A small ball is tied to a string and set rotating with negligible friction in a vertical circle. If the ball moves over the top of the circle at its slowest possible speed (so that the tension in the string is negligible), what is the tension in the string at the bottom of the circle, assuming there is no additional energy added to the ball during rotation?


An explanation would be very much appreciated as there are a few things I am confused about

- why is tension negligible at the top? Isn't there still a tension force pulling inward? I thought there would be two forces acting on the ball at the top of the circle, Fg and [tex]F_T[/tex] ?
- is finding a numerical value for this answer even possible? we don't have the mass of the ball

The mass of a proton and neutron and the positive charge of the proton accounts for why the electrons are thousands of times smaller than the nucleus and negatively charged.

Electrons are one of the three fundamental particles that make up an atom.

Electrons are negatively-charged particles which are found in certain regions of space around the nucleus of an atom at a particular instant.

The nucleus is composed of protons and neutrons. The protons are positively-charged while the neutrons are neutral. Thu, the negative charge of the electron balances the positive charge of the nucleus.

The mass of a proton is about 1840 times heavier than the electron. Thus, the nucleus is many thousand times heavier than the electron.

In conclusion, the negative charge of the electron ensures an atom is neutral.

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The boom makes an angle of θ = 60.2° with the vertical wall and the tension in the horizontal rope is mathematically given as

[tex]T_1=730.85 \mathrm{~N}[/tex]

[tex]T_1'=\frac{1980.51 \mathrm{~N}}{}[/tex]

Generally, the equation for is  mathematically given as

1) Tension in vertical rope,

[tex]T_{1}=74.5 \times 9.81\\T_1=730.85 \mathrm{~N}[/tex]

2) Tension in horizontal rope,

[tex]\sum{Mg} =0\\Mg\frac{l}{2} \sin \theta+T_{1} \frac{l}{2} \sin \theta &=T_{2} l \cos \theta \\[/tex]

[tex]T_{2} &=\frac{M g(l / 2) \sin \theta+T_{1}(l / 2) \sin \theta}{l \cos \theta} \\\\&=\frac{M g \tan \theta}{2}+\frac{T_{1} \tan \theta}{2} \\\\T_{2} &=\frac{142 \times 9.81 \tan 61.8}{2}+\frac{730.85 \times \tan 61.8}{2} \\\\=& 1299+681.51[/tex]

[tex]T_1=\frac{1980.51 \mathrm{~N}}{}[/tex]

In conclusion, the tension in the horizontal rope is

[tex]T_1=\frac{1980.51 \mathrm{~N}}{}[/tex]

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Answer: 2.90mi/hr/s

Explanation:

Acceleration = Final Velocity - Initial over time

Acceleration = 27.8mi/hr over 9.58s.

Answer is 2.90mi/hr/s

Hope I Helped!

80000 Joule is the change in the internal energy of the gas.

ΔW = -pdV

ΔW = -pd (V₂ -V₁)

ΔW = - 1.65×10⁵ pa (0.320m³ - 0.110m³)

     = - 0.35×10⁵ pa.m³

     = - 35000 (N/m³)(m³)

     = -35000 Nm

ΔW = -35000 Joule

Therefore, work done by the system = -35000 Joule

ΔV = ΔQ + ΔW

Given:

ΔQ = 1.15×10⁵ Joule

ΔW = -35000 Joule

ΔU = 1.15×10⁵ Joule - 35000 Joule

      = 80000 Joule.

Therefore, the change in the internal energy of the gas= 80000 Joule.

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At the top of the circle, the net force on the ball is pointing downward, so that by Newton's second law

[tex]\sum F = -ma \implies F_{\rm tension} + F_{\rm weight} = \dfrac{mv^2}R[/tex]

where [tex]a=\frac{v^2}R[/tex] because the ball is undergoing circular motion with constant speed.

Plug in everything you know and solve for [tex]v[/tex].

[tex]4.0\,\mathrm N + (0.17\,\mathrm{kg}) g = \dfrac{(0.17\,\mathrm{kg})v^2}{0.62\,\rm m} \\\\ \implies v^2 = \dfrac{0.62\,\rm m}{0.17\,\rm kg} \left(4.0\,\mathrm N + (0.17\,\mathrm{kg}) g\right) \\\\ \implies v^2 \approx 21 \dfrac{\mathrm m^2}{\mathrm s^2} \implies \boxed{v \approx 4.5\dfrac{\rm m}{\rm s}}[/tex]

Plug this into the acceleration equation and solve for [tex]a[/tex].

[tex]a = \dfrac{21\frac{\mathrm m^2}{\mathrm s^2}}{0.62\,\rm m} \implies \boxed{a \approx 33\dfrac{\rm m}{\mathrm s^2}}[/tex]

Manufacturers of pails prefer a cone shape because it has a suitable base as well as more space for its contents.

The most common shape of pails is the shape of the frustum of a cone.

Pails are useful to contain liquids as well as some grainy solids like sand.

Because of their unique shapes, pails are able to rest on their bases and also has enough space to contain enough liquid as their top part spreads outwards.

In conclusion, the choice of shape of pails is to ensure they rest on the base and also have enough space for their contents.

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The velocity of sound in air is 358m/s

Given;

v= 2f(L2-L1)

= 2.2.56.(1- 0.3)

=358 m/s

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Answer:

The focal length is R/2 = 25 cm / 2 = 12.5 cm

A ray from the center of curvature is focused back on itself (R cm)

As the angle of the ray is changed to being parallel to the axis the ray from the mirror will be brought closer to the mirror      

f(parallel) < focus (back upon itself)

compare  angles of  incidence and reflection

The Lenz's law gives the direction of induced current. According to this law, the induced current opposes the cause that produces it.

Lenz's law states that: The current induced in a circuit due to a change in a magnetic field is directed to oppose the change in flux and to exert a mechanical force which opposes the motion.

According to the question,

If we keep the magnet stationary and moved the coil back and forth within the magnetic field, an electric current would be induced in the coil.

Then by either moving the wire or changing the magnetic field we can induce a voltage and current within the coil and this process is known as Electromagnetic Induction.

When the coil AB is approaching towards north pole of the magnet, the magnetic flux linking to the coil increases.

Now according to Lenz's law,

This magnetic field created will oppose its own or we can say opposes the decrease in flux through the coil and this is possible only if approaching coil side attains south polarity, as we know dissimilar poles attract each other.

Once we know the magnetic polarity of the coil side, we can easily determine the direction of the induced current by applying right hand rule. In this case, the current flows in the A to B direction.

The right-hand rule. If you point your pointer finger in the direction the positive charge is moving, and then your middle finger in the direction of the magnetic field, your thumb points in the direction of the magnetic force pushing on the moving charge.

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The frequency of sound at the given temperature is 200.58 Hz.

The frequency of sound at the given temperature is calculated as follows;

v = fλ

f = v/λ

where;

f = 343/1.71

f = 200.58 Hz

Thus, the frequency of sound at the given temperature is 200.58 Hz.

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Answer:

convection

Explanation:

Convection is a process by which heat is transferred by the movement of a heated fluid such as air or water.

The answer is Conduction: the process of heat is directly transmitted through a substance when there is a difference in temperature.

If resistor A, B and C are arranged in series, same current will flow in all the resistors and 2A will flow is resistor C.

This is the type of circuit arrangement in which the resistors are arranged in series order.

In this type of circuit arrangement, same current flows in every component of the circuit.

Thus, if resistor A, B and C are arranged in series, same current will flow in all the resistors and 2A will flow is resistor C.

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Based on the nature of friction:

Friction is the opposition to the relative motion of an object over another at their surfaces of contact.

The coefficient of friction is a ratio of the frictional force and the normal reaction.

The coefficient of friction of rough surfaces is greater than that of smooth surfaces.

In the given experiment:

In conclusion, the experiment demonstrates that the coefficient of friction  is a constant for given surfaces and does not depend on the mass of the object.

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Answer:

6600J

Explanation:

the formula for work is: W= F x d

F- force, d- distance

The direction of torque τ this method is mathematically given as

D=X  

Option A is correct.

Generally, the equation for torque is  mathematically given as

τ = r X F

Since F is the force exerted on the body at r, we need to know the direction of this torque with regard to the body's center of mass.

In conclusion, the direction of this method is

D=X   Option A.

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Answer:

electric motors is the answer

The approximate magnitude of the force between them is [tex]-4.032*10^-^6 N[/tex]

According to Coulomb, the electric force for charges at rest has the following properties:

Like charges repel each other; unlike charges attract.

Thus, two negative charges repel one another, while a positive charge attracts a negative charge.

The equation in Coulomb's law is :

[tex]F =\frac{{kq_1q_2}}{r^2}[/tex]

Where F is the force between charges, k is a constant, q₁ is the charge of the first particle, q₂ is the charge of the second particle and r is the distance between the two particle charges.

According to the question,

The given values are:-

q₁ =  +8.0 × 10⁻⁹

q₂ = –1.4 × 10⁻⁸

Substituting to the equation:

[tex]F =\frac{{kq_1q_2}}{r^2}[/tex]

=[tex]\frac{ { 9*10^{9} * 8* 10^{-9} *-1.4*10^{-8} }}{(5x10^-1)^2}[/tex]

= -4.032 x 10⁻⁶ N

Therefore,

-4.032 x 10⁻⁶ N is the approximate magnitude of the force between them.

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The component of the total velocity in the x - direction is 6.96 m/s.

The component of the total velocity in the y - direction is 2.95 m/s.

The component of the total velocity in the x - direction is calculated as follows;

v(x) = vtot cosθ

where;

v(x) = 7.56 x cos(23)

v(x) = 6.96 m/s

v(y) = vtot sinθ

v(y) = 7.56 x sin(23)

v(y) = 2.95 m/s

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According to Newton's second law

The force the escaping gas exerts of the rocket is 10.42 N.

The force the escaping gas exerts of the rocket is calculated as follows;

F = m(v - u)/t

where;

F = (0.25)(40 - 15)/0.6

F = 10.42 N

Thus, the force the escaping gas exerts of the rocket is 10.42 N.

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Answer:

0.18 N or 180 N

Explanation:

Mass,m = 150g

acceleration,a = 1.2m/s2

CHANGE FROM g TO kg

1kg =1000g

so 150g =150/1000 = 0.15kg

But Force, F = mass,m × acceleration,a

F=ma

F=0.15×1.2

F= 0.18 N

The tension in rope B is determined as 46.17 N.

Tension in rope A is the resultant tension of the rope B and C.

T(C) = T(B) = T

where;

T² + T² = 65.3²

2T² = 4,264.09

T² = 4,264.09/2

T² = 2,132.045

T = √2,132.045

T = 46.17 N

Thus, the tension in rope B is determined as 46.17 N.

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Compressibility of a substance is defined as the ratio of volumetric strain to the change in pressure. It is also equal to the reciprocal of the bulk modulus of the substance. It is denoted by K (kappa).

, for an isothermal process.

As we know that, work done for isothermal reversible expansion is given by-

Short-duration spacecraft typically have one backup system and carry their own supply of oxygen. A large portion of the required oxygen is produced on long-duration missions, such as the International Space Station (ISS), which has been in orbit since 1998. Different sources provide the oxygen utilized on the ISS. The water electrolyzer is the primary source of metabolic oxygen. As an alternative to the electrolyzer, oxygen candles (also known as SFOGs) can produce metabolic oxygen. Additionally, oxygen is carried up whenever a cargo ship docks and stored in two tanks on the ISS Airlock. The electrolyzer electrolyzes water to create oxygen by running an electric current through it. Since water is a poor electrical conductor by itself, a little quantity of common salt is dissolved in the water to improve its electrical conductivity. Water is split into hydrogen and oxygen throughout the process.

We must keep in mind that oxygen by itself cannot be inhaled; it must be combined in the proper ratio with nitrogen to make it breathable. Two tanks aboard the ISS are used to store nitrogen, and the cargo ships that travel by from time to time also transport nitrogen cylinders. Through the electrical grid of the station, the solar panels on the station supply the necessary electricity for the oxygen generators. The majority of the required water is transported to the station by cargo supply ships. Condensers, which draw water vapor even from the station's air, ensure that not a drop of water is wasted. Using the proper equipment, water is also recycled from the astronauts' urine.

Through a suitable vent, the hydrogen gas produced during the electrolysis process is released into space. Pressurized tanks at the airlock nodes at the space station are pumped with oxygen when the cargo vehicles arrive there. Pressurized tanks there are also pumped with nitrogen. It goes without saying that the station's atmospheric controls combine the gases in the right amounts for the atmosphere of Earth and then distribute the combination throughout the cabin. The production of oxygen in space is impossible.