A skier of mass m starts from rest at the top of a solid sphere of radius r and slides down its frictionless surface.
The net force on the skier in the radial direction must be equal to the centripetal force in order to sustain circular motion.
[tex]$F_{\mathrm{radial}}=\frac{m v^2}{r}$[/tex]where [tex]v[/tex] denotes the skier's tangential instantaneous speed. Gravity and the normal force are the two forces at work on the skier. While the gravitational force is constantly radially outward, the normal force is always dependent on the angle [tex]\theta[/tex]. Therefore, the net force in the radial direction is, if the skier is at an angle of [tex]\theta[/tex] down the sphere.
[tex]$F_{\text {radial }}=m g \cos \theta-N$[/tex]
where N is the normal force's magnitude. When these two equations are combined, we get,
[tex]$\frac{m v^2}{r}=m g \cos \theta-N$[/tex]
Using the principle of energy conservation, we now substitute v with values we already know. The loss of potential energy equals the increase in kinetic energy, which on a sphere is written as,
[tex]$\frac{1}{2} m v^2=m g r(1-\cos \theta)$[/tex]
As the skier begins at rest, there is no kinetic energy at the top of the sphere. After removing [tex]v^2[/tex], we are left with the equation,
[tex]$2 m g(1-\cos \theta)=m g \cos \theta-N$[/tex]
Quantifying the situation when the skier exits the sphere is the last aspect of the issue. We can see that when theta equals 0, we get N = mg, which means that the normal force acting on the skier precisely balances the force of gravity. N decreases as the skier descends the sphere's surface, balancing the equation until it equals zero at a certain angle. This occurs precisely when,
[tex]$2 m g(1-\cos \theta)=m g \cos \theta$[/tex]
The skier is no longer in contact with the sphere when the normal force acting on the skier is zero, as the sphere no longer exerts any force on the skier. This is assumed to be the prerequisite for the skier to leave the ground.
After calculating [tex]\theta[/tex], we have,
[tex]$2 m g=3 m g \cos \theta$[/tex]
[tex]$\Longrightarrow \theta=\cos ^{-1}(2 / 3) \approx 48.19^{\circ}$[/tex]
First, we can note that this response is unaffected by the physical parameters m, r, and g. No matter how heavy he is, how huge the sphere is, or how powerful gravity is, the skier will exit the sphere at the same angle.
However, we will discover from dimensional analysis that this independence is actually not all that remarkable. Consider the units of the variables we've provided,
[tex]$[m]=$ kilograms,$\quad[r]=$ meters,$\quad[g]=$ meters $\cdot$ seconds $^{-2}$[/tex]
Any algebraic statement containing m, r, and g cannot be transformed into a dimensionless quantity. As a result, we draw the conclusion that the solution to our problem cannot depend on these values as an angle is a dimensionless quantity.
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A car moves in a straight line at 20.0 m/s for 8.00 miles, then at 30.0 m/s for another 8.00 miles. a. Is the car's average speed less than, greater than, or equal to 25.0 m/s
The average speed of the car is 24 m/s. The average speed of the car is therefore below 25.0 m/s.
What is speed ?The description of rapidity. a change in the location of an object in either direction or speed. How fast something is going is determined by the distance travelled and the time required to cover that distance. Speed is a scalar quantity since it just has an arrow-like direction and no magnitude.
What is distance ?The entire movement of an item, independent of direction, is called distance. Distance may be characterized as the quantity of ground covered, regardless of the starting or finishing points of an item.
distance (d) = 9 miles = 14.4841 km
d = 14484.1 m
1 miles = 1609.34 m
t₁= 14484.1/ 20
= 724.2 sec
t₂= 14484.1/ 30= 482.8 sec
total time ( t) = t+t
t= 724.2+ 482.8 = 1207 sec
Vavg = 2d/t= 2*14484.1/1207
Vavg = 24m/s
24< 25
lessthan 25m/s
car average speed (Vavg) = 24 m/s.
Therefore, the car average speed is 24 m/s.
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___________ have the highest rates of star formation
The largest individual galaxies in the universe are known as _________.
The collective activity of many supernova events in a relatively small volume of a galaxy can create ___________.
The energy for all active galactic nuclei is thought to come from in-fall of matter into _________.
_________ are often characterized by sources of immense energy located hundreds of thousands of light-years away on either side of their centers.
Explanation:
Starburst galaxies have the highest rates of star formation.
Central dominant galaxies are the ones which are largest individual galaxies in the universe.
The collective activity of many supernova events in a relatively small volume of a galaxy can create galactic wind.
The energy for all active galactic nuclei is thought to come from in-fall of matter into supermassive black holes.
Radio galaxies are often characterized by sources of immense energy located hundreds of thousands of light-years away on either side of their centers.
a 6 meter ladder is against a wall. if its bottom is pull at a constant of 0.5 m/sec, how fast is the ladder top sliding when it reaches 3 metersuo the wall
Hence, the ladder top to touch ground the ladder base should pull back a distance of ( 6 - 3 ) = 3 meters on ground As the rate of sliding of base of ladder is 0.5 meter per second , it takes a time of [ 3/ (0.5) ] = 6 seconds.
What is a simple definition of distance?What is Distance? Distance is the total movement of an object without any regard to direction. We can define distance as to how much ground an object has covered despite its starting or ending point.
How is a distance measured?Distance measures length. For example, the distance of a road is how long the road is. In the metric system of measurement, the most common units of distance are millimeters, centimeters, meters, and kilometers.
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Can anyone answer this science question NO LINKS !!!!
Answer:
position 3
Explanation:
in position 3 PE is least as height is least
so KE is most as energy is always conserved
Which component of a galaxy is often found between the stars and looks like a cloud or smoke?
Dust
Gas
Object
Star
Answer:
Hey I would say Dust
hope this helped
Answer:
The answer is A/Dust
Explanation:
hello please help i’ll give brainliest
Answer:
The geological features that is not created by the movement of the Earth's plates is Canyons.
¿Por qué un niño en un carrito parece caer hacía atrás cuando el carrito se le da un súbito empujón hacía delante?
Answer: El tronco ejerce un igual y la fuerza opuesta hacia delante de ti, por la tercera ley de Newton .
Explanation:
What measure do we use to determine the amount of potential energy in a battery?
The amount of energy stored in a battery is measured in watt-hours (Wh), kilowatt-hours (kWh), or ampere-hours (Ah) (Ahr).
What is the potential energy means?Potential energy is stored energy that is affected by the relative position of various components of a system. When a spring is squeezed or extended, its potential energy increases. A steel ball has higher potential energy when lifted above ground than when it falls to Earth.
What is the potential energy means?Because every item moved from its resting posture has stored energy, it is referred to as potential energy because it has the ability to accomplish work when released.
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A small cart on a 5.0-m long air track moves with a speed of 0.75 m/s. Bumpers at either end of the track cause the cart to reverse direction and maintain the same speed. Find the period and frequency of this motion.
The frequency of the cart's motion for a distance of 10.0 meters is 0.075 Hz (Hertz), which means the cart completes 0.0775 round trips per second.
1) Period (T):
The period (T) is the time taken for one complete round trip. The cart travels from one end to the other and back in one round trip.
T = (distance/speed)
T = (10.0 / 0.75 )
T = 13.33 seconds
So, the period of the cart's motion for a distance of 10.0 meters is approximately 13.33 seconds.
2) Frequency (f):
The frequency (f) is the number of complete round trips per unit time. It is the reciprocal of the period.
f = 1 / T
f = 1 / 13.33
f = 0.075 Hz
So, the frequency of the cart's motion for a distance of 10.0 meters is approximately 0.075 Hz (Hertz), which means the cart completes approximately 0.0775 round trips per second.
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A typical sound wave has a wavelength of 1 meter. The wavelength of green light is about 500 billionths of a meter. Which type of wave will tend to diffract more through a narrow gap that is about 1 centimeter wide? Explain.
Answer: Sound wave diffracts more.
Explanation: Width of gap d is smaller than wavelength λ of the gap.
You can estimate it from equation d sin α = n λ
The constant n is order of diffraction, n = 0,1,2,..
sin α = n λ / d is greater when λ/d is greater.
Sound wave will tend diffract more through a narrow gap that is about 1 centimeter wide.
What is Diffraction?Diffraction is the spreading of waves around obstacles. Diffraction takes place with sound; with electromagnetic radiation, such as light, X-rays, and gamma rays; and with very small moving particles such as atoms, neutrons, and electrons, which show wave like properties.
d sin α = n λ
Width of gap d is smaller than wavelength λ of the gap.
The constant n is order of diffraction, n = 0,1,2,..
sin α = n λ / d
Diffraction is greater when λ/d is greater.
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What are the angles for the two dark bands closest to the central maximum.
Express your answers in terms of b and λ. Separate the two angles with a comma.
asin(λb),asin(−λb)
The identical formula for the two angles is Asin(b),Asin(b).
The general word for interference effects involving edges or apertures is diffraction. In waves with longer wavelengths than those of light, diffraction is more common. Diffraction, for instance, is what causes sound to swell when it goes through a doorway or bend around corners. Diffraction causes water waves along a rocky coast to widen as they pass through the rocks. Usually, Fresnel and Fraunhofer diffraction regimes are distinguished.
Fresnel diffraction is the regime in which the diffracted waves are observed relatively close to the site of the diffraction (in comparison to the size of the item causing the diffraction). Working with Fresnel diffraction is typically very challenging. The Fraunhofer diffraction regime is the more manageable of the two.
angle 1 = asin(λb),
angle 2 = asin(−λb)
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A mass of 0.343 kg moves down a 5 meter ramp in 5.8 seconds. What is its velocity and kinetic energy
According to the given information the velocity is .0148 m/s2 and the kinetic energy is 3.78 J.
What is the straightforward meaning of velocity?The movement that an item or particle experiences with regard to time is expressed vectorially as velocity. One metre per second (m/s) is the accepted unit of flow speed (also known as speed).
What does velocity in SI mean?The metric speed unit is the meter per minute (m/s). A different way to express velocity magnitude is in centimeters per second (cm/s).
vilocity = 5/(5.8×5.8)
= 0.148
kinetic energy = 1/2mv^2
= 1/2 × (0343 × 0.148×0.148)
= 3.78 J
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If you rub an air filled balloon on your hair it is possible to stick on the wall and have it statically remain there. Explain how this is possible and be sure to answer the following questions in your explanation: (A) is the balloon a conductor or an insulator? (B) is the wall a conductor or an insulator?
The balloon will be drawn to the wall once it has been rubbed sufficiently to build up a sufficient negative charge. Even though the wall should generally be neutrally charged, its charges can change, causing a positively charged region to pull the negatively charged balloon toward it.
The balloon gains electrons when it is rubbed against your hair or a piece of wool cloth, making it negatively charged. Once charged, the two balloons will move away from one another because like charges repel and like charges attract (the paper will be attracted to the charged balloons.)The pull of an electrostatic force is what keeps the ball clinging to the wall.The balloon becomes charged when we rub it with a synthetic cloth, and when it is brought close to a wall, the electrostatic force causes it to be drawn to the neutral wall.To know more about conductor here
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30 points!
Which statement accurately describes a similarity all planets share?
They lack enough gravity to clear their orbit of debris.
They orbit the satellites of other planets.
They are very close in comparative densities.
They have sufficient gravity to make themselves round.
Statement D. They have sufficient gravity to make themselves round accurately describes a similarity between all planets in terms of this movement and the presence of mass to form such a celestial body.
Why do all planets have gravity and orbit around major celestial bodies?All planets need to have gravity in order to orbit around major celestial bodies, i.e., stars such as in the case of the earth planet or Mars, they orbit around the Sun which is the star of the solar system. The presence of the attractive force of gravity allows planets to move in a cycle across their stars.
Therefore, with this data, we can see that all planets have gravity and orbit around major celestial bodies and thus they can be considered to share the particularity to have a well defined orbit due to the presence of mass.
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For the same angle of incidence, the angle of 'refraction in
three different media A, B and C are 10°, 25° and 40°,
respectively. In which medium the velocity of light will be
maximum?
Answer:
In the medium where the angle of incedence is 10°
Explanation:
This is because angle of incedence is directly proportional to refractive index of a medium.
Since refractive index is inversely proprtional to speed of light in medium, it will be the case.
What is the wavelength of longitudinal wave
Which of the following is NOT considered crucial for life to exist on some world?
A. Liquid water
B. At atmosphere
C. Source of nutrients
D. Source of energy that can be used by life
Answer
Atmosphere is not required in some world
If the current carried by a conductor is doubled, how are each of the following affected?
(a) The charge carrier density- ____ (b) The current density____ (c) The electron drift velocity ____
(d) The average time interval between collision____ is halved. is quartered. is unchanged
doubles
triples
quadruples.
(a) The charge carrier density doubles,(b) The current density doubles, (c) The electron drift velocity doubles, (d) The average time interval between collision halved.
I = nq[tex]v_{d}[/tex]A
where n is the charge/volume
I is the current.
q is the charge per carrier
[tex]v_{d}[/tex] is the drift velocity of the charge carriers
A is the cross-sectional area of current flow
Here,
a) The charge carrier density (n) doubles if I doubles.
b) The charge carrier density (J = I/A is the current density). If I doubles, J doubles.
c) The electron drift velocity ([tex]v_{d}[/tex]) doubles if I doubles.
d) The average time interval between collisions depends inversely on [tex]v_{d}[/tex]. If I doubles, [tex]v_{d}[/tex] doubles, so the average time between collisions is halved.
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The process of seafloor spreading
Answer:
Seafloor spreading is a geologic process in which tectonic plates—large slabs of Earth's lithosphere—split apart from each other. ... As tectonic plates slowly move away from each other, heat from the mantle's convection currents makes the crust more plastic and less dense
Explanation:
hope it helps stay safe
Answer:
Magma comes out of the rift valley.
Magma cools to rock and hardens.
Rock is pushed away as new rock is formed at MOR.
Oceanic crust and continental crust meet at the trench.
Oceanic crust bends down under the continental crust.
Gravity pulls rock towards mantle.
Rock melts to mantle.
Explanation:
Hope it helps!
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The number of pices of sausage needed by a pizza restaurant is given by the equation S= 21 n. In this equation, n is the number of pizzas the resturant will make. How many pieces of sausage are needed to make 55 pizzas? A. 34 B. 1155 C. 76 D. 855
The piece of sausage need to make 55 pizza is 21 × 55 = 1155.
How long does it take to make a pizza on average?The typical baking time for a pizza is 8 to 15 minutes, and larger, thicker pizzas bake more slowly than thin-crust, petite pizzas with few toppings. Just a friendly reminder: never lose sight of the pizza.
The two pizza rule is what?The "2 pizza rule" is a formula for determining how many people to invite to a gathering. Every meeting had to be small enough for two large pizzas to feed everyone, according to the rule.
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17. A uniform rod of length 120cm and mass 0.7kg, is suspended horizontally by two vertical strings at points 12cm from each end. If masses of 4.0 and 2.0kg are hung on it at points 20cm respectively from one end and 25cm. from the other, what would the tension in the strings be?
pls answer quickly
Answer:
To solve this problem, you can use the principle of transverse static equilibrium. This states that the sum of the forces acting on an object must be equal to zero for the object to be in equilibrium. In this case, the forces acting on the rod are the tension in the strings, the weight of the rod, and the weight of the masses hung on the rod.
First, you can find the weight of the rod by multiplying its mass by the acceleration due to gravity:
Wrod = mrod * g
= 0.7 kg * 9.8 m/s^2
= 6.86 N
Next, you can find the weight of the 4.0-kg mass by multiplying its mass by the acceleration due to gravity:
W1 = m1 * g
= 4.0 kg * 9.8 m/s^2
= 39.2 N
You can find the weight of the 2.0-kg mass in the same way:
W2 = m2 * g
= 2.0 kg * 9.8 m/s^2
= 19.6 N
To find the tension in the strings, you can use the principle of transverse static equilibrium. The forces acting on the rod are the tension in the strings, the weight of the rod, and the weight of the masses hung on the rod. You can represent these forces as vectors acting at the points where the strings are attached to the rod. The vectors representing the tension in the strings will be equal in magnitude but opposite in direction. The vectors representing the weight of the rod and the masses will act vertically downward.
[asy]
unitsize(2cm);
pair P1, P2, P3, P4;
P1 = (0,0);
P2 = (1,0);
P3 = (0.8,0);
P4 = (0.2,0);
draw((-1,0)--(2,0));
draw((0,-1)--(0,1));
draw(P1--P3,red,Arrow(6));
draw(P2--P4,red,Arrow(6));
draw(P3--P4,red,Arrow(6));
draw((P1)--(P1+(0,-0.7)));
draw((P2)--(P2+(0,-4)));
draw((P2)--(P2+(0,-2)));
label("$T_1$", (P1 + P3)/2, red);
label("$T_2$", (P2 + P4)/2, red);
label("$W_{rod}$", (P3 + P4)/2, red);
label("$W_1$", (P2 + P4 + (0,-4))/2, red);
label("$W_2$", (P2 + P4 + (0,-2))/2, red);
label("$12$ cm", (0,0.2), red);
label("$20$ cm", (0.4,-0.4), red);
label("$25$ cm", (0.75,-0.4), red);
[/asy]
The sum of the forces in the x-direction must be equal to zero, so you can set up the following equation:
T1 - T2 = 0
The sum of the forces in the y-direction must also be equal to zero, so you can
A 64 g plastic ball is moving to the left at 24 m/s . How much work must be done on the ball to cause it to move to the right at 24 m/s
The ball requires a total of zero work to go to the right at 24 m/s.
Take into account the ball's kinetic energy.
Vi = -24 ms-1 for the initial velocity
Final velocity: vf = +24ms⁻¹
K = 12mvf²- 12mvi² = 12m(vf² - vi²) = 12m(242 - 242) = 0,
meaning that the ball does not undergo any effort.
As an alternative, think about the effort made to stop the ball.
W1 = ½m(0 – 24²) = 0.5 × 0.06 × –576 = –17.28J
Work required to accelerate the ball from rest to +24 milliseconds per second was W2 = 12m(242 - 0) = 0.5 0.06 576 = +17.28 J.
Therefore, the sum of the work is W = W1 + W2 = -17.28 + 17.28 = 0 J.
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A 1 kilogram object is thrown horizontally and a 2 kilogram object is dropped vertically at the same instant and from the same point above the ground. If friction is neglected, at any given instant both objects will have the same
a) Total velocity
b) Momentum
c) Height
d) Kinetic energy
If friction is neglected, at any given instant both objects will have the same c) Height.
What is friction?
Friction is the resistance to motion that results from two objects rubbing against one another. Two objects rubbing against one another causes friction. Motion is opposed by friction, which works against the motion.
When an object slides over another object, friction slows it down. As a result, energy is used. However, the energy does not fade away. Kinetic energy, also referred to as moving energy, is transformed into heat energy. We rub our hands together when it's cold because of this. Rub them together, and friction and heat will result.
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The ,______provides rigidity and protection to the plant cell
Answer:
cell wall hope this will help
Aniyah is driving down 7th street. She drives 150 meters in 25
seconds. Assuming she does not speed up or slow down, what
is her speed in meters per second?
Answer:
6m/s
Explanation:
formula used; S= d/t
the "7th Street"doesn't matter it's just apart of the scenario. The only thing that matters is the distance and time which we have. the speed in seconds is 6. I had the same question on my phsyics quiz lol.
What is the acceleration of the particle at t 0?
The acceleration of the particle at t=0 is zero because the particle is in rest position and did not moving at any of the instance or travelling at an uniform speed through out the whole journey or yet did not start from the source point.
Acceleration is the rate of change of velocity. At any point on a trajectory, the magnitude of the acceleration is given by the rate of change of velocity in both magnitude and direction. Acceleration of the body that we can consider is the increasing value of the velocity of any object at a constant rate and that of wee can calculate. Hence by the primary information that we have we can formerly consider that the acceleration which is acting on the particle at t=0 is zero because the particle is in rest position and did not moving at any of the instance or travelling at an uniform speed through out the whole journey or yet did not start from the source point.
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una pelota se deja caer desde la posición de reposo delo alto de un edificio, sin tomar en cuenta la resistencia del aire, calcula posición y la velocidad de la pelota después de: a) 1 segundo b) 1.5 segundos c) 2.5 segundos
Answer:
You can not find out an answer with this information
Explanation:
Provide some sort of graph
A musical note has a frequency of 512 Hz. If the wavelength of the note is 0.685 m, what is the speed of the sound of that note?
Answer:
350.72 m/s
Explanation:
Formula for velocity of wave is;
v = fλ
Where;
v is speed
f is frequency
λ is wavelength
We are given;
f = 512 Hz
λ = 0.685 m
Thus;
v = 512 × 0.685
v = 350.72 m/s
this occurs when a person comes into contact with hazard
Answer:
Exposure occurs when a person comes into contact with hazard
Find the equivalent resistance of this
circuit.
R
R3
420 12
160 12
R₂
320 12
Rea = [?] 52
Answer:
RT = 341.62 Ohms
Explanation:
Given the following data;
R1 = 420 Ohms
R2 = 320 Ohms
R3 = 160 Ohms
To find the equivalent resistance;
From the circuit, we can see that R1 and R2 are connected in parallel;
Mathematically, the total equivalent resistance of resistors connected in parallel is given by the formula;
[tex] RT = \frac {R1*R2}{R1 + R2} [/tex]
Substituting into the formula, we have;
[tex] RT1 = \frac {420*320}{420 + 320} [/tex]
[tex] RT1 = \frac {134400}{740} [/tex]
RT1 = 181.62 Ohms
Next, we resolve the resistors to form a series circuit.
RT = RT1 + R3
RT = 160 + 181.62
RT = 341.62 Ohms