Angela has a bucket of mass 2 kg tied to a string. She places a drinking glass of mass 0.5 kg in the bucket. She spins the bucket in a vertical circle of radius 1.5 m. You want to find out how fast she must swing the bucket to keep the glass from falling out.

a. Draw the free-body diagram for the glass when it is at the top of the circle.
b. What is the equation for the net force on the glass at the top of the circle in terms of w, FN, m, v, and r?
c. The glass will fall out of the bucket if the normal force between the glass and bucket equals zero. How fast must she spin the bucket to prevent this from happening?
d. The string will break if the tension on it is more than 100 N. Over what range of speeds can she keep the glass in the bucket and prevent the string from breaking?

Answer:

The food supply chain comprises all the stages that food products go through, from production to consumption

Explanation:

Any temperature, as long as gravity is strong enough, may cause hydrogen fusion in the Sun, which requires a temperature of millions of degrees. Option A is correct.

When the temperature in the core hits around 100 million degrees, the helium will begin to fuse into carbon in a mechanism known as the triple-alpha process

Any temperature may result in hydrogen fusion in the Sun, which needs a temperature of millions of degrees, as long as gravity is strong enough.

Hence option A is correct.

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if a volume of air is warmed it expands due to increased translational kinetic energy as it expands it will start to cool.

We can then conclude that at constant pressure, temperature and volume are directly proportional: temperature increases, volume increases; decrease temperature, decrease volume.

In this case, the higher the temperature, the greater the kinetic energy that acts on the molecules of this gas, so when the gas expands, these molecules find more space and collide less, which will cause the gas to cool.

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Modern observations have shown that the geometry of the universe is flat and the universe mist be infinite.

Geometry refer to a branch of mathematics that encapsulates measurements of lines, shapes, dimensions, points and shapes.

Therefore, Modern observations have shown that the geometry of the universe is flat and the universe mist be infinite.

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pluto is best decribed as smallest planet

From the calculation, the value of the acceleration is 5.8 m/s^2.

The term uniform acceleration refers to a situation in which the velocity increases by equal amounts in equal time intervals.

Given the fact that the car started from rest and reached a velocity of  780.34 mph or 348.84 m/s in 1 minute of 60 seconds;

v = u + at

a = v/t

a = 348.84 m/s/ 60 seconds

a = 5.8 m/s^2

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The resistance of the unknown resistor is determined as 0.39 ohms.

The total resistance of the circuit is calculated as follows;

V = IR

R = V/I

R = (3.5)/10

R = 0.35 ohms

The resistors are in parallel arrangement

1/R = 1/R₁ + 1/R₂ + 1/R₃

1/0.35 = 1/5 + 1/10 + 1/R₃

100/35 = 3/10 +  1/R₃

20/7 = 3/10 +  1/R₃

1/R₃ = 20/7 - 3/10

1/R₃ = (200 - 21)/70

1/R₃ = 179/70

R₃ = 70/179

R₃ = 0.39 ohms

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The increase in potential energy of his mother if her mass is 56.0 kg will be 6031.97 J.

The energy that an item has due to its location in a gravitational field is known as gravitational potential energy.

The potential energy increases by 3773 J

PE₂-PE₁=mg(h₂-h₁)

3773 J = 35.0 × 9.81 × (h₂-h₁)

(h₂-h₁) = 10.98

Case 2 ;

ΔPE =?

ΔPE=mg(h₂-h₁)

ΔPE=56.0 × 9.81 ×10.98

ΔPE=6031.97 J.

Hence, the increase in potential energy of his mother if her mass is 56.0 kg will be 6031.97 J.

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Answer:

1.708 g/cm^3

Explanation:

Density = mass/volume

           =  84.7 g / 49.6 cm^3 = 1.708  g/cm^3

Stars with fairly circular orbits about the galactic center is found in the disk

Stars are one of the astronomical object that is usually very bright.

A circular orbit star is a star that moves in circular direction and not elliptical orbit which is most common to starts.

Therefore, Stars with fairly circular orbits about the galactic center is found in the disk

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The blu-ray standard that defines rewritable disks is BD-RE which stands for Blu-ray Disc Recordable.

BD-RE stands for Blu-ray Disc Recordable and it refers to two direct to disc optical disc recording technologies that can be recorded on to a Blu-ray-based optical disc with an optical disc recorder.

Thus, the blu-ray standard that defines rewritable disks is BD-RE which stands for Blu-ray Disc Recordable.

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The range of diameters and luminosities displayed by elliptical galaxies is 3000 to 700,000 light years and Mv-23 down to Mv- -16 mag respectively

Elliptical galaxies are type of galaxies with a smooth ellipsoidal shape.

They are the most abundant galaxies in the universe.

Their diameter ranges from 3, 000 to 700, 000 light years.

Their luminosity ranges from Mv-23 down to Mv- -16 mag

Therefore, the range of diameters and luminosities displayed by elliptical galaxies is 3000 to 700,000 light years and Mv-23 down to Mv- -16 mag respectively.

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Answer:

b

Explanation:

An insulator does not transfer thermal or electrical energy but a conductor does

The power exerted by the cyclist is determined as 50 W.

The power exerted by the cyclist is calculated as follows;

P = FV

where;

P = 20 x 2.5

P = 50 W

Thus, the power exerted by the cyclist is determined as 50 W.

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The statements that describe a benefit of the scientific method are as follows:

Thus, the correct options are B, C, and D.

The scientific method may be defined as a strategy of research in which a problem is recognized, relevant data is collected, a conjecture is composed of this data, and the assumption is empirically tested to determine the outcome of particular research.

The scientific method never explains or provides an answer to any question immediately because it consists of a scripted format with certain parameters.

The scientific method uses the identical vocabulary for sharing information with one another in particular terminology.

Therefore, it is well described above.

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All move at the same speed.

Explanation:

Electronic magnetic spectrum includes radio waves, micro waves, infra red, visible light, ultra violet, x-rays, gamma rays. These all electromagnetic waves travel at the same speed of light of about 300,000,000 m/s through vacuum. Though they have different wavelength, their speed is same.

Both the butterfly and the large car will have equal forces but in opposite direction.

Newton's third law of motion states that action and reaction are equal and opposite. That is, the force exerted on an object is equal to the reaction experienced by the object.

Fa = - Fb

where;

Thus, both the butterfly and the large car will have equal forces but in opposite direction.

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Answer:

[tex]\huge\boxed{50g}[/tex]

Definition:

Half-life- The time taken for half of the radioactive isotopes to decay.

Explanation:

How does radioactive decay work? Radioactive decay is a process by which unstable nuclei become more stable through the emission of alpha or beta particles or gamma rays.

Since a half-life is the time taken for half of the isotopes to decay, we can simply divide the initial mass of 100 grams by 2; this gives us 50 grams.

1) Divide 100g by 2.

[tex]\frac{100g}{2}=50g[/tex]

Answer:

HERTZ=HZ

Explanation:

The friend who has the greater displacement is the one who takes the longest path.

The displacement is the shortest distance travelled by the particle. It is the vector quantity which re[presents both the magnitude and direction.

Given, two friends leave a movie theater and take different buses to the same ice cream shop. One bus takes a longer route driving on a high-speed highway, while the other takes a shorter route on lower-speed local roads.

According to the definition. the displacement is neither larger not shorter but it is the shortest distance traveled by the person or particle.

Thus, friend who has longer path has larger displacement.

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If [tex]\vec A[/tex] and [tex]\vec B[/tex] are perpendicular, then their dot product is zero. This means

[tex]\vec A \cdot \vec B = (\vec\imath + 5\,\vec\jmath + n\,\vec k) \cdot (2\,\vec\imath - \vec\jmath + \vec k) = 2 - 5 + n = 0[/tex]

Solving for n is trivial; it follows that n = 3.

Explanation:

you should first find the proportionality constant or the spring constant(as we see it as a spring).the find the value of x so that the force is 3N

Answer:

The car will stop after 4 seconds after moving the distance of 0.08km.

Explanation:

The reading above it clearly states that a car is moving at a speed of 72Km/hr. And it asking for the distance the car move when it stops after 4 seconds.

Looking at speed formula , speed=distance÷time.

But in this problem we I finding distance, so in speed formula make distance the subject.

Before going ahead you should have this in mind the unit for distance is Km and m . Our speed is in Km/hr but our time is in second. In this case change 4 seconds to hour which is 0.00111 hr .you change second to hour because hr will cancel hr when solving for distance giving distance unit Km

Distance = speed × time

Distance= 72km/hr × 0.00111 hr

hour cancel hour

Distance= 72km × 0.00111

Distance = 0.08km

Therefore the car will stop after 4 seconds after moving the distance of 0.08km.

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conversion :

72 km/h = 72 × (1000/3600) = 20 m/s

so, in 4 seconds it travel

The total amount of charge and energy will be 1.20 C and 7.20 J respectively

A capacitor is a device that can store electrical energy. It is a two-conductor configuration separated by an insulating medium that carries charges of equal size and opposite sign.

An electric insulator or vacuum, such as glass, paper, air, or a semiconductor termed a dielectric, can be used as the non-conductive zone.

Given data;

Voltage,V= 12V

Capicitance,C=100mF = 100 × 10⁻³ F

The total amount of charge is;

Q=CV

Q=100 × 10⁻³ ×  12 V

Q=1.20 C

The energy stored by the capacitor;

[tex]\rm U = \frac{1}{2}CV^2 \\\\ \rm U = \frac{1}{2}\times 100 \times 10^{-3} \times (12 \ V)^2 \\\\ U= 7.20 \ J[/tex]

The energy stored by a capacitor will be 7.20 J.

Hence, the total amount of charge and energy will be 1.20 C and 7.20 J respectively

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Answer:

32400 J

Explanation:

K.E.=(1/2)(200)(18^2)

The speed the golf must have initially to reach the hole is 31.32`1 m/s.

When an object is thrown at an angle from the horizontal direction, the object is said to be in projectile motion. The object which follows the projectile motion.

A golfer wishes to chip a shot into the hole 50m away on flat level ground. if the ball flies to a maximum height of 25m.

The angle with which the ball flies,

tan θ = 25 m/ (50m/2)

tan θ =1

θ  =45°

If u is the initial speed, the maximum height of the ball is

H = u² sin²θ / 2g

Put the values, we get

25 =  u² sin²45 / (2x9.81)

u = 31.321 m/s

Thus, the initial speed is 31.321 m/s

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Answer:

look below! :)

Explanation:

Radiation transfers heat through electromagnetic waves

conduction transfers heat through direct contact of things

convection transfers heat through movement of air or water

Answer:

20.37m/s

Explanation:

For this problem, we'll need a basic kinematic equation for both directions

Vertical direction:

[tex]y(t)=\frac{1}{2}a_{y}t^{2}+v_{o_y}t+y_{o}[/tex]

Knowing that the acceleration in the y-direction is due to gravity, and is constant near the surface of the Earth, where the rock is being thrown, we get [tex]a_{y}=g=-10m/s^{2}[/tex].  We're also given that the initial vertical height is 83m, so [tex]y_o=83m[/tex].  Additionally, we're given that the stone is thrown horizontally, and thus initially, it has no vertical velocity.  Only velocity in the x-direction.  Thus, [tex]v_{o_y}=0m/s[/tex].  Substituting known values into our equation:

[tex]y(t)=\frac{1}{2}(-10)t^{2}+(0)t+(83)[/tex]

[tex]y(t)=-5t^{2}+83[/tex]

This equation is true for all times until the acceleration changes (isn't constant... i.e. when it hits the ground).

What now?

We want to find the specific time when it does hit the ground.  Why?  Because this is the point in time where we know some extra information about what is happening in the x direction, and that will help us deal with the x-direction equation.  

When the stone does hit the ground, the output of this function (measuring the height of the stone) is zero, which leaves only one unknown value, t... the time associated with that y:  the time that it takes to hit the ground:

[tex]0=-5(t_{ground})^{2}+83\\-83=-5(t_{ground})^{2}\\\frac{-83}{-5}=(t_{ground})^{2}\\16.6=(t_{ground})^{2}\\\sqrt{16.6}=\sqrt{(t_{ground})^2}\\4.074309757seconds=t_{ground}[/tex]

Again, this is the time that the stone hits the ground.  Knowing how special this time is, one might give it a special subscript to keep track of it.  

[tex]t_{ground}=4.074309757seconds[/tex]

Horizontal direction

Reusing the basic kinematic equation for the horizontal direction:

[tex]x(t)=\frac{1}{2}a_{x}t^{2}+v_{o_x}t+x_{o}[/tex]

Note that in the horizontal direction, there is no acceleration (after the rock is released), so [tex]a_{x}=0[/tex].  Also, if we define the base of the cliff as our origin, then at the top of the cliff where the rock is released, the initial x-position is still zero, aka, [tex]x_{o}=0[/tex]

[tex]x(t)=\frac{1}{2}(0)t^{2}+v_{o_x}t+(0)\\x(t)=v_{o_x}t[/tex]

While we don't know the initial horizontal velocity, we do know an output of the function for one specific input... we know that when the stone hits the ground, that the stone's horizontal distance is 93m from the cliff.  So, if we input [tex]t_{ground}[/tex] into this function, it will give an output of 93.  The only remaining unknown is the initial velocity in the x direction.  One equation, one unknown, we can solve this:

[tex]x(t_{ground})=v_{o_x}t_{ground}\\83=v_{o_x}(4.074309757)\\\frac{83}{4.074309757} =v_{o_x}\\20.37154879m/s =v_{o_x}\\[/tex]

If there were a component of initial velocity in the y direction, we would need to use the Pythagorean theorem to combine them.  However, as the initial y component of velocity is zero, the initial velocity is simply the initial x velocity.

Paying attention to directions, round to the answer to the nearest hundredth:

[tex]20.37m/s =v_{o}\\[/tex]

The way you will know that a figure represents a vector is that it will have magnitude and direction.

A figure that is a vector will typically have magnitude and direction. This means that it will be represented by an arrow(s)  with its' magnitude also showing.

Whereas, on the opposite side, the figure is termed as a scalar if it doesn’t have a direction.

Thus, we can know a vector diagram if the magnitude and direction are indicated.

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