Global warming will produce rising sea levels partly due to melting ice caps but also due to the expansion of water as average ocean temperatures rise. We will estimate this effect in this problem, assuming the thermal coefficient of volume expansion is 210×106/∘C for sea water. Calculate the change in length, in meters, of a column of water 1.00 km high for a temperature increase of 1.00∘C. Note that this calculation is only approximate because ocean warming is not uniform with depth.

The main reasons for having few impact craters on Earth compared to moon is due to the presence of atmosphere, water bodies and tectonic activities.

Explanation:

Impact craters are formed on the surface of any object when another very high velocity object hits the surface of the particular object. As force exhibited by any object is directly proportional to the product of mass and acceleration of the object.

In case of moon or other natural satellites, there are no means of reducing the acceleration or mass of the incident high velocity object. But in earth, the presence of different layers of atmosphere causes sufficient friction to reduce the size as well as acceleration of the impeding high velocity object.

Then the presence of larger volume of water bodies on the Earth's surface reduces the chance of hitting on land areas. The third important factor reducing the impact craters are the variation in tectonic plates which helps in keeping only recent impacts on the Earth's surface and erase the old impacts.

So the presence of different layers of atmosphere, water bodies and tectonic plats are the main reasons for having fewer impact craters on Earth compared to the Moon.

To solve this problem we will apply the linear motion kinematic equations. With the equation describing the position with respect to acceleration (gravity), initial velocity and time, we will find time.

Our values are,

[tex]h = 2.5m[/tex]

[tex]x = 0.9m[/tex]

1) We know that, the time, the ball in the air depends on the maximum height.

Therefore the height is calculated as

[tex]h = v_{yi}t+\frac{1}{2} gt^2[/tex]

There is not initial velocity then replacing,

[tex]2.5 = 0t + \frac{1}{2}9.8t^2[/tex]

[tex]t = \sqrt{\frac{2(2.5)}{9.8}}[/tex]

[tex]t = 0.714s[/tex]

By symmetry, the time taken to reach ground is equal to the time taken to reach the maximum height, then

[tex]T = t+t[/tex]

[tex]T = 2*0.714s[/tex]

[tex]T = 1.426s[/tex]

2 ) In the time t=1.428s, the ball moves horizontally a distance x = 0.9

Then the horizontal velocity,

[tex]v_x = \frac{x}{t} = \frac{0.9m}{1.428s}[/tex]

[tex]v_x = 0.6302m/s[/tex]

3 ) The ball's speed just before the second bounce is found as

[tex]v_y = v_{yi} +gt_{down}[/tex]

Replacing we have

[tex]v_y = 0+(9.8)(0.714)[/tex]

[tex]v_y = 6.9972m/s[/tex]

4 ) The angle of the velocity vector with respect to the ground right after the first bounce is

[tex]\theta = tan^{-1} (\frac{v_y}{v_x})[/tex]

[tex]\theta = tan^{-1} (\frac{6.9972}{0.6302})[/tex]

[tex]\theta = 84.8\°[/tex]

Answer:

62.64 RPM.

Explanation:

Given that

m= 4.6 g

r= 19 cm

μs = 0.820

μk = 0.440.

The angular speed of the turntable = ω rad/s

Condition just before the slipping starts

The maximum value of the static friction force =Centripetal force

[tex]\mu_s\ m g=m\ \omega^2\ r\\ \omega^2=\dfrac{\mu_s\ m g}{m r}\\ \omega=\sqrt{\dfrac{\mu_s\ g}{ r}}\\ \omega=\sqrt{\dfrac{0.82\times 10}{ 0.19}}\ rad/s\\\omega= 6.56\ rad/s[/tex]

[tex]\omega=\dfrac{2\pi N}{60}\\N=\dfrac{60\times \omega}{2\pi }\\N=\dfrac{60\times 6.56}{2\pi }\ RPM\\N=62.64\ RPM[/tex]

Therefore the speed in RPM will be 62.64 RPM.

Answer:

[tex]\Delta t =1.31\ s[/tex]

Explanation:

given,

coefficient of kinetic friction, μ = 0.25

Speed of sled at point A = 8.6 m/s

Speed of sled at point B = 5.4 m/s

time taken to travel from point A to B.

we know,

J = F Δ t

J is the impulse

where  F is the frictional force.

t is the time.

we also know that impulse is equal to change in momentum.

[tex]J = m(v_f - v_i)[/tex]

frictional force

F = μ N

where as N is the normal force

now,

[tex]F\Delta t = m(v_f -v_i)[/tex]

[tex]\mu m g \times \Delta t = m(v_f-v_i)[/tex]

[tex]\mu g \times \Delta t = v_f-v_i[/tex]

[tex]\Delta t =\dfrac{v_f-v_i}{\mu g}[/tex]

[tex]\Delta t =\dfrac{8.6-5.4}{0.25\times 9.8}[/tex]

[tex]\Delta t =1.31\ s[/tex]

time taken to move from A to B is equal to 1.31 s

Answer:

Time taken by the sled is 1.31 s

Solution:

As per the question:

Coefficient of kinetic friction, [tex]\mu_{k} = 0.25[/tex]

Velocity at point A, [tex]v_{A} = 8.6\ m/s[/tex]

Velocity at point A, [tex]v_{B} = 5.4\ m/s[/tex]

Now,

To calculate the time taken by the sled to travel from A to B:

According to the impulse-momentum theorem, impulse and the change in the momentum of an object are equal:

Impulse, I = Change in momentum of the sled, [tex]\Delta p[/tex]        (1)

[tex]I = Ft[/tex]                                 (2)

where,

F = Force

t = time

p = momentum of the sled

Force on the sled is given by:

[tex]F = \mu_{k}N[/tex]

where

N = normal reaction force = mg

where

m = mass of the sled

g = acceleration due to gravity

Thus

[tex]F = \mu_{k}mg[/tex]                     (3)

Using eqn (1), (2) and (3):

[tex]\mu_{k}mgt = m\Delta v[/tex]

[tex]\mu_{k}gt = v_{A} - v_{B}[/tex]

[tex]t = \frac{v_{A} - v_{B}}{\mu_{k}g}[/tex]

[tex]t = \frac{8.6 - 5.4}{0.25\times 9.8}[/tex]

t = 1.31 s

Final answer:

The percent uncertainty of a blood pressure measurement of 120 mm Hg with an uncertainty of ±2 mm Hg is 1.67%. Using this percentage, the uncertainty in a blood pressure measurement of 71 mm Hg would be ±1.2 mm Hg, after rounding to one decimal place.

Explanation:

To calculate the uncertainty in a blood pressure measurement of 71 mm Hg, given the percent uncertainty is the same as that for a measurement of 120 mm Hg with an uncertainty of ± 2 mm Hg, we first find the percent uncertainty of the original measurement.

The percent uncertainty is calculated by dividing the uncertainty by the actual measurement and then multiplying by 100 to get a percentage:

Percent Uncertainty = (Uncertainty / Measurement) × 100

For the measurement of 120 mm Hg, the percent uncertainty is:

(2 mm Hg / 120 mm Hg) × 100 = 1.67%

Assuming the same percent uncertainty for a blood pressure measurement of 71 mm Hg, you would use the same percentage to find the uncertainty:

Uncertainty = Percent Uncertainty × Measurement / 100

Uncertainty in 71 mm Hg = 1.67% × 71 mm Hg / 100 = 1.187 mm Hg

Since we typically round to the nearest whole unit or significant digit the uncertainty would be ± 1.2 mm Hg (rounded to one decimal place).

Answer:

New force between them will become [tex]\frac{1}{36}[/tex] times

Explanation:

Let the charge on both the object are [tex]q_1\ and\ q_2[/tex] and distance between them is is given 1 cm

So r = 1 cm = 0.01 m

Electric force between them is given F

According to Coulomb's between two charges is given by

[tex]F=\frac{1}{4\pi \epsilon _0}\frac{q_1q_2}{r^2}=\frac{Kq_1q_2}{r^2}[/tex]

According to question [tex]F=\frac{Kq_1q_2}{0.01^2}=\frac{Kq_1q_2}{10^{-4}}[/tex]-----------eqn 1

Now distance is increased by 5 cm so new distance = 5+1 = 6 cm = 0.06 m

So new force [tex]F_{new}=\frac{Kq_1q_2}{0.06^2}=\frac{Kq_1q_2}{36\times 10^{-4}}[/tex]------------------eqn 2

Comparing eqn 1 and eqn 2

[tex]F_{new}=\frac{F}{36}[/tex]

To solve this problem we will apply the linear motion kinematic equations, for this purpose we will define the time of each of the sections in which the speed is different. After determining the segments of these speeds we can calculate the average distance and the average speed. Our values are given as

x = 180 km

v = 95 km / h

Speed can be described as the displacement of a body per unit of time, and from that definition clearing the time we would have

[tex]v = \frac{x}{t} \rightarrow t = \frac{x}{v}[/tex]

[tex]v = \frac{180}{95}[/tex]

[tex]v = 1.89473 hrs[/tex]

From the statement we have that the total time is 4.5, then he remaining time is

[tex]t' = T-t =4.5-1.89473 = 2.60526 hrs[/tex]

When it starts to rain there is a phase change in the speed which is given by

[tex]v' = 65km/h[/tex]

Then the distance travel in this velocity

[tex]x' = v ' t '[/tex]

[tex]x' = 65*2.60526[/tex]

[tex]x = 169.34 km[/tex]

(a).  Distance of your hometown from school ,

[tex]x " = x + x '[/tex]

[tex]x'' = 180+169.34[/tex]

[tex]x= 349.34 km[/tex]

(b) The  average speed

[tex]V = \frac{x "}{ T}[/tex]

[tex]v = \frac{349.34 km}{4.5 h}[/tex]

[tex]v = 77.63 km/ h[/tex]

Final answer:

The student's hometown is 350 km away from school, and their average speed for the trip was 77.78 km/h.

Explanation:

To determine how far the student's hometown is from school and their average speed, we need to use their driving speeds and times. Firstly, let's calculate the time taken to travel the first 180 km at 95 km/h.

Time = Distance \/ Speed = 180 km \/ 95 km/h = 1.8947 hours (approximately 1.89 hours).

Since the total travel time is 4.5 hours, the time spent driving in the rain at 65 km/h is 4.5 hours - 1.89 hours = 2.61 hours.

Distance driven in the rain = Speed × Time = 65 km/h × 2.61 hours = 169.65 km (approximately 170 km).

Therefore, the total distance from school to the student's hometown is the sum of both distances: 180 km (before rain) + 170 km (in rain) = 350 km.

Now, to find the average speed, we use the total distance and total time.

Average speed = Total distance \/ Total time = 350 km \/ 4.5 hours = 77.78 km/h.

Thus, the hometown is 350 km away from school, and the student's average speed for the trip was 77.78 km/h.

Answer:

Incomplete question.

Complete question given below

a) 2.7933 C/s

b) 714.45 s

Explanation:

Even when shut down after a period of normal use, a large commercial nuclear reactor transfers thermal energy at the rate of 150 MW by the radioactive decay of fission products. This heat transfer causes a rapid increase in temperature if the cooling system fails {1 watt = 1 joule/second or 1 W = 1 J/s and 1 MW = 1 megawatt.

(a) Calculate the rate of temperature increase in degrees Celsius per second  if the mass of the reactor core is  1.60105*10^6 kg and it has an average specific heat of  0.3349 kJ/kgº.

(b) How long would it take to obtain a temperature increase of  which could cause some metals holding the radioactive materials to melt?

Part a)

[tex]Q_{rate} = m*c*\frac{dT}{dt}\\\frac{dT}{dt} = \frac{Q_{rate}}{m*c} \\\\\frac{dT}{dt} = \frac{150*10^6}{1.6 * 10^5*334.9} \\\\\frac{dT}{dt} = 2.7993 C/s[/tex]

Part b)

[tex]dt = \frac{dT}{2.7993} \\\\dt = \frac{2000}{2.7993} \\\\dt = 714.45 s[/tex]

Final answer:

The acceleration due to gravity at the altitude of the Columbia shuttle is approximately 8.95 m/s^2, which is about 91% of Earth's surface gravity.

Explanation:

To determine the acceleration due to gravity at the altitude at which Columbia is orbiting, we apply the universal law of gravitation, which is represented by the formula:

F = G Mm/r²

From this formula, we can derive the expression for acceleration due to gravity (g):

g = GM/r²

Given:

Radius of Earth (rE) = 6.4 × 106 m

Altitude of Columbia (h) = 0.3 × 106 m

Mass of Earth (M) = 6.0 × 1024 kg

Gravitational constant (G) = 6.67408 × 10-11 m3kg-¹s-²

Total distance from the center of Earth (r) = rE + h

The resulting equation for the acceleration due to gravity at the altitude of Columbia is:

g = (6.67408 × 10-11 m3kg-1s-2) × (6.0 × 1024 kg) / (6.7 × 106 m)²

Upon calculating, this yields an acceleration due to gravity of approximately 8.95 m/s². This acceleration is about 91% of the gravitational acceleration at Earth's surface, which is 9.8 m/s².

Explanation:

For the given question, distance is given on x-axis and force is given on y-axis. Both distance and force are showing an interval of 5 with starting point 0.

Hence, work in 5 m to 12.5 m is equal and opposite to 12.5 m to 20 m. Since, work is equal then it means that kinetic energy at 5 m will also be equal to the kinetic energy at 20 m.

Therefore, we can conclude that the kinetic energy of the 2 kg object when d equals 20 m is the same as when d is most nearly  5 m.

Final answer:

The velocity of the 2 kg object when d equals 20 m is most nearly 20.4 m/s.

Explanation:

The equation for kinetic energy is K = 1/2mv^2, where K is the kinetic energy, m is the mass, and v is the velocity of the object. To find the velocity when d equals 20m, we can use the equation K = 1/2mv^2 and rearrange it to solve for v. We know the mass of the object is 2kg and the kinetic energy is the same, so we can set up the equation as follows:

1/2(2kg)(v)^2 = 1/2(2kg)(20.4m/s)^2

Simplifying the equation, we find that v is approximately 20.4m/s. Therefore, when d equals 20m, the velocity of the object is most nearly 20.4m/s.

Answer:

The time it would take to sail around the world in a sailboat is 1000 hour.        

Explanation:

It is given that,    

The circumference of the Earth, [tex]d=10^4\ mile[/tex]

The speed of a sailboat, [tex]v=10\ mile/hour[/tex]

We need to find the time it would take to sail around the world in a sailboat. It can be calculated using the definition of velocity. It is given by :

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

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

[tex]t=\dfrac{10^4\ mile}{10\ mile/hour}[/tex]

t = 1000 hour

So, the time it would take to sail around the world in a sailboat is 1000 hour. Hence, this is the required solution.

Answer:

1

Explanation:

Explanation:

Given:

source temperature T1= 825° C = 1099 K

Sink temperature T2= 15°C = 288 K

Heat Supplied to the engine Qs= 3200 KW

a) Efficiency of a Carnot engine is

[tex]\eta =1-\frac{T_1}{T_2}[/tex]

[tex]=1-\frac{1099}{288}[/tex]

=0.7379

=73.79%

b)

[tex]\eta= \frac{Power delivered}{power recieved}[/tex]

let W be the powe delivered

[tex]0.7379= \frac{W}{3200}[/tex]

W= 2361.408 KW

c) Heat rejected to the cold temperature Qr= Qs-W

= 3200-2361.408=838.60 KW

d) Entropy change in the sink

[tex]\Delta S= \frac{Qr}{T_{sink}}[/tex]

=838.60/288= 2.911 W/K

Answer:

a. [tex]\eta_{th}=0.7377=73.77\%[/tex]

b. [tex]P=2360655.7377\ W[/tex]

c. [tex]Q_o=839344.2622\ W[/tex]

d. [tex]\Delta s=2914.3897\ J.K^{-1}[/tex]

Explanation:

Given:

a.

Since the engine is a Carnot engine:

[tex]\eta_{th}=1-\frac{T_L}{T_H}[/tex]

[tex]\eta_{th}=1-\frac{288}{1098}[/tex]

[tex]\eta_{th}=0.7377=73.77\%[/tex]

b.

Now the power delivered:

since here we are given with the rate of heat transfer

[tex]P=\eta_{th}\times Q_i[/tex]

[tex]P=0.7377\times 3200000[/tex]

[tex]P=2360655.7377\ W[/tex]

c.

rate of heat rejection to the sink:

[tex]Q_o=Q_i-P[/tex]

[tex]Q_o=3200000-2360655.73770491808[/tex]

[tex]Q_o=839344.2622\ W[/tex]

d.

[tex]\Delta s=\frac{Q_o}{T_L}[/tex]

[tex]\Delta s=\frac{839344.2622}{288}[/tex]

[tex]\Delta s=2914.3897\ J.K^{-1}[/tex]

Answer:

none

Explanation:

a. the unit of height does not carry a square( m^2 is unit of area)

b. time cannot be in m/s. it is unit of speed

c. m/s^2 are the units of acceleration

None of the options are correct on the basis of dimensional analysis.

(a)The height of the Transamerica Pyramid is 332 m².

the dimension of height is not correct, it must be m instead of m².

(b)The time duration of a fortnight is 66 m/s.

the dimension of time is s ( seconds) not m/s (meter/second).

(c) The speed of the train is 9.8 m/s².

The dimentsion of speed is m/s (meter/second) not m/s².

Hence, none of the options are correct.

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Complete Question: A charge q1 = 2.2 uC is at a distance d= 1.63m from a second charge q2= -5.67 uC. (b) Find a point between the two charges on the horizontal line where the electric potential is zero. (Enter your answer as measured from q1.)

Answer:

d= 0.46 m

Explanation:

The electric potential is defined as the work needed, per unit charge, to bring a positive test charge from infinity to the point of interest.

For a point charge, the electric potential, at a distance r from it, according to Coulomb´s Law and the definition of potential, can be expressed as follows:

V = [tex]\frac{k*q}{r}[/tex]

We have two charges, q₁ and q₂, and we need to find a point between them, where the electric potential due to them, be zero.

If we call x to the distance from q₁, the distance from q₂, will be the distance between both charges, minus x.

So, we can find the value of x, adding the potentials due to q₁ and q₂, in such a way that both add to zero:

V = [tex]\frac{k*q1}{x}[/tex] +[tex]\frac{k*q2}{(1.63m-x)}[/tex] = 0

⇒[tex]k*q1* (1.63m - x) = -k*q2*x[/tex]:

Replacing by the values of q1, q2, and k, and solving for x, we get:

⇒ x = (2.22 μC* 1.63 m) / 7.89 μC = 0.46 m from q1.

Answer:

binding energy will be [tex]0.1633\times 10^{-15}J[/tex]

Explanation:

We have given wavelength of photon [tex]\lambda =121pm=121\times 10^{-12}m[/tex]

Velocity of light [tex]c=3\times 10^8m/sec[/tex]

Plank's constant [tex]h=6.6\times 10^{-34}Js[/tex]

So energy of photon [tex]E=\frac{hc}{\lambda }=\frac{6.6\times 10^{-34}\times 3\times 10^8}{121\times 10^{-12}}=1.636\times 10^{-15}J[/tex]

Mass of electron [tex]m=9.1\times 10^{-31}kg[/tex]

Velocity of electron is given [tex]v=56.9\times 10^6m/sec[/tex]

So kinetic energy of electron [tex]KE=\frac{1}{2}mv^2=\frac{1}{2}\times 9.1\times 10^{-31}\times (56.9\times 10^6)^2=1.473\times 10^{-15}J[/tex]

So binding energy = plank's energy - kinetic energy

[tex]=1.636\times 10^{-15}-1.473\times 10^{-15}=0.1633\times 10^{-15}J[/tex]

So binding energy will be [tex]0.1633\times 10^{-15}J[/tex]

The binding energy of an electron in an X-ray photoelectron experiment can be calculated by first determining the energy of the incoming photon and the kinetic energy of the ejected electron. The binding energy is then the difference between these two energies.

To calculate the binding energy of an electron in an X-ray photoelectron experiment, we'll require the principles of quantum mechanics and the concept of photoelectric effect. The energy of the incoming photon can be calculated using the equation:

E_photon = h*c/λ

where h is Planck's constant, c is the speed of light, and λ is the photon's wavelength. Converting the wavelength to the correct unit (meters), we get the energy of the photon.

Next, we calculate the kinetic energy of the ejected electron, using the equation:

E_kinetic = 0.5*m*v^2

where m is the mass of the electron, and v is its speed. Again, ensure that the speed is in the correct unit (meters per second).

The binding energy E_b of the electron then is the energy of the photon minus the kinetic energy of the electron:

E_b = E_photon - E_kinetic

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Answer:

4009.21658986 Hz

Explanation:

v = Speed of sound in air = 348 m/s

L = Length of tube = 2.17 cm

Fundamental frequency for a tube where one end is closed and the other end open is given by

[tex]f=\dfrac{v}{4L}\\\Rightarrow f=\dfrac{348}{4\times 2.17\times 10^{-2}}\\\Rightarrow f=4009.21658986\ Hz[/tex]

The fundamental frequency of the canal is 4009.21658986 Hz

Answer:

(a) The x component of the net electrostatic force on charge q3 is 0.195N

(b) The x component of the net electrostatic force on charge q3 is 0.021N

Explanation:

The force of q1 on q3 is a repulsive force and those of q2 and q4 on q3 are attractive forces. From second diagram at the bottom of the page in the attachment below it can be seen that the force of q1 on q3 is directed vertically downward and has on y component while the force of q4 on q3 is directed to the right and has on x component. The force of q2 on q3 has both x and y components. The full solution can be found in the attachment below.

Thank you for reading.

The electric force between two charged bodies at rest is called as electrostatic force.

The values are the following:

The x component of the net electrostatic force = 0.17 N

The y component of the net electrostatic force = 0.045 N

For component X

[tex]= (8.99 \times 10^{9} N.m2/ C^{2} \dfrac{(2.0\times10^{-7} )^2} {(0.050 m)^2}(-2 +\frac{2}{2\sqrt{2} } )\\ = 0.17 N[/tex]

X= 0.17 N

For component Y

Y = 0.045 N.

Hence, X= 0.17 N and Y = 0.045 N.

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Answer:

25.1%

Explanation:

Let's say m is the true weight and M is the weight of the counterweight.

The original distance between the pans and the center is 25.1 cm / 2 = 12.55 cm.  The fulcrum is then moved 1.4 cm towards the counterweight.

Sum of the moments about the fulcrum:

m (12.55 + 1.4) − M (12.55 − 1.4) = 0

13.95 m − 11.15 M = 0

13.95 m = 11.15 M

M / m = 13.95 / 11.15

M / m = 1.251

The true weight is being marked up by 25.1%.

The true weight of the goods being marked up by the shopkeeper is 25.1%.

A lever is a simple machine made up of a beam or rigid rod that pivots at fulcrum. A lever is a rigid body that can rotate on a single point. The lever is classified into three types based on the locations of the fulcrum, load, and effort.

Let the true mass is m.

and  the reading f the mass is M.

The initial distance between the two pan is 25.1 cm.

So, The initial distance between the pan and the fulcrum is  = 25.1 cm / 2 = 12.55 cm.

The fulcrum is moved 1.4 cm towards the counterweight by the dishonest  shopkeeper.

At equilibrium: the moment of force of two hands from fulcrum is equal. Hence,

mg (12.55 + 1.4)  = Mg (12.55 − 1.4)

13.95 m = 11.15 M

M / m = 13.95 / 11.15

M / m = 1.251

Hence, the true weight is being marked up by = {(M-m)/m}×100%

= {(1.251-1)×100%}

= 25.1%.

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The velocity of the object at t=3 seconds is calculated by differentiating the given position function and substituting t=3 into the derived velocity function, resulting in a value of 0.25 m/s.

This problem is about finding the velocity of an object given a position function x(t)=4t²/(t+1), which describes the object's position at any time 't'. To find the velocity at a specific time, you need to take the derivative of the position function, which gives you a velocity function v(t).

The derivative of x(t) with respect to 't' is v(t) = 4t(t+1)-4t²/ (t+1)² = 4/(t+1)². So, when t0=3, the velocity v(3) = 4/(3+1)² = 4/16 = 0.25 m/s.

In conclusion, at t = 3 seconds, the velocity of the object is 0.25 m/s.

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The question seeks to determine the velocity of an object at a specific time given its position function. However, the position function provided in the question appears to contain a typo or error, therefore it is not possible to calculate the velocity without the correct function.

The question involves calculating the velocity of an object at a given time t based on its position function. To find the velocity at time t = 3 seconds, we'll need to take the derivative of the position function. This is a principle from physics dealing with kinematics. However, the function provided, which is x(t) = 4t2t+1, seems to be incorrect or has a typo as it is not usable in its current form. Assuming that the correct position function might have been x(t) = 4t^2/(2t+1), the derivative or velocity function would be v(t) = d/dt [x(t)]. Nevertheless, since we do not have a correct function to work with, we cannot find a specific numerical value for the velocity at t = 3 seconds.

Answer:

A. [tex]\omega=11.1121\ rad.s^{-1}[/tex]

B. [tex]f=1.7685\ Hz[/tex]

C. [tex]T=0.5654\ s[/tex]

Explanation:

Given:

A)

for a spring-mass system the frequency is given as:

[tex]\omega=\sqrt{\frac{k}{m} }[/tex]

[tex]\omega=\sqrt{\frac{56.8}{0.46}}[/tex]

[tex]\omega=11.1121\ rad.s^{-1}[/tex]

B)

frequency is given as:

[tex]f=\frac{\omega}{2\pi}[/tex]

[tex]f=\frac{11.1121}{2\pi}[/tex]

[tex]f=1.7685\ Hz[/tex]

C)

Time period of a simple harmonic motion is given as:

[tex]T=\frac{1}{f}[/tex]

[tex]T=0.5654\ s[/tex]

Answer:

as soon as they touch the sheet, it returns to its initial position due to the decrease in the load on the rubber ball.

Explanation:

When you rub a foam rod that is an insulator with felt it acquires some loads, when separated these two the barrel is loaded

When approaching the loaded rubber rod, suppose positively, to the aluminum ball that is a metal, the positive charge attracts the free electors of the aluminum until a balance of the electric force and the tension of the wire in which it is hung is established The aluminum foil therefore the aluminum foil approaches the rubber ball, due to the electrostatic attraction, the closer the aluminum wave deflects.

When the ball touches the sheet, the free charges of the metal pass to the insulator neutralizing the existing charges, whereby the electric field and the electric force decrease. Consequently the aluminum sheet descending and moving away from the rubber ball.

 In summary, as soon as they touch the sheet, it returns to its initial position due to the decrease in the load on the rubber ball.

Due do the friction charged develop in the ball, the foil and ball attract.

When the ball and rod contact the charge neutralized and the attraction force decreased, which separate the ball and rod.

When the insulating material are rubbed against each other, the electric charge generate between them.

The effect of friction charge between rod and ball leads to,

Hence due to the friction charged develop in the ball, the foil and ball attract.

When the ball and rod contact the charge neutralized and the attraction force decreased, which separate the ball and rod.

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Answer:

A: 5.67*10^-5 N

B: 3.49*10^-5 N

C: -9.16*10^-5 N

Explanation:

[tex]\\A\\F_{A} = F_{BA} + F_{CA} =G*\frac{m_{b}*m_{a}}{r^2_{AB}} + G*\frac{m_{c}*m_{a}}{r^2_{AC}} \\\\= (6.67*10^(-11))*(\frac{363*517}{0.5^2} + \frac{154*363}{0.75^2})\\\\= 5.67*10^-5 N \\\\B\\\\F_{B} = -F_{BA} + F_{CB} =-G*\frac{m_{b}*m_{a}}{r^2_{AB}} + G*\frac{m_{c}*m_{b}}{r^2_{BC}} \\\\= (6.67*10^(-11))*(-\frac{517*363}{0.5^2} + \frac{517*154}{0.25^2})\\\\= 3.49*10^-5\\\\[/tex]

[tex]F_{C} = -F_{CA} - F_{CB} =-G*\frac{m_{b}*m_{c}}{r^2_{BC}} - G*\frac{m_{c}*m_{a}}{r^2_{AC}} \\\\= (6.67*10^(-11))*(-\frac{517*154}{0.25^2} - \frac{154*363}{0.75^2})\\\\= -9.16*10^-5[/tex]

Answer:

-7 C

Explanation:

Assuming that object other than the styrofoam balls was part of the charge transfer. In order to maintain charge balance, the initial charge of the system must equal the ending charge. If all balls were uncharged initially, the ending charge on the third ball must be:

[tex]C_1+C_2+C_3 = 0\\3+4+C_3=0\\C_3=-7[/tex]

There must be -7 C of charge on the third ball.

Answer:

Horizontal component of velocity will be 61.28 ft/sec

Vertical component of the velocity will be 51.423 ft/sec

Explanation:

We have given velocity of football v = 80 ft/sec'

Angle at which football is thrown [tex]\Theta =40^{\circ}[/tex]

Now we have to fond the horizontal and vertical component of the velocity

Horizontal component of velocity [tex]v_x=vcos\Theta =80\times cos40^{\circ}=80\times 0.766=61.28ft/sec[/tex]

Vertical component of the velocity [tex]v_y=vsin\Theta =80\times sin40^{\circ}=51.423ft/sec[/tex]

Explanation:

Given that,

Mass of the raindrops, [tex]m=0.5\ g=0.0005\ kg[/tex]

Charges, [tex]q=1\ mC=10^{-3}\ C[/tex]

Distance between raindrops, d = 1 cm = 0.01 m

(a) The force due to motion of raindrop is balanced by the electric force between charges. It is given by :

[tex]ma=\dfrac{kq^2}{r^2}[/tex]

a is the acceleration of the raindrop

[tex]a=\dfrac{kq^2}{r^2m}[/tex]

[tex]a=\dfrac{9\times 10^9\times (10^{-3})^2}{(0.01)^2\times 0.0005}[/tex]

[tex]a=1.8\times 10^{11}\ m/s^2[/tex]

(b) It is clear that the acceleration is too large. It can break apart the rain drop.

(c) If the charge is of the factor of [tex]10^{-8}\ C[/tex], the charge would be more reasonable.            

Hence, this is the required solution.  

To find the acceleration of the charged raindrops, we can use Coulomb's Law and Newton's second law. The acceleration is found to be 1.8 x 10^13 m/s^2, which seems unreasonable for raindrops. The assumption of the raindrops acquiring charges of 1.00 mC is likely responsible for this result.

To calculate the acceleration of the two charged raindrops, we can use Coulomb's Law, which states that the force between two charges is given by: F = (k*q1*q2)/r^2, where F is the force, k is the electrostatic constant, q1 and q2 are the charges, and r is the distance between them. The force experienced by each raindrop is equal in magnitude but opposite in direction.

The acceleration of each raindrop can be found using Newton's second law: F = m*a, where F is the net force, m is the mass of the raindrop, and a is the acceleration. Rearranging the equation, we have: a = F/m. Substituting the values into the equations and solving for acceleration, we find: a = (k*q^2)/(m*r^2). Plugging in the values, we have: a = (9 x 10^9 N*m^2/C^2 * (1 x 10^-3 C)^2) / (0.500 g * 10^-3 kg/g * (1 x 10^-2 m)^2). After calculating the values, we find that the acceleration of the two raindrops due to their charges is 1.8 x 10^13 m/s^2.

(b) What is unreasonable about this result? The result seems unreasonable because the acceleration is extremely high. Normally, objects with masses like raindrops would experience much lower accelerations. (c) The premise or assumption responsible for this result is that the raindrops have acquired charges of 1.00 mC, which is an extremely high charge for raindrops and likely not possible in reality.

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Answer: FR=2.330kN

Explanation:

Write down x and y components.

Fx= FSin30°

Fy= FCos30°

Choose the forces acting up and right as positive.

∑(FR) =∑(Fx )

(FR) x= 5-Fsin30°= 5-0.5F

(FR) y= Fcos30°-4= 0.8660-F

Use Pythagoras theorem

F2R= √F2-11.93F+41

Differentiate both sides

2FRdFR/dF= 2F- 11.93

Set dFR/dF to 0

2F= 11.93

F= 5.964kN

Substitute value back into FR

FR= √F2(F square) - 11.93F + 41

FR=√(5.964)(5.964)-11.93(5.964)+41

FR= 2.330kN

The minimum force is 2.330kN

To determine the magnitude of force F to minimize the resultant FR of three forces, we can use the rule for finding the magnitude of a vector. By taking the square root of the sum of the squares of the components, we can find the magnitude of F.

The question is asking to determine the magnitude of force F so that the resultant FR of the three forces is as small as possible. To find the magnitude of the resultant force, we need to use the rule for finding the magnitude of a vector. We take the square root of the sum of the squares of the components. In this case, we have F = F₁ + F₂, and we can plug in the values given to find the magnitude of F.

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Answer:

[tex]F_1=2.53\ 10^{-4} \ N[/tex]

The net force goes to the right

Explanation:

Electrostatic Force

Let's consider the situation where 2 point charges q1 and q2 are separated by a distance d. An electrostatic force appears between them whose magnitude can be computed by the Coulomb's formula

[tex]\displaystyle F=\frac{k\ q_1\ q_2}{d^2}[/tex]

Where k is the constant of proportionality

[tex]k=9.10^9\ Nw.m^2/c^2[/tex]

Two equally-signed charges repel each other, two opposite-signed charges attract each other.

We need to find the total net force exerted on q1 by q2 and q3. We're assuming the charges are placed to the right of the origin, so the distribution is shown in the figure below.

Since q3 repels q1, its force goes to the right, since q2 attracts q1, its force goes to the right also, thus the total force on q1 is :

[tex]F_1=F_{31}+F_{21}[/tex]

It's directed to the right

Let's compute the individual forces. q3 is separated 2 cm from q1, so d=0.02 m

[tex]\displaystyle F_{31}=\frac{9.10^9\ 4.5\ 10^{-9}\ 1.5\ 10^{-9}}{0.02^2}[/tex]

[tex]F_{31}=0.000151875\ N[/tex]

[tex]\displaystyle F_{21}=\frac{9.10^9\ 3\ 10^{-9}\ 1.5\ 10^{-9}}{0.02^2}[/tex]

[tex]F_{21}=0.00010125\ N[/tex]

[tex]F_1=F_{31}+F_{21}=0.000151875\ N+0.00010125\ N=0.000253125 \ N[/tex]

Expressing the force in scientific notation

[tex]\boxed{F_1=2.53\ 10^{-4}\ N}[/tex]

The net force goes to the right

Solution: The magnitude of the net force acting on q₁ is : Fn = 25.312 [N]

and the direction is in the direction of the positive x axis

The electric force between two charges q₁ and q₂, is according to Coulombs´law as:

F₂₁ = K ×  q₁ × q₂ / d₁₂²

In that equation

F₂₁  is the force exerted by charge q₂ on the charge q₁

It is pretty obvious that F₂₁  = F₁₂, and the force is of rejection if the charges are of the same sign or attraction if they are of opposite signs

Now in this case we calculate F₂₁

F₂₁ = [9×10⁹ × ( 1.5)×10⁻⁹ × (3)×10⁻⁹] /(0.02)²

F₂₁ = 40.5 × 10⁻⁹/ 4 × 10⁻⁴

F₂₁ = 10.125 × 10⁻⁵ [N]

F₂₁  is in the direction of the positive x   ( attraction force)

And

F₃₁ =  [9×10⁹ × ( 1.5)×10⁻⁹ × (4.5)×10⁻⁹] /(0.02)²

F₃₁ = 15.188× 10⁻⁵  [N]

F₃₁ is in the direction of the positive x ( rejection force)

Then the net force is  Fn  = 10.125 + 15.188  

Fn = 25.312 [N]    in direction of x positive

Final answer:

Even if two forces are equal in magnitude and opposite in direction, they can still create a net torque if they are applied at different points that are at different distances from the object's pivot point.

Explanation:

In physics, particularly when discussing Newton's third law, it is essential to recognize that while two forces may be equal in magnitude and opposite in direction, they do not necessarily result in equilibrium if they are acting on different systems. When considering the possibility of a net torque, it is crucial to understand that torque is not just about the magnitude of the force, but also its point of application and the distance from the pivot point (or the axis of rotation).

To produce a torque, a force must be applied in such a manner that it causes the object to rotate around a pivot point. If two equal and opposite forces are applied at different points on an object, and those points are at different distances from the pivot point, then a net torque can occur.

For example, imagine a seesaw with equal forces pushing down on either end. If these forces are applied at different distances from the fulcrum (pivot point), the seesaw will rotate due to the net torque, despite the forces being equal and opposite. This demonstrates that even with equal and opposite forces, the effect on the object's rotational motion depends on the forces' points of application and their distances from the pivot point.

Answer: The answer is 258

Explanation: The distance between the nuclei of the atoms in a diatomic molecule X2 is measured to be 516pm

Therefore the atomic radius of X2 is

516/2=258