done in stretching a spring by a distance of 0.5 m if the restoring force is 24N?

Answers

Answer:

3Nm

Explanation:

work = 0.5 x 12 x 0.5 = 3

The work done in stretching the spring by a distance of 0.5 m, with a restoring force of 24 N, is 6 joules.

To calculate the work done in stretching a spring, we can use the formula for work done by a spring:

Work = (1/2) * k *[tex]x^2[/tex]

where:

k = spring constant

x = distance the spring is stretched

Given that the restoring force (F) acting on the spring is 24 N, and the distance the spring is stretched (x) is 0.5 m, we can find the spring constant (k) using Hooke's law:

F = k * x

k = F / x

k = 24 N / 0.5 m

k = 48 N/m

Now, we can calculate the work:

Work = (1/2) * 48 N/m * [tex](0.5 m)^2[/tex]

Work = (1/2) * 48 N/m * [tex]0.25 m^2[/tex]

Work = 6 joules

Therefore, the work done in stretching the spring by a distance of 0.5 m, with a restoring force of 24 N, is 6 joules.

To know more about work done, here

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Two lenses of focal length 4.5cm and 1.5cm are placed at a certain distance apart, calculate the distance between the lenses if they form an achromatic combination

Answers

Answer:

3.0cm

Explanation:

For lenses in an achromatic combination, the following condition holds, assuming the two lenses are of the same materials;

d = [tex]\frac{f_1 + f_2}{2}[/tex]     ---------(i)

Where;

d= distance between lenses

f₁ = focal length of the first lens

f₂ = focal length of the second lens

From the question;

f₁ = 4.5cm

f₂ = 1.5cm

Substitute these values into equation (i) as follows;

d = [tex]\frac{4.5+1.5}{2}[/tex]

d = [tex]\frac{6.0}{2}[/tex]

d = 3.0cm

Therefore, the distance between the two lenses is 3.0cm

A 2.0-kg object moving 5.0 m/s collides with and sticks to an 8.0-kg object initially at rest. Determine the kinetic energy lost by the system as a result of this collision.

Answers

Answer:

20J

Explanation:

In a collision, whether elastic or inelastic, momentum is always conserved. Therefore, using the principle of conservation of momentum we can first get the final velocity of the two bodies after collision. This is given by;

m₁u₁ + m₂u₂ = (m₁ + m₂)v          ---------------(i)

Where;

m₁ and m₂ are the masses of first and second objects respectively

u₁ and u₂ are the initial velocities of the first and second objects respectively

v  is the final velocity of the two objects after collision;

From the question;

m₁ = 2.0kg

m₂ = 8.0kg

u₁ = 5.0m/s

u₂ = 0        (since the object is initially at rest)

Substitute these values into equation (i) as follows;

(2.0 x 5.0) + (8.0 x 0) = (2.0 + 8.0)v

(10.0) + (0) = (10.0)v

10.0 = 10.0v

v = 1m/s

The two bodies stick together and move off with a velocity of 1m/s after collision.

The kinetic energy(KE₁) of the objects before collision is given by

KE₁ = [tex]\frac{1}{2}[/tex]m₁u₁² +  [tex]\frac{1}{2}[/tex]m₂u₂²       ---------------(ii)

Substitute the appropriate values into equation (ii)

KE₁ = ([tex]\frac{1}{2}[/tex] x 2.0 x 5.0²) +  ([tex]\frac{1}{2}[/tex] x 8.0 x 0²)

KE₁ = 25.0J

Also, the kinetic energy(KE₂) of the objects after collision is given by

KE₂ = [tex]\frac{1}{2}[/tex](m₁ + m₂)v²      ---------------(iii)

Substitute the appropriate values into equation (iii)

KE₂ = [tex]\frac{1}{2}[/tex] ( 2.0 + 8.0) x 1²

KE₂ = 5J

The kinetic energy lost (K) by the system is therefore the difference between the kinetic energy before collision and kinetic energy after collision

K = KE₂ - KE₁

K = 5 - 25

K = -20J

The negative sign shows that energy was lost. The kinetic energy lost by the system is 20J

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