An overweight boy and a skinny girl are balanced on a massless seesaw. If they both move forward such that they are one-half their original distance from the pivot point, what will happen to the seesaw?

a) Final velocity after docking: +0.094 m/s

b) Kinetic energy loss: 31.6 J

c) Final velocity after docking: -0.056 m/s

d) Kinetic energy loss: 31.6 J

Explanation:

a)

Since the system of two satellites is an isolated system, the total momentum is conserved. So we can write:

[tex]p_i = p_f[/tex]

Or

[tex]m_1 u_1 + m_2 u_2 = (m_1 + m_2)v[/tex]

where, in the reference frame in which the first satellite was originally at rest, we have:

[tex]m_1 = 4.50\cdot 10^3 kg[/tex] is the mass of the 1st satellite

[tex]m_2 = 7.50\cdot 10^3 kg[/tex] is the mass of the 2nd satellite

[tex]u_1 = 0[/tex] is the initial velocity of the 1st satellite

[tex]u_2 = +0.150 m/s[/tex] is the initial velocity of the 2nd satellite

v is their final velocity after docking

Solving for v,

[tex]v=\frac{m_2 u_2}{m_1 +m_2}=\frac{(7.50\cdot 10^3)(0.150)}{4.50\cdot 10^3 + 7.50\cdot 10^3}=0.0938 m/s[/tex]

b)

The initial kinetic energy of the system is just the kinetic energy of the 2nd satellite:

[tex]K_i = \frac{1}{2}m_2 u_2^2 = \frac{1}{2}(7.50\cdot 10^3)(0.150)^2=84.4 J[/tex]

The final kinetic energy of the two combined satellites is:

[tex]K_f = \frac{1}{2}(m_1 +m_2)v^2=\frac{1}{2}(4.50\cdot 10^3+7.50\cdot 10^3)(0.0938)^2=52.8 J[/tex]

Threfore, the loss in kinetic energy during the collision is:

[tex]\Delta K = K_f - K_i = 52.8 - 84.4=-31.6 J[/tex]

c)

In this case, we are in the reference  frame in which the second satellite is at rest. So, we have

[tex]u_2 = 0[/tex] (initial velocity of satellite 2 is zero)

[tex]u_1 = -0.150 m/s[/tex] (initial velocity of a satellite 1)

Therefore, by applying the equation of conservation of momentum,

[tex]m_1 u_1 + m_2 u_2 = (m_1 + m_2)v[/tex]

And solving for v,

[tex]v=\frac{m_1 u_1}{m_1 +m_2}=\frac{(4.50\cdot 10^3)(-0.150)}{4.50\cdot 10^3 + 7.50\cdot 10^3}=-0.0563 m/s[/tex]

d)

The initial kinetic energy of the system is just the kinetic energy of satellite 1, since satellite 2 is at rest:

[tex]K_i = \frac{1}{2}m_1 u_1^2 = \frac{1}{2}(4.50\cdot 10^3)(-0.150)^2=50.6 J[/tex]

The final kinetic energy of the system is the kinetic energy of the two combined satellites after docking:

[tex]K_f = \frac{1}{2}(m_1 + m_2)v^2=\frac{1}{2}(4.50\cdot 10^3+ 7.50\cdot 10^3)(-0.0563)^2=19.0 J[/tex]

Therefore, the kinetic energy lost in the collision is

[tex]\Delta K = K_f - K_i = 19.0 -50.6 = -31.6 J[/tex]

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Answer:

[tex]\lambda = 25.79\ cm[/tex]

Explanation:

given,

Wave vibrates = 37.6

time = 27.9 s

maximum distance travel = 450 cm

time = 11.3 s

wavelength = ?

frequency of wave

[tex]f=\dfrac{37.6}{27.9}[/tex]

f = 1.35 Hz

Speed of wave

[tex]v = \dfrac{450}{11.3}[/tex]

v = 39.82 cm/s

wavelength of wave

v = fλ

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

[tex]\lambda =\dfrac{34.82}{1.35}[/tex]

[tex]\lambda = 25.79\ cm[/tex]

Hence, wavelength of the wave is equal to 25.79 cm.

Final answer:

The wavelength of a wave can be calculated using the speed of the wave and its frequency. In this case, the wavelength is 29.50 cm.

Explanation:

Wavelength: The wavelength of a wave is the distance between two similar points on the medium that have the same height and slope. In this case, the wavelength can be found using the formula: λ = v/f, where v is the speed of the wave and f is the frequency.

Given Data: Number of vibrations = 37.6, Time = 27.9 s, Distance traveled = 450 cm, Time = 11.3 s.

Calculation: Speed of the wave = Distance/Time = 450 cm / 11.3 s = 39.82 cm/s. Frequency = Number of vibrations / Time = 37.6 / 27.9 = 1.35 Hz. Therefore, Wavelength = 39.82 cm / 1.35 Hz = 29.50 cm.

Answer:

The correct answer is a Low earth orbit.

Explanation:

A low earth orbit can be understood as an earth orbit with an altitude of 1,000 miles or less. It is a satellite sustem that employs many satelites, in fact, most man-made objects that are currently in outer-space are part of this low earth orbit. (LEO).

The most famous LEO satellite system is the one from planet earth. Almost every space flight that human beings have ever done are done in LEO, and every spacial station is located in this zone.

In conclusion, A low earth orbit satellite system employs many satellites, each in an orbit at an altitude of less than 1,000 miles.

Answer:A(n) low Earth Orbit (LEO) satellite system employs many satellites, each in an orbit at an altitude of less than 1,000 miles.

Explanation:A low Earth orbit (LEO) is an Earth-centered orbit with an altitude of 2,000 km (1,200 mi) or less (approximately one-third of the radius of Earth), or with at least 11.25 periods per day (an orbital period of 128 minutes or less) and an eccentricity less than 0.25. Most of the manmade objects in outer space are in LEO.

There is a large variety of other sources that define LEO in terms of altitude. The altitude of an object in an elliptic orbit can vary significantly along the orbit. Even for circular orbits, the altitude above ground can vary by as much as 30 km (19 mi) (especially for polar orbits) due to the oblateness of Earth's spheroid figure and local topography

Answer:

The correct answer is less momentum.

Explanation:

The momentum of an object is directly linked to the force exerted on that object. In a longer barrel, the shot cannonball will have a greater impulse changing to occur a larger momentum and therefore a higher speed will be applied to the bullet, contrary to what would happen in a shorter barrel.

Final answer:

The cannonball shot from a short cannon does not have more momentum, velocity, or impulse by virtue of the cannon's length alone, since momentum and impulse depend on both the force applied and the time the force acts on the cannonball.

Explanation:

If a cannonball is shot from both a long and a short cannon with the same amount of force, we need to understand that force, momentum, and impulse are interrelated but distinct concepts in physics. The product of an object's mass and velocity is its momentum.

Impulse is the change in momentum, often calculated as force multiplied by the time the force is applied. Because the question states that the force is the same, the impulse given to the cannonball would be identical regardless of the cannon length, assuming the force is applied over the same time period.

However, a longer cannon might allow the cannonball more time to accelerate, potentially resulting in greater final velocity and therefore more momentum, since momentum is mass times velocity. Conversely, a shorter cannon may allow less time for the force to act, possibly resulting in a lower velocity and, by extension, less momentum.

Thus, the cannonball from the short cannon does not necessarily have more velocity only, as it depends on the time the force acts on the cannonball.

In summary, the answer choice would be that the short cannon cannonball does not categorically have more momentum, velocity, or impulse based solely on the length of the cannon.

Answer:

the answer is at least 3 feet

Explanation:

In order to ensure that a cable is not affected by electromagnetic interference, it should be at least 3 feet  away from fluorescent lighting.

This is because, cables can be adversely affected by electromagnetic interference - which is a disturbance that affects an electrical circuit due to either electromagnetic induction or radiation emitted from an external source - and insulation alone cannot provide adequate protection for these cables.

Therefore, the cables should be kept a few feet away from flourescent lighting in order to prevent this interference.

To minimize the EMI on a cable from fluorescent lighting, it should be kept at a distance of at least 2 feet or 0.6 meters. The distance can vary depending on the cable type, the electromagnetic field size and the data's sensitivity.

To minimize the electromagnetic interference (EMI) effect on a cable from fluorescent lighting, it is recommended to maintain a distance of at least 2 feet or 0.6 meters. This is because the fluorescent light produces a magnetic field that can interact with the cable and cause electromagnetic interference. The above mentioned distance is considered a safe threshold, yet it can vary depending on the type of cable, the strength of the electromagnetic field produced by the light and the sensitivity of the data being transmitted.

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Answer:

[tex]\omega=0.12\frac{rad}{s}[/tex]

Explanation:

In a uniform circular motion, since a complete revolution represents 2π radians, the angular velocity, which is defined as the angle rotated by a unit of time, is given by:

[tex]\omega=\frac{2\pi}{T}(1)[/tex]

Here T is the period, that is, the time taken to complete onee revolution:

[tex]T=\frac{2\pi r}{v}(2)[/tex]

Replacing (2) in (1):

[tex]\omega=\frac{2\pi}{\frac{2\pi r}{v}}=\frac{v}{r}\\\omega=\frac{19.1\frac{m}{s}}{158m}\\\omega=0.12\frac{rad}{s}[/tex]

The angular speed of the racing car is approximately 0.1208861 rad/s.

The angular speed of the racing car can be calculated using the formula that relates linear speed (v) to angular speed and the radius (r) of the circular path, which is:

[tex]\[ v = r \cdot \omega \][/tex]

Given that the linear speed (v) of the car is 19.1 m/s and the radius (r) of the circular track is 158 m, we can solve for the angular speed (Ï) as follows:

[tex]\[ \omega = \frac{v}{r} \][/tex]

[tex]\[ \omega = \frac{19.1 \text{ m/s}}{158 \text{ m}} \][/tex]

[tex]\[ \omega =\frac{19.1}{158} \text{ rad/s} \][/tex]

[tex]\[ \omega \ = 0.1208861 \text{ rad/s} \][/tex]

Therefore, the angular speed of the racing car is approximately 0.1208861 rad/s.

To express this in a more simplified fraction, we can write:

[tex]\[ \omega \ = \frac{19.1}{158} \text{ rad/s} \][/tex]

[tex]\[ \omega \ = \frac{191}{1580} \text{ rad/s} \][/tex]

[tex]\[ \omega \ = \frac{191}{1580} \times \frac{10}{10} \text{ rad/s} \][/tex]

[tex]\[ \omega \ = \frac{1910}{15800} \text{ rad/s} \][/tex]

[tex]\[ \omega \ = \frac{191}{1580} \text{ rad/s} \][/tex]

Since 191 and 1580 do not have any common factors other than 1, this fraction is already in its simplest form. Thus, the final answer for the angular speed of the racing car is:

[tex]\[ \ {0.1208861 \text{ rad/s}} \][/tex]

Answer : The energy of one photon of hydrogen atom is, [tex]3.03\times 10^{-19}J[/tex]

Explanation :

First we have to calculate the wavelength of hydrogen atom.

Using Rydberg's Equation:

[tex]\frac{1}{\lambda}=R_H\left(\frac{1}{n_i^2}-\frac{1}{n_f^2} \right )[/tex]

Where,

[tex]\lambda[/tex] = Wavelength of radiation

[tex]R_H[/tex] = Rydberg's Constant  = 10973731.6 m⁻¹

[tex]n_f[/tex] = Higher energy level = 3

[tex]n_i[/tex]= Lower energy level = 2

Putting the values, in above equation, we get:

[tex]\frac{1}{\lambda}=(10973731.6)\left(\frac{1}{2^2}-\frac{1}{3^2} \right )[/tex]

[tex]\lambda=6.56\times 10^{-7}m[/tex]

Now we have to calculate the energy.

[tex]E=\frac{hc}{\lambda}[/tex]

where,

h = Planck's constant = [tex]6.626\times 10^{-34}Js[/tex]

c = speed of light = [tex]3\times 10^8m/s[/tex]

[tex]\lambda[/tex] = wavelength = [tex]6.56\times 10^{-7}m[/tex]

Putting the values, in this formula, we get:

[tex]E=\frac{(6.626\times 10^{-34}Js)\times (3\times 10^8m/s)}{6.56\times 10^{-7}m}[/tex]

[tex]E=3.03\times 10^{-19}J[/tex]

Therefore, the energy of one photon of hydrogen atom is, [tex]3.03\times 10^{-19}J[/tex]

Answer:

a constant downward net force.

Explanation:

The diver experiences a constant downward net force because while on his was up he decelerates until he gets to his maximum height when the acceleration is zero, during this phase force is not constant. While on his way down neglecting influences of air or atmosphere he falls with a constant downward net acceleration hence his net downward force will be constant.

Answer:

Explanation:

Given

Electric Field Strength [tex]E_0=2.07\times 10^5\ N/C[/tex]

Charge on electron [tex]q=1.6\times 10^{-19}\ C[/tex]

Force on any charged particle in an Electric field is given by

[tex]Force=charge\ on\ electron\times Electric\ Field\ strength [/tex]

[tex]F=1.6\times 10^{-19}\times 2.07\times 10^5[/tex]

[tex]F=3.312\times 10^{-14}\ N[/tex]

as the electric field is pointing downward therefore force will be acting downward on a positively charged particle but opposite for an electron i.e. in upward direction                                                  

The roofing tile will land around 3.1 meters away from the roof edge. This is found by using equations of motion and breaking the problem into vertical and horizontal components.

To solve this, we can break the problem down into two dimensions (horizontal and vertical) and use equations of motion. On the vertical, the roofing tile starts off 10 m above the ground, and falls under acceleration due to gravity. On the horizontal, the tile leaves the roof edge with a horizontal speed of 6 m/s * cos(30), and continues with this speed (since there's no horizontal acceleration).

The time it takes the tile to hit the ground can be found using the equation y = v(initial)*t - 0.5*g*t^2. Assuming upward is positive and taking the initial velocity on the vertical as 6 m/s * sin(30), y = -10 m, v(initial) = 3 m/s and g = 9.8 m/s^2, we can solve for t to get approximately 0.598 seconds.

The distance from the exit point on the roof can be found by multiplying the horizontal speed 5.2 m/s (6 m/s * cos(30)) by the time (0.598 sec) to get approximately 3.1 m.

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Answer:

The resistance is 626.0 Ω.

Explanation:

Given that,

Power of compact bulb= 100 W

Power of incandescent bulb = 23.0 W

Time [tex]t= 1.00\times10^{4}\ hours[/tex]

What is the resistance of a “100 W”fluorescent bulb? (Remember the actual rating is only 23W of powerfor a 120V circuit)

We need to calculate the resistance of the bulb

Using formula of power

[tex]P=\dfrac{V^2}{R}[/tex]

[tex]R=\dfrac{V^2}{P}[/tex]

Where, P = power

R = resistance

V = voltage

Put the value into the formula

[tex]R=\dfrac{120^2}{23}[/tex]

[tex]R=626.0\ \Omega[/tex]

Hence, The resistance is 626.0 Ω.

Answer:

115799.256V/m

Explanation:

Given V = 623v, d = 5.38mm = 0.00538m

Strength of electric field E = V/d

E = 623/0.00538

= 115799.256V/m

Answer:

b.) 4h

Explanation:

Answer:

15 gallons.

Gallons = (Pounds) ÷ (Pounds ÷ Gallons)

Explanation:

To bring an aircraft's weight under the maximum certificated gross weight by 90 pounds, 15 gallons of gasoline should be drained.

If an aircraft is loaded with 90 pounds over the maximum certificated gross weight and needs to be brought within the weight limit by draining fuel, we need to calculate how much fuel, in pounds, should be drained. Gasoline's weight can vary slightly with temperature, but for general aviation purposes, it's usually taken to be about 6 pounds per gallon.

Hence, to remove 90 pounds of weight, the amount of fuel that should be drained would be 90 divided by 6.
Performing the calculation, 15 gallons of fuel should be drained to remove 90 pounds of weight from the aircraft and bring it back to or below the maximum certificated gross weight.

Answer:

Time taken, t = 0.16 seconds

Explanation:

Given that,

Initial speed of blood, u = 0

Final speed of blood, v = 25 cm/s = 0.25 m/s

Distance, d = 2.1 cm = 0.021 m

Using first equation of motion as :

v = u + at

u = 0

[tex]v=at\\0.25 =at[/tex]

Let t is the time taken. Using second equation of motion as :

[tex]d=ut+\dfrac{1}{2}at^2[/tex]

[tex]d=\dfrac{1}{2}at\times t[/tex]

[tex]t=\dfrac{2d}{at}[/tex]

Since, at = 0.25

So,

[tex]t=\dfrac{2\times 0.021}{0.25}[/tex]

t = 0.16 seconds

So, the time taken by the blood to accelerate is 0.16 seconds.    

Answer:

Time period of oscillation on moon will be equal to 3.347 sec

Explanation:

We have given mass which is attached to the spring m = 3.42 kg

Spring constant K = 12 N/m

We have to find the period of oscillation

Period of oscillation is equal to [tex]T=2\pi \sqrt{\frac{m}{K}}[/tex], here m is mass and K is spring constant

So period of oscillation [tex]T=2\times 3.14\times \sqrt{\frac{3.42}{12}}[/tex]

[tex]T=2\times 3.14\times 0.533=3.347sec[/tex]

So time period of oscillation will be equal to 3.347 sec

As it is a spring mass system and from the relation we can see that time period is independent of g

So time period will be same on earth and moon

Answer:

hard line, soft line

Explanation:

Answer:

(3) 690 N

Explanation:

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

The formula for force is given as,

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

Where F = force, m = mass, a = acceleration.

Also,

a = (v-u)/t................... Equation 2

Where v = Final velocity, u = initial velocity, t = time.

Given: u = 6.0 m/s, v = 0 m/s (bring to stop), t = 0.65 s.

Substitute into equation 2

a = (0-6)/0.65

a = -6/0.65

a = -9.23 m/s²

Also given: m = 75 kg

Substitute again into equation 1

F = 75(-9.23)

F = -692.25 N

The negative sign tells that the force oppose the motion of the player

F ≈ 690 N

Hence the right option is (3) 690 N

The magnitude of the average force required to stop the player in 0.65 second is 690 N. And option (3) is correct.

Given data:

The mass of hockey player is, m = 75 kg.

The speed of hockey player is, v = 6.0 m/s.

The reaction time is, t = 0.65.

Use the concept of impulse - momentum theorem to obtain the value of average force acting on the hockey player as,

As per the impulse - momentum theorem,

[tex]F = \dfrac{mv}{t}[/tex]

Here, F is the average force exerted on the hockey player.

Solving as,

[tex]F = \dfrac{75 \times 6}{0.65 }\\\\F \approx 690 \;\rm N[/tex]

Thus, the magnitude of the average force required to stop the player in 0.65 second is 690 N. And option (3) is correct.

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Final answer:

If the charges are pushed together so the separation is 25 centimeters, the force on each charge will be 16 N.

Explanation:

In electrostatics, the force between two charged particles is given by Coulomb's law. The formula to calculate the force is F = k * (q1 * q2) / r^2, where F is the force, k is the electrostatic constant, q1 and q2 are the charges of the particles, and r is the distance between them.

Using this formula, if the distance between the charges is decreased from 1 meter to 25 centimeters, the force on each charge will increase. The force is inversely proportional to the square of the distance, so when the distance is reduced to 0.25 meters (25 centimeters), the force will be 16 times stronger. Therefore, the force on each charge will be 16 N.

Answer:

Explanation:

check the attached for the solution

Answer:

b.#NAME?

Explanation:

Remember, in Spreadsheet programs like Ms Excel several types of errors can occur such as value error.

However, since Seymour explains that there is a mistyped function name in the sheet it is more likely to display on the affected cell as #NAME?.

For example the function =SUM is wrongly spelled =SOM.

Therefore it is important to make sure the function name is spelled correctly.

Answer:

Sonogram

Explanation:

A sonogram is a medical diagnostic method that is commonly uses sound waves in order to generate images of any tissues, organs, or some other internal structures inside the human body. This sonogram does not use any kind of harmful radiations like the X-rays. These are sound waves of high frequencies.

This is widely used by doctors for health checkups. The other name for sonogram is ultrasound.

Answer:

The speed at the bottom of the driveway is3.67m/s.

Explanation:

Height,h= 5sin20°= 1.71m

Potential energy PE=mgh= 2000×9.8×1.71

PE= 33516J

KE= PE- Fk ×d

0.5mv^2= 33516 - (4000×5)

0.5×2000v^2= 33516 - 20000

1000v^2= 13516

v^2= 13516/1000

v =sqrt 13.516

v =3.67m/s

Explanation:

Besides human error, other sources of error include friction on the cart (we assumed there is no friction, but in reality, that's never the case), and instrument errors (imprecision in the spring scale).

Besides human error, experiments can also encounter sampling errors, nonsampling errors, uncertainty factors, and spontaneous errors. These can be caused by an inaccurate sampling process, equipment malfunctions, variability in samples, and limitations in the measuring device.

Possible sources of error in an experiment, besides human error, could include sampling errors and non-sampling errors. Sampling errors occur when the sample utilized may not be large enough or not accurately representative of the larger population.

This can lead to inaccurate assumptions and conclusions. Non-sampling errors, on the other hand, are unrelated to the sampling process and could be a result of equipment or instrument malfunction (like a faulty counting device). An example for this would be an uncertainty in measurement induced by the fact that smallest division on a measurement ruler is 0.1 inches.

Further, variability in samples can also lead to errors called spontaneous errors. These can be due to natural phenomena such as exposure to ultraviolet or gamma radiation, or to intercalating agents. Lastly, uncertainty factors can contribute to errors as well. These factors include limitations of the measuring device, inaccuracies caused by the instrument itself (e.g., a paper cutting machine that causes one side of the paper to be longer than the other).

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Answer:

A) Fx = 45.3N Fy = 21.1N

B) Fm = 45.3N R = 196N Ff = 35.4N

C) i) 0KJ ii) 11.5KJ iii) 11.5KJ iv) 0KJ

D) 23KJ

E) 0.047

Explanation:

a) Horizontal component of the force Fx = 50cos 25° = 45.3N

Vertical component = 50sin25° = 21.1N

b) Magnitude of the applied force = moving force Fm = Fx = 50cos25° =45.3N

Magnitude of the weight = mg = 20×9.8 = 196N

Magnitude of normal force which is the reaction is equal to the weight = mg = 20×9.8 = 196N

Frictional force = moving force = 50cos45° = 35.4N

c) since workdone = Force done × perpendicular distance in the direction of the force

- workdone on the moving force is 0Joules since it has no perpendicular distance

- workdone on weight is the weight × distance = (20×9.8)×12 = 11.5KJ

= work done on normal force = workdone by the weight = 11.5KJ

Workdone on the frictional force is is 0Joules since the force is along the horizontal (no perpendicular distance)

d) the total work done = work done by Applied Force +Weight + Normal Force + Frictional Force= 0+11.5+11.5 = 23KJ

e) the coefficient of friction = moving force / normal reaction = 45.3/196 = 0.047

Explanation:

A.

Horizontal component, Fy = F * cos(a)

= 50cos25

= 50 * 0.91

= 45.32 N

Vertical component,Fx = F * sin(a)

= 50sin25

= 50 * 0.42

= 21.13 N

B.

Applied force = 50 N

Weight,W = m * g

= 20 * 9.81

= 196.2 N

Normal force, N = W - Fx

= 200 - 21.13

= 179 N

Frictional force = Fy

= 45.32 N.

C.

Workdone by Normal and Weight forces are = 0, because they both act perpendicular to the movement.

Workdone by friction = Workdone by applied forces

= force * distance

= 12 * 45.32

= 543.84 J

D.

Total amount of work done on the crate = 0 (the movement with a constant speed).

E.

The coefficient of friction, u = Fy/(W - Fx)

= 45.5/(196.2 - 21.13)

= 0.26

Answer: Fmin = (m₁ + m₂) μsg

Explanation:

To begin, we would first define the parameters given in the question.

Mass of the box = m₁

Mass of the board = m₂

We have a Frictionless surface given that Fr is acting as the frictional force between the box and the board.

from our definition of force, i.e. the the frictional force against friction experienced by the box, we have

Fr = m₁a ...................(1)

Also considering the force between the box and the board gives;

Fr = μsm₁g .................(2)

therefore equating both (1) and (2) we get

m₁a = μsm₁g

eliminating like terms we get

a = μsg

To solve for the minimum force Fmin  that must be applied to the board in order to pull the board out from under the box, we have

Fmin  = (m₁ + m₂) a  ...........(3)

where a = μsg, substituting gives

Fmin = (m₁ + m₂) μsg

cheers i hope this helps

The constant force with the least magnitude that must be applied to the board in order to pull the board out from under the the box is  [tex]\mu_{s} g({m_{1}+m_{2}})[/tex].

Given data:

The mass of small box is, [tex]m_{1}[/tex].

The mass of board is, [tex]m_{2}[/tex].

The length of board is, L.

The coefficient of static friction between the board and box is, [tex]\mu_{s}[/tex].

The linear force acting between the box and the board provides the necessary friction to box. Therefore,

[tex]F=F_{f}\\F=\mu_{s}m_{1}g\\m_{1} \times a = \mu_{s} \times m_{1}g\\a= \mu_{s} \times g[/tex]

a is the linear acceleration of board.

Then, the minimum force applied on the board is,

[tex]F_{min}=({m_{1}+m_{2}})a\\F_{min}=({m_{1}+m_{2}})(\mu_{s} \times g)\\F_{min}=\mu_{s} g({m_{1}+m_{2}})[/tex]

Thus, the constant force with the least magnitude that must be applied to the board in order to pull the board out from under the the box is

[tex]\mu_{s} g({m_{1}+m_{2}})[/tex].

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Answer: Option (B) is the correct answer.

Explanation:

Expression for centripetal acceleration is as follows.

                a = [tex]r \omega^{2}[/tex] .......... (1)

Also, we know that

             [tex]\omega = \frac{2 \pi}{T}[/tex] ........... (2)

Putting the value from equation (2) into equation (1) as follows.

             a = [tex]r (\frac{2 \pi}{T})^{2}[/tex]

                = [tex]r \frac{2 (\pi)^{2}}{4}[/tex]

As,       [tex]a \propto \frac{1}{T^{2}}[/tex]

               a = [tex]\frac{k}{T^{2}}[/tex]

or,              [tex]aT^{2} = k[/tex]

Now, we will reduce a to [tex]\frac{a}{2}[/tex]. So, new value of [tex]T^{2}[/tex] will be equal to [tex]2T^{2}[/tex].

Therefore, value of new period will be as follows.

           [tex]T' = \sqrt{2T^{2}}[/tex]

                      = [tex]\sqrt{2}T[/tex]

Thus, we can conclude that the new period is equal to [tex]T \sqrt{2}[/tex].

The new period should be [tex]T\sqrt{2}[/tex]

The expression for centripetal acceleration should be [tex]a = r\omega^2[/tex]

Now

we know that [tex]w = 2\pi \div T[/tex]

Now here we put the values

[tex]a = r(2\pi\div T)^2\\\\= r (2(\pi)^2\div 4\\\\Since\ a \alpha \frac{1}{T^2}\\\\ aT^2 = K[/tex]

Now here we have to decrease to a by 2. So the new T value should be [tex]2T^2[/tex]

So, the new period should be

[tex]T = \sqrt{2T^2}\\\\ = \sqrt{2T}[/tex]

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Explanation:

Let the speed of river be r and speed of boat be b.

Distance traveled = 24 km

Time taken to travel 24 km with current = 2 hr

We have

          Distance = Speed x Time

          24 = (b + r) x 2

          b + r = 12 --------------------eqn 1

Time taken to travel 24 km against current = 3 hr

We have

          Distance = Speed x Time

          24 = (b - r) x 3

          b - r = 8 --------------------eqn 2

eqn 1 + eqn 2

          2b = 20

            b = 10 km/hr

Substituting in eqn 1

            10 + r = 12

                     r = 2 km/hr

Speed of boat in still water = 10 km/hr

Speed of current of river = 2 km/hr

The speed of the boat in still water is 10 km/h and the speed of the current is 2 km/h. This is a solved by using a system of linear equations with speed of the boat and the current as variables.

This problem is a case for a system of linear equations. Let's denote the speed of the boat in still water as b km/h and the speed of the current as c km/h. When the boat travels down the river, the boat and the current speeds are added, because they move in the same direction. When the boat travels up the river, the speeds are subtracted, because they move in opposite directions.

So we have the following equations:

The solution to this system of equations will give you the speed of the boat in still water and the speed of the current. Adding these two equations together, we get:

Therefore, b = 10 km/h, which is the speed of the boat in still water. Substitute b = 10 km/h into the first equation to find the speed of the current, c = 12 km/h - 10 km/h = 2 km/h.

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There is an omission of some sentences in the question which affects the answering of question B and C, so we will based the omission of the sentences on assumption in order to solve the question that falls under it.

NOTE: The omitted sentences are written in bold format

A tennis ball has a mass of 0.059 kg. A professional tennis player hits the ball hard enough to give it a speed of 41 m/s (about 92 miles per hour.) The ball moves toward the left, hits a wall and bounces straight back to the right with almost the same speed (41 m/s).

As indicated in the diagram below, high-speed photography shows that the ball is crushed about d = 2.0 cm at the instant when its speed is momentarily zero, before rebounding.

A) What is the average speed of the ball during the period from first contact with the wall to the moment the ball's speed is momentarily zero?

B) How much time elapses between first contact with the wall, and coming to a stop?

C) What is the magnitude of the average force exerted by the wall on the bal dring contact?

D) In contrast, what is the magnitude of the gravitational force of the Earth on the ball?

Answer:

a) [tex]V_{avg} = 20.5m/s[/tex]

b) 9.76 × 10⁻⁴s

c) 247.9 N

d) 5.8 N

Explanation:

Given  that;

Initial speed [tex](V_i)[/tex] = 0

Final speed [tex](V_f)[/tex] = 41 m/s

Distance (d) = 0.002

mass (m) = 0.059 kg

g = 9.8 m/s²

a)

The average speed of the ball can be calculated as;

[tex]V_{avg} = \frac{V_i+V_f}{2}[/tex]

[tex]V_{avg} = \frac{0+41}{2}[/tex]

[tex]V_{avg} = 20.5m/s[/tex]

b)

The time elapsed can be calculated by using the second equation of motion which is given as:

[tex]S=(\frac{V_i+V_f}{2})t[/tex]

If we make time (t) the subject of the formula; we have:

[tex](V_i+V_f)t=2S[/tex]

[tex]t= (\frac{2S}{V_I+V_f})[/tex]

[tex]=\frac{2(0.02)}{41+0}[/tex]

[tex]=\frac{0.04}{41}[/tex]

= 0.000976

=9.76 × 10⁻⁴s

c)

the magnitude of the average force (F) exerted by the wall on the bal dring contact can be determined using;

Force (F) = mass × acceleration

where acceleration [tex](a)= \frac{Vo}{t}[/tex]

[tex]\frac{41}{0.00976}[/tex]

acceleration (a) = 4200.82 m/s²

F = m × a

= 0.059 × 4200.82

= 247.85

≅ 247.9 N

d)

the magnitude of the gravitational force of the Earth on the ball

Force (F) = mass (m) × gravity (g)

= 0.059kg × 9.8 m/s²

= 5.782 N

≅ 5.8 N

The average speed of the tennis ball during contact with the wall is zero, and without the time of contact, we cannot determine the time elapsed or the average force exerted by the wall. However, the gravitational force on the ball is 0.5782 N.

The question relates to the change in momentum and the forces involved when a tennis ball bounces off a wall. Specifically, a tennis ball with a mass of 0.059 kg is hit at a speed of 41 m/s, bounces off a wall, and comes back at the same speed. To tackle the posed questions, it is essential to apply concepts from Newton's laws of motion and the conservation of momentum.

The average speed of the ball during contact is zero since the speed decreases uniformly from 41 m/s to zero.

Without the time of contact with the wall, this cannot be determined. Previous examples of collisions show time of contact can vary, so it must be provided to answer this part of the question.

To calculate the magnitude of the average force exerted by the wall on the ball, we would need the time of contact with the wall. Since it is not given, this cannot be calculated accurately.

The magnitude of the gravitational force of the Earth on the ball is calculated as the product of the mass of the ball and the acceleration due to gravity (9.8 m/s²), which is 0.059 kg * 9.8 m/s² = 0.5782 N.

Answer:

Option 4

Explanation:

A constellation can be defined as that region formed by the stars in such a way that the formation by the group of stars in that area appear to seem an imaginary pattern of some mythological creature, animal, god or some inanimate object formed apparently.

Thus in accordance with the above definition a constellation is a group of stars that forms some apparent pattern in the celestial sphere.