A playground toy has four seats, each 6.4kg , attached to very light rods of length r= 1.5m , as seen from below in the figure.
If two children, with masses of 16kg and 23kg , sit in seats opposite one another, what is the moment of inertia about the rotation axis?

Answer:

a) 20.34 N

b)17.64 N

c)16.47 N

d)38.63m

Explanation:

a) F=m*a. Earth gravity is 9.8m/s2. If the elevator goes upwards, tension on the rope will be higher. To find the tension we need to all accelerates. Total accelerates effects the elevator is a=9.8+1.5=11.3 m/s2. Then;

[tex]F=1.8*11.3=20.34[/tex]

the tension is 20.34N

b) There is no accelerate in this situation therefore the tension is:

F=1.8*9.8=17.64 N

c) In this situation elevator goes down. We need to subtract gravity from elevator acceleration. a=9.8-0.65=9.15m/s2

F=1.8*9.15=16.47 N

d) Total distance is:

[tex]x=0.5*a*t^2+v*t+v*t-0.5*a*t^2\\=0.5*1.5*2.2^2+9*(1.5*2.2)+2*(1.5*2.2)-0.5*0.65*2^2\\=38.63 m[/tex]

Answer:

The answer to your question is 4.82 x 10²⁷ atoms of Hydrogen

Explanation:

Data

final mass = 8.0 kg

mass of hydrogen = 1.0 u

number of hydrogens = ?

Process

1.- Use proportions to solve this problem

                  1 u -------------------------  1.66 x 10⁻²⁷ kg

                 x u -------------------------  8 kg

                 x = (8 x 1) / 1.66 x 10⁻²⁷

                 x = 8 / 1.66 x 10⁻²⁷

                x = 4.82 x 10 ²⁷ u or 4.82 x 10²⁷ atoms of Hydrogen

Answer:

A small force over a long time period.                                        

Explanation:

The second law of motion gives the relationship between the external force and the change in momentum of the object. The rate of change of linear momentum is equal to the external force applied. It is given by :

[tex]F=\dfrac{\Delta p}{\Delta t}[/tex]

[tex]\Delta p=F\times \Delta t[/tex]

It is clear that for the smallest change in momentum, a small force should be applied for a long period of time. Hence, the correct option is (c) "a small force over a long time period".

Answer:

D. a small force over a short time period

C is incorrect.

To solve the problem, we use the kinematic equation for distance considering the initial velocity, acceleration due to gravity, and the distance from the top of the cliff to 6m above the ground. The equation gives two possible times: one when the rock is on the way up, and one when it's on the way down.

In this physics question, we are dealing with kinematic equations which describe the motion of the rock. The equation we will use for this question is d = vit + 0.5gt^2, where 'd' represents total distance, 'vi' is initial velocity, 'g' is acceleration due to gravity and 't' is time.

Here, d = 43m - 6m = 37m (distance from the top of the cliff to 6m above the ground), vi = 26m/s (initial velocity of the rock when thrown upwards), and g = 9.8m/s^2 (acceleration due to gravity, but since the rock is thrown downwards, we take it as positive).

Now plug these values into the equation, you have two possible times- one for the rock on its way up and one for on its way down.

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Answer:

Four central postulates that emerges from Charles Darwin and Russel Wallace are detailed below. As there is no option provided in the question hence any option beyond the meaning of these four points will not be from these four postulates.

Explanation:

The four postulates were:  

1st:

The number of individuals produced in a generation of a specie is more than that of the ones who survive. Some of them cannot withstand the environmental conditions and die.

2nd:

Observable characteristics of an individual can vary and this variation is inherited by parental cells/genes.

3rd:

The individuals who have characteristics which are suitable to the environment exists and survives while other ones do not bear the environment and die soon.

4th:

Reproductive isolation is the evolutionary mechanism which prevents members of different species from producing offspring but whenever this occurs, most of the times, new specie is formed. The survival of this new specie again depends upon suitability of its characteristics with environment.

Answer:

-M6

-G2

-A5

-O9

Explanation:

Answer:

A. Weight

Explanation:

Mass And Weight

Mass is a fundamental property of objects and is defined as a measure of the amount of matter in the object. The symbol for mass is m and its SI unit is the kilogram (kg). At normal speeds, i.e. much smaller than the speed of light, the mass is considered as a constant property.

The weight W is defined as the force of gravity on the object, that is, the gravitational attraction between the object and the Earth. Its SI unit is the Newton (Nw or N).

Answer:

Southwest

Explanation:

when the car is moving around a circular track at constant speed, velocity changes due to change in the direction. The direction at any instant is given by tangent drawn at the point on the circular path.

At instant 1: direction is northwards

At instant 2: direction is westwards

Let the constant speed be v. Then, at instant 1, the velocity would be:

[tex]v_1=v \hat j[/tex]

At instant 2, the velocity would be:

[tex]v_2 = v (-\hat i)[/tex]

Change in velocity = [tex]v_2-v_1 = v(-\hat i - \hat j)[/tex]

The direction of car's average change would be southwest.

The car's average change in velocity has a northwest direction.

The direction of the car's average change in velocity is determined by the direction of the velocity vectors at the two instances. In this case, when the car is driving northward, its velocity vector points towards the north. Later, when the car is driving westward, its velocity vector points towards the west. Therefore, the car's average change in velocity will have a direction that is a combination of north and west, which is the northwest direction.

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Answer:

217.611 N

331.407 N

Explanation:

m = Mass of monkey = 11.6 kg

v = Velocity of the monkey = 3.5 m/s

r = Radius = 65.3 cm

g = Acceleration due to gravity = 9.81 m/s²

Centripetal force is given by

[tex]F_c=\dfrac{mv^2}{r}\\\Rightarrow F_c=\dfrac{11.6\times 3.5^2}{0.653}\\\Rightarrow F_c=217.611\ N[/tex]

The magnitude of the centripetal force is 217.611 N

Balancing the forces we get

[tex]F_c=T-mg\\\Rightarrow T=F_c+mg\\\Rightarrow T=217.611+11.6\times 9.81\\\Rightarrow T=331.407\ N[/tex]

The tension in the monkey's arm is 331.407 N

There is no horizontal force

Explanation:

When you jump across the stream, your motion is the same of the motion of a projectile, which consists of two independent motions:

We notice that as you are in the air, there is only one force acting on your body: the force of gravity, whose direction is downward, and causes your body to accelerate downward with an acceleration equal to

[tex]g=9.8 m/s^2[/tex]

However, there is no force acting on you in the horizontal direction: therefore, your acceleration in this direction is zero, and so your horizontal velocity is constant (that's why you keep moving forward).

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Answer:

3.56×10²⁶ Kg.

Explanation:

Note: The gravitational force is acting as the centripetal force.

Fg = Fc........................... Equation 1

Where Fg = gravitational Force, Fc = centripetal force.

Recall,

Fg = GMm/r²......................... Equation 2

Fc = mv²/r............................. Equation 3

Where M = mass of the planet, m = mass of the moon, r = radius of the orbit and G = Universal gravitational constant.

Substituting equation 2 and 3 into equation 1

GMm/r² = mv²/r

Simplifying the equation above,

M = v²r/G .............................. Equation 4.

The period of the moon in the orbit

T = 2πr/v

Making v the subject of the equation,

v = 2πr/T............................. Equation 5

where r = 7.0×10⁷ m, T = 6 h 38 min = (6×3600 + 38×60) s = (21600+2280) s

T = 23880 s, π = 3.14

v = (2×3.14×7.0×10⁷ )/23880

v = 18409 m/s

Also Given: G = 6.67×10⁻¹¹ Nm²/kg²

Also substituting into equation 4

M = 18409²×7.0×10⁷ /(6.67×10⁻¹¹)

M = 3.56×10²⁶ Kg.

Thus the mass of the planet =  3.56×10²⁶ Kg.

The mass of the planet is required.

The mass of the planet is [tex]3.56\times 10^{26}\ \text{kg}[/tex]

M = Mass of planet

r = Radius of orbit = [tex]7\times 10^7\ \text{m}[/tex]

t = Time period = [tex]6\times 60\times 60+38\times 60=23880\ \text{s}[/tex]

G = Gravitational constant = [tex]6.674\times 10^{-11}\ \text{Nm}^2/\text{kg}^2[/tex]

Mass is given by

[tex]M=\dfrac{4\pi^2r^3}{t^2G}\\\Rightarrow M=\dfrac{4\pi^2\times (7\times 10^7)^3}{23880^2\times 6.674\times 10^{-11}}\\\Rightarrow M=3.56\times 10^{26}\ \text{kg}[/tex]

The mass of the planet is [tex]3.56\times 10^{26}\ \text{kg}[/tex]

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"Anti-Lock" brake systems release the brakes momentarily when wheel speed sensors indicate a locked wheel during braking and traction.

Explanation:

The safety anti-skid braking system is known as "anti-lock braking system" having huge application on land vehicles like one, two and multiple wheeler vehicles and aircraft. During braking, it avoids wheels to get locked by building tractive contacts to the road's surface.

This seems to be an automated system work on the principles of techniques - threshold and cadence braking. The wheel velocity sensors are utilized by ABS to find whether one or more than one wheels chose to get lock while braking.

Answer:

Anti- Lock

Explanation:

Anti- lock brake systems(ABS) is a safety system used in hindering the wheels from locking up when the brake is applied.

Braking release the brakes momentarily when wheel speed sensors indicate a locked wheel during braking and traction.

Control systems apply the brakes momentarily to one of the drive wheels whenever the wheel speed sensors indicate a wheel is going faster than the others during acceleration.

Answer:

[tex]1.18454\times 10^{-19}\ Pa[/tex]

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

m = Mass of bullet = [tex]2.6\times 10^{23}\ kg[/tex]

r = Radius of barrel = [tex]2.8\times 10^{23}\ m[/tex]

[tex]v^2-u^2=2as\\\Rightarrow a=\dfrac{v^2-u^2}{2s}\\\Rightarrow a=\dfrac{370^2-0^2}{2\times 0.61}\\\Rightarrow a=112213.11475\ m/s^2[/tex]

Pressure is given by

[tex]P=\dfrac{F}{A}\\\Rightarrow P=\dfrac{ma}{\pi r^2}\\\Rightarrow P=\dfrac{2.6\times 10^{23}\times 112213.11475}{\pi (2.8\times 10^{23})^2}\\\Rightarrow P=1.18454\times 10^{-19}\ Pa[/tex]

The pressure of the expanding gas is [tex]1.18454\times 10^{-19}\ Pa[/tex]

Answer:

the distance between the​ lawyer's home and her office is 124 miles

Explanation:

given information:

first lets assume that

x-axis (west = positive, east = negative)

y-axis (north = positive, south = negative)

thus,

distance of the house = (-88,18)

distance of the office = (13, -54)

thus, the distance between the​ lawyer's home and her office

R = √(x₂ - x₁)² + (y₂ - y₁)²

   = √(13 - (-88))² + (-54 -18)²

   = 124 miles

Answer:

c. The astronaut does not need to worry: the charge will remain on the outside surface.

Explanation:

The all-metal chamber (conductor) receives an external electromagnetic field, so it is positively charged in the direction the electromagnetic field is going, and negatively charged in the opposite direction. Since the chamber is polarized, it generates an electric field equal in magnitude, but opposite the external electromagnetic field, then the net electric field inside the conductor is 0.

When all boxes (conductors) receive environmental electromagnetic frequencies, they become electrostatically attracted inside the plane of the magnetic wave and charged negatively in a reverse way.

Therefore, the answer is " Option c".

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Answer:

Following are the correct options.

1. In a uniform electric field, the field lines are straight, parallel and uniformly spaced. ( As the field strength does not change in the uniform electric field that is why the field lines are parallel, equally spaced etc).

2. Electric field lines near positive point charges radiate outward. (Due to repulsive forces field lines radiate in outward direction)

3.The electric force acting on a point charge is proportional to the magnitude of the point charge. ( As columb law states that the electrostatic forces between the point charges is proportional to the product of their magnitude and inversely proportional to square of distance between them).

Explanation:

In a uniform electric field, electric field lines are straight, parallel, and uniformly spaced while near positive point charge it emits outwards. Also, the electric force on a point charge is proportional to its magnitude. But, lines near negative point charges radiate inward, not circle clockwise. The electric field created by a point charge isn't constant across space, but diminishes with distance.

Of the five statements you provided:

Therefore, statements 1, 2 and 3 are true, while 4 and 5 are false.

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Answer

given,

mass of steel ball, M = 4.3 kg

length of the chord, L = 6.5 m

mass of the block, m = 4.3 Kg

coefficient of friction, μ = 0.9

acceleration due to gravity, g = 9.81 m/s²

here the potential energy of the bob is converted into kinetic energy

[tex]m g L = \dfrac{1}{2} mv^2[/tex]

[tex]v= \sqrt{2gL}[/tex]

[tex]v= \sqrt{2\times 9.8\times 6.5}[/tex]

      v = 11.29 m/s

As the collision is elastic the velocity of the block is same as that of bob.

now,

work done by the friction force = kinetic energy of the block

[tex]f . d = \dfrac{1}{2} mv^2[/tex]

[tex]\mu m g. d = \dfrac{1}{2} mv^2[/tex]

[tex]d=\dfrac{v^2}{2\mu g}[/tex]

[tex]d=\dfrac{11.29^2}{2\times 0.9 \times 9.8}[/tex]

    d = 7.23 m

the distance traveled by the block will be equal to 7.23 m.

Final answer:

The collision between the steel ball and the block is perfectly elastic. By using the equation µN = ff, we can calculate the frictional force and the acceleration of the block.

Explanation:

The collision between the steel ball and the block is a perfectly elastic collision, meaning that both momentum and kinetic energy are conserved.

When the ball strikes the block, it transfers its momentum to the block, causing the block to move with the same velocity as the ball had before the collision.

Because the coefficient of friction between the block and the shelf is given as 0.9, we can use the equation µN = ff to find the frictional force and calculate the acceleration of the block.

Answer:

Being an elastic object, rubber ball will be an ideal choice as it will bounce off the bowling pit and will experience a large change in momentum in comparison with the beanbag which will either slow down or come to a halt upon hitting a bowling pit. That is why rubber ball will experience a greater impulse and the bowling pin will experience the negative impulse of the rubber ball.

For Rubber Ball

Upon elastic collision it will reverses the direction and move with velocity equal or less then original

change in momentum = P

[tex]P = m(v_{f} -v_{i})\\v_{f}=-v_{i} \\ P = -2mv_{i}[/tex]

For Beanbag

value of impulse will large if velocity is zero.

[tex]v_{f}=0\\ P = -mv_{i}[/tex]

Explanation:

The rubber ball will impact a greater force on the heavy bowling pin because its kinetic energy will be conserved while the beanbag will impact lesser force due to loss of kinetic energy.

A collision between two objects can be elastic or inelastic.

The impulse experienced by each throwing object is equal to change in the momentum of the object.

[tex]J = \Delta P[/tex]

The rubber ball will impact a greater force on the heavy bowling pin because its kinetic energy will be conserved while the beanbag will impact lesser force due to loss of kinetic energy.

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Explanation:

The Natural Greenhouse Effect However, the amount that directly escapes to space is only about 12 percent of incoming solar energy. The remaining fraction—a net 5-6 percent of incoming solar energy—is transferred to the atmosphere when greenhouse gas molecules absorb thermal infrared energy radiated by the surface.

Answer:

b. Medicine balls

Explanation:

A medicine ball (also called an exercise ball, or a health ball) is a weighted ball about the shoulder diameter (approx. 13.7 inches), often used for recovery and strength training.... In 1705 similar large balls had been used in Persia.So you can use your medicine ball as a projectile to boost the strength of your throws.

Explanation:

First let us find the initial velocity,

We have after 8 seconds the displacement is zero,

We have equation of motion s = ut + 0.5 at²

        Initial velocity, u = ?

        Acceleration, a = -9.81 m/s²

        Time, t = 8 s      

        Displacement,s = 0 m

     Substituting

                      s = ut + 0.5 at²

                      0 = u x 8 + 0.5 x -9.81 x 8²

                      u = 39.24 m/s

Initial velocity is 39.24 m/s.

Now this case is similar to case where a rock is thrown at 39.24 m/s downward.

We have equation of motion v² = u² + 2as

      Initial velocity, u = 39.24 m/s  

      Acceleration, a = 9.81 m/s²  

      Final velocity, v = ?

      Displacement, s = 25 m  

     Substituting  

        v² = u² + 2as

        v² = 39.24² + 2 x 9.81 x 25

        v = 45.06 m/s

The speed of the rock just before it reaches the water 25.0 m below the point where the rock left your hand  is 45.06 m/s

Answer:

The answer to your question is angle = 18.46°

Explanation:

Data

d = 75 m

v₀ = 35 m/s

α = ?

Formula

                     [tex]d = \frac{vo^{2}sin2\alpha}{g}[/tex]

solve for sin2α

                  sin 2α = [tex]\frac{dg}{vo^{2}}[/tex]

Substitution

                 sin 2α = [tex]\frac{75(9.81)}{35^{2}}[/tex]

Simplify

                sin 2α = [tex]\frac{735.75}{1225}[/tex]

Divide

                sin 2α = 0.600

Get sin⁻¹

                      2α = 36.9°

Divide by 2

                        α = 18.5°                

Answer: y = 40 + 21t

Explanation:

Apply the equation of distance covered.

d = vt + C

Where d is the distance covered

v = velocity , t = time

C = constant = initial distance covered

For the case above....

d = y

y(t) = vt + C

But y(0) =40 = C

C = 40ft

velocity v = 21 ft/s

Therefore, the equation of the altitude is given by;

y(t) = 21t +40

y = 40 + 21t

The function representing the helicopter's altitude as it gains height is y = 21t + 40. The helicopter gains altitude at a rate of 21 feet per second and it starts at 40 feet above the ground.

The function that represents this situation is a linear function because the change in the helicopter's altitude is constant over time.

The formula for a linear function is y = mx + b, where m is the slope (rate of change), b is the y-intercept (initial value), y is the dependent variable (altitude in this case), and x is the independent variable (time in this case).

In this scenario, we're given that the helicopter starts 40 feet above the ground (our y-intercept, b) and it's gaining altitude at 21 feet per second (our slope, m).

Therefore, the function to represent the helicopter’s altitude, y, after t seconds can be written as y = 21t + 40.

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Answer:

To calculate the period of satellite orbiting around a planet, we use Kepler's third law;

Square of T = [(4π)/(G*m)] * R^3.

Therefore,

T = sqrt{[(4π)/(G*m)]*R^3}.

T is the period, m is mass orbiting satellite, G is gravitational constant, R is the radius of of the planet, r is the radius of the orbiting satellite.

For Satellite 1, r is one-half of the planet, that is r = (3/2) * R

For satellite 2, r = R

Explanation:

Answer:

Beta radiation

Explanation:

Beta radiation is a radioactive phenomenon of nuclear decay in which an unstable atom or isotop, by transforming a neutron into a proton, or by transforming a proton into a neutron, becomes stable. For example, the decay of carbon 14 produces beta radiation.

Answer:

[tex]d=490\ m[/tex] is his final displacement from the point A after 60 seconds.

Explanation:

Given:

Cyclist is moving away from A.

Now as the cyclist is moving away from point A his change in displacement after the mentioned time:

[tex]\Delta d=v.t[/tex]

[tex]\Delta d = 4.1 \times 60[/tex]

[tex]\Delta d=246\ m[/tex]

Now the the final displacement from point A after the mentioned time:

[tex]d=d_i+\Delta d[/tex]

[tex]d=244+246[/tex]

[tex]d=490\ m[/tex]

Answer:

b) M=20g

Explanation:

For this exercise we must use the Archimedes principle that states that the thrust that a body receives is equal to the weight of the dislodged liquid.

         B = ρ g V

Let's use balance healing for this case

Initial.

          B - W = 0

The weight of the body can be related to its density

          W = ρ V_body g

         ρ_liq g (½ V_body) = m g

Final

   Some masses were added

          M = 20 g = 0.020 kg

        B - W - W₂ = 0

        ρ_liq  g  V_Body = m g + M g

Let's replace and write the system of equations

     ½ ρ_liq  V_body = m

         ρ  V_body = m + M

We solve the equations

        2 m = m + M

        m = M

         m = 20 g

The answer is b

They travel at a speed of 0.68 m/s south ([tex]90^{\circ}[/tex] south of west)

Explanation:

We can solve this problem by using the law of conservation of momentum: in fact, in absence of external forces, the total momentum of the two players must be conserved before and after they collide.

Mathematically:

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

where, taking north as positive direction:

[tex]m_1 = 92 kg[/tex] is the mass of the first player

[tex]u_1 = -5.8 m/s[/tex] is the initial velocity of the first player (south, so negative)

[tex]m_2 = 110 kg[/tex] is the mass of the second player

[tex]u_2 = 3.6 m/s[/tex] is the initial velocity of the second player (north, so positive)

[tex]v[/tex] is the final combined velocity of the two players

Solving for v, we find the final velocity of the two players combined:

[tex]v=\frac{m_1 u_1 + m_2 u_2}{m_1+m_2}=\frac{(92)(-5.8)+(110)(3.6)}{92+110}=-0.68 m/s[/tex]

where the negative sign indicates their final direction is south.

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To find the final speed and direction after the tackle, we use the conservation of momentum. The fullback and lineman's initial momenta are calculated and combined to find the total initial momentum, which equals the final momentum because momentum is conserved. The direction is either south (90 degrees) or north (270 degrees) depending upon the sign of the final velocity.

To solve this physics problem, we will use the principle of conservation of momentum, which states that in the absence of external forces, the total momentum of a system remains constant. The formula for momentum (p) is the product of mass (m) and velocity (v), or p = mv.

Before the tackle, the fullback's momentum is southward and the lineman's is northward. We treat south as the positive direction. Thus, the initial momentums of the fullback and lineman are:

The total initial momentum (pinitial) is the sum of these:

pinitial = pFB + pL

After the tackle, the players stick together and move as one mass (M = 92 kg + 110 kg), with a final velocity (V), so:

pfinal = MV

Since momentum is conserved, pinitial = pfinal, and we can solve for V:

V = pinitial / M

Once we calculate the final velocity, the direction is south if V > 0, north if V < 0. To convert the direction into an angle south of west, note that if they move southward, the angle is simply 90 degrees (directly south), while any northward movement would result in a 270-degree angle.

Answer:

Sublimation

Explanation:

Example: Dry ice, camphor

Answer / Explanation:

For proper clarity, let us recall Coulomb's Law,

Where, m = mass of an electron = 9.1 x 10⁻³¹

    q = The electric charge of the electron = 1.6 x 10 ⁻¹⁹

    r = The distance between the two electrons

    G = Universal gravitational constant = 6.67 x 10⁻¹¹Nm²/Kg²

     K = 8.9 x 10 ⁹ Nm²/C²

Now, considering the fact that the number of electron removed from the spheres was not given,

We assume this to be = "n"

Where the electric charge of the electron = 1.6 x 10 ⁻¹⁹ . n (where n = number of electron removed from each sphere)

Since we were not given the mass of the sphere, we try to calculate it from the volume using the formula:

V = 4/3πr³,

However, from coulombs law, mass of the electron =  9.1 x 10⁻³¹

Consequentially, where electrostatic repulsion = gravitational attraction

Therefore, recalling the formula,

Kq₁ q₂ / R² = Gмm / R²

Now inserting the value from the constant stated initially,

we have,

  (8.9 x 10 ⁹)(1.6 x 10 ⁻¹⁹n)(1.6 x 10 ⁻¹⁹n)/R² =  (6.67 x 10⁻¹¹)(9.1 x 10⁻³¹)/R₂

Doing a proper calculation of the above,

we should get n =  6.805838 × 10⁶

The answer is 6.805838 × 10⁶