Explanation:
u=0
v=100
T=1min that 60 second
a=?
Formula
=
V=U+AT
100=0+a×60
100=60a
a=100/60 =1.66
To find Distance
S=ut+1/2at×t
s=0×60+1/2×1.66×60×60
s=0+1/2×1.66×3600
s=0.83×3600
s=2988
How does potential energy convert to kinetic energy in the loop the loop section of a roller coaster
The loop-the-loop works in the same way, with the highest point of the loop representing the roller coaster's potential energy. It converts to kinetic energy on the way down and out of the loop-the-loop and rolls onto the next stomach-churning thrill.
What is potential energy ?Potential energy is the energy held by an object as a result of its position in relation to other objects, internal stresses, electric charge, or other factors.
Because of its position, an object can store energy. When a demolition machine's heavy ball is held in an elevated position, it stores energy. This stored positional energy is known as potential energy. Similarly, the position of a drawn bow allows it to store energy.
When potential energy is released, it is propelled into motion by gravity or elastic forces, among other catalysts.
Thus, The loop-the-loop works in the same way, with the highest point of the loop representing the roller coaster's potential energy.
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Which of the following energy sources are in some way derived from the Sun?
Answer:
Wave Energy and Biomass Energy sources.
Explanation:
The main sources of energy available on earth are Coal, Geothermal, Nuclear, Petroleum, Hydro, Biomass, and Wave, from which nuclear and geothermal are resultant of radioactive materials whereas Coal and Petroleum are resultant of Fossil Fuels.
Biomass energy is produced by living organisms, for example, corn is used as biomass material, which stores energy through photosynthesis, and the photosynthesis process is only possible with Sun.
Wave energy is resultant of the sun's uneven heating of the ocean which makes tides and then the motion of the waves utilize to harness the energy.
Fred the fisherman has been told that, because
of refraction, a fish in water will
appear
nearer the water's surface than it really is.
to be
He draws a diagram to try to work this out.
I think it will look lower, not higher.' he says.
Explain what Fred has done wrong.
Due to light refraction, any fish in the water can see a fisherman on the bank a little more clearly than one might anticipate. When the light hits the water's surface, it “bends” down by around 13 degrees, leaving the image. Thus option A is correct.
What refraction affect the fisherman?When it reaches the surface, light emanating from the fish refracts (changes direction). When viewed from above the water, a fish appears to be closer to the surface than it actually is.
Therefore, Fred the fisherman has been told that, because of refraction, a fish in water will appear.
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The graph shows the motion of a squirrel that leaves its nest to find food.
Which segment of the graph represents the squirrel heading toward its nest?
A. S
B. Q
C. T
D. R
The segment of the graph represents the squirrel heading toward its nest is S. The correct option is A.
What is a graph?The graph of a function f in mathematics is the collection of ordered pairs, where display style f(x)=y. These pairs are Cartesian coordinates of points in two-dimensional space, and so form a subset of this plane in the typical situation when x and f(x) are real integers.
They are employed to arrange data in order to highlight patterns and correlations. This information is displayed as a shape on a graph.
Therefore, the correct option is A. S.
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How many energy levels do the electrons occupy for a neutral Oxygen atom?
Electrons occupy neutral oxygen atom has 8 electrons.
How many electrons are there in a neutral atom of oxygen?Now you can statistic out how many electrons, protons and neutrons Oxygen has: Atomic number which is all the time smaller of the two numbers is 8. Hence 8 protons. Because the atom is impartial, there are also 8 electrons. Oxygen likes to have two extra electrons to make it happy. Each lithium atom provides one.
the first two electrons will inhabit the 1s orbital while the next two electrons will occupy the 2s orbital. The endure four electrons will occupy the 2p orbital. The correct design for a neutral oxygen atom.
So we can conclude that Oxygen is the eighth element with a total of 8 electrons. In writing the electron layout for oxygen the first two electrons will go in the 1s orbital.
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What is the frequency if you have a period of 5.1 seconds
Answer:
0.20 Hz
Explanation:
Period formula:
T = 1 / f
rearrange to solve for T (which is period)
F = 1/T
= 1/5.1
= 0.20 Hz
If you want 3 sig figures it would go up to 0.196, but I just rounded to two to get 0.20.
A magazine rack has a center of gravity 16 cm above the floor, as shown in the figure below (Figure 1). Through what maximum angle, in degrees, can the rack be tilted without falling over?
The magazine rack can turn through 73 degrees without falling over
What is the angle?We know that we can be able to obtain the angle that has been turned when we obtain the tangent of the angle that is made by the direction of the ball.
Now we know that we can be able to get the ange that has been turned when we apply the idrea of a righta ngled triangle. In which case, we would have the following;
Angle turned = tan-1 (16/5)
= 73 degrees
Thus, the angle that is turned is 73 degrees.
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If you double the diameter of a cylindrical wire, you double its conductivity but reduce its resistivity by one half.
Please Explain.
Answer:
Resistivity and conductivity are reciprocal quantities.
Doubling one will cause the other to be reduced to one half.
Charge q2 in the figure(Figure 1) is in static equilibrium. Assume that q = 4.4 nC .
What is q1?
Express your answer to two significant figures and include the appropriate units.
The magnitude of charge q₁ is equal to magnitude of charge q₂.
What is the magnitude of charge q₁?
The magnitude of charge q₁ is calculated by applying Coulomb's law of electrostatic force as shown below.
The electric force between q₁ and q is calculated as follows;
F₁ = kq₁q / r²
where;
k is Coulomb's constantr is the distance between q and q₁F₁ = ( 9 x 10⁹ x 4.4 x 10⁻⁹ x q₁) / (0.1)²
F₁ = 3960q₁
The electric force between q₂ and q is calculated as follows;
F₂ = kq₂q / r²
F₂ = ( 9 x 10⁹ x 4.4 x 10⁻⁹ x q₂) / (0.1)²
F₂ = 3960q₂
Since the charge q₂ is in static equilibrium with q and q₁, then
F₁ + F₂ = 0
3960q₁ = - 3960q₂
q₁ = -q₂
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our solar system______Spur, of the_______arm of the milky way galaxy
Answer: At least 100 billion stars, including our Sun, make up the Milky Way, a spiral galaxy with a diameter of around 100,000 light-years. In the Milky Way, where are we located? The Orion Arm, also known as the Orion Spur, is a short, incomplete arm between the Sagittarius and Perseus arms that is close to where our Sun is positioned.
Explanation:
Question
A graph of v(t) is shown for a world-class track sprinter in a 100-m race. (See Figure 2.67).
(a) What is his average velocity for the first 4 s?
(b) What is his instantaneous velocity at t=5 s?
(c) What is his average acceleration between 0 and 4 s?
(d) What is his time for the race?
(a) The average velocity of the sprinter for the first 4 seconds is 12 m/s.
(b) The instantaneous velocity of the sprinter at time, t = 5 s is 12 m/s.
(c) The average acceleration of the sprinter between 0 and 4 s is 3 m/s².
(d) The time of race of the sprinter is 12 s.
What is the average velocity for the first 4 s?
The average velocity of the sprinter is the change in the total displacement of the sprinter with total time of motion.
From the given graph, the average velocity of the sprinter for the first 4 seconds is 12 m/s.
The instantaneous velocity of the sprinter at time, t = 5 s from the graph corresponds to 12 m/s, since the velocity of the sprinter from 4 s to 12 seconds is constant.
The average acceleration of the sprinter between 0 and 4 s is calculated as follows;
a = ( 12 m/s - 0 m/s ) / ( 4 s - 0 s )
a = 3 m/s²
The total time of race of the sprinter according to the graph is 12 seconds.
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a cannonball is shot horizontally off a 10.5m high castle wall at 47.4 m/s. How far from the base of the wall does the cannonball land? (Unit=m)
The cannonball lands 68.73 meters from the base of the wall.
The time it takes for the cannonball to fall from the castle wall to the ground is given by:
t = sqrt(2h/g)
= sqrt(210.5/10)
= sqrt(2.1)
= 1.45 seconds
The distance the cannonball travels horizontally in this time is given by:
d = vt
= 47.4 * 1.45
= 68.73 m
The total distance from the base of the wall is therefore 68.73 m.
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which is a reason to use digital signals instead of analog signals to transmit information?
B. Noise decreases the loudness of analog signals but does not affect the loudness of digital signals.
Noise is any extraneous interference that can affect the quality of a signal being transmitted.
Noise can cause analog signals to become weaker or distorted, which can reduce the loudness of the signal and make it more difficult to interpret. In contrast, noise does not affect the loudness of digital signals in the same way.
Digital signals are transmitted using a series of ones and zeros, which can be easily distinguished from noise. This means that digital signals are less susceptible to the effects of noise, and are generally considered to be more reliable than analog signals for this reason.
Other reasons to use digital signals instead of analog signals include the fact that digital signals are easier to store and transmit over long distances, and that they can be more easily processed by computers.
[tex]\bold{ \: \purple{Hope \: This \: Helps \: You!}}[/tex]
B. Noise decreases the loudness of analog signals but does not affect the loudness of digital signals.
Noise is any extraneous interference that can affect the quality of a signal being transmitted. Noise can cause analog signals to become weaker or distorted, which can reduce the loudness of the signal and make it more difficult to interpret. In contrast, noise does not affect the loudness of digital signals in the same way.
Digital signals are transmitted using a series of ones and zeros, which can be easily distinguished from noise. This means that digital signals are less susceptible to the effects of noise, and are generally considered to be more reliable than analog signals for this reason.
Other reasons to use digital signals instead of analog signals include the fact that digital signals are easier to store and transmit over long distances, and that they can be more easily processed by computers.
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Consider an A-L circuit with a DC voltage source, as shown in the figure (Eireure-1)
This circuit has a current I₀ when t<0. At t-0 the switch is thrown removing the DC voltage source from the circuit. The current decays to I(t) at time t.
What is the power, PR(t), flowing into the resistor, R, at time t ?
Express your answer in terms of I(t) and R.
Part B
What is the power flowing into the inductor?
Express your answer as a function of R and I(t).
Find out your answer below:
The power, the resistor and time is I²₀R e-2Rt/L and - I₀²R e-2Rt/L .
Work rate or energy delivery time is expressed as W/t, where W is the quantity of work completed or energy delivered, and t is the time interval.
A passive electrical device with two terminals that controls or limits the flow of electricity across electrical circuits. The main function of a resistor is to lower the voltage and reduce the current flow in a specific area of the circuit.
a) L di/dt + iR = 0 -Rt/L
= I = I₀ e
At t=0. I = I₀
= Pr = I²R = I₀ R e = -2Rt/t
= Pr (t) = I²₀R e-2Rt/L
b) Energy of inductor = 1/2 L I²
= 1/2 L I₀² e-2Rt/L
Power, Pl (t) = dE/dt
= d/dt (1/2 LI₀² e-2Rt/L)
= 1/2 t I₀² ( e-2Rt/L) e-2Rt/L
Pl (t) = - I₀²R e-2Rt/L
Therefore, the power, the resistor and time is I²₀R e-2Rt/L and - I₀²R e-2Rt/L .
I hoped this helped you!
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no need for an explanation, i need answers
The angular momentum of the particle in the x-component, y-component, and z-component are 3.12, 2.84, and 1.19 kg.m/s² respectively.
What is angular momentum?Angular momentum can be defined as the rotational form of linear momentum. Angular momentum is a physical conserved quantity.
The angular momentum in the terms of linear momentum can be represented as:
[tex]\displaystyle \vec L= \vec r\times \vec p = m\vec r \times \vec v[/tex]
Given, the mass of the particle, m = 70 Kg
The displacement of the vector of the particle, [tex]\vec r = (5.0, -5.5)[/tex]
The velocity of the vector of the particle, [tex]\vec u = (3.2, 0, -8.1)[/tex]
The angular momentum of the particle, L can be calculated as:
[tex]\displaystyle \vec L= m\vec r \times \vec u[/tex]
[tex]\displaystyle \vec L= m(5.0,-5.5, 0)\times (3.1,0,-8.1)[/tex]
[tex]\displaystyle \vec L= 0.070 \times (44.55, 40.5, 17.05) .Kg.m/s^2[/tex]
[tex]\displaystyle \vec L= (3.12, 2.84, 1.19) \; kg.m/s^2[/tex]
Therefore, the x-component of angular momentum = 3.12 kg.m/s²
The y-component of angular momentum = 2.84 kg.m/s²
The z-component of angular momentum = 1.19 kg.m/s²
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forces 2i-j+k, 3i+4j+4k, 5i+3j+3k acts through points with position vector 3i+2k, 4i-5j+ak, -4i-2j+4k respectively. Find the value of a,if the system of forces is in equilibrium
The value of a, if the system of forces is in equilibrium is 2.
What is the value of a for the equilibrium force?
If the system of forces is in equilibrium the sum of all the forces will be equal to zero.
∑F = 0
2i -j + k + 3i + 4j + 4k + 5i + 3j + 3k - (3i+2k + 4i-5j + ak -4i-2j+4k) = 0
The value of a is calculated by summing all the corresponding vectors and equating them.
10i + 6j + 8k - (3i -7j + 6k + ak ) = 0
10i + 6j + 8k - 3i + 7j - 6k - ak = 0
7i + 13 j + 2k - ak = 0
2k - ak = 0
ak = 2k
a = 2
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(Figure 1) shows Sue along the straight-line path between her home and the cinema, where d=3.2 mi. Assume the positive direction is to the right.
Part A
If Sue walks home, what is her displacement if her home is the origin?
Express your answer in miles.
Part B
If Sue walks home, what is her displacement it the cinema is the origin? Assume the positive direction is to the right. Express your answer in miles.
(a) If Sue walks home, her displacement if her home is the origin is -2 mi.
(b) If Sue walks home, her displacement if the cinema is the origin is -5.2 mi.
What is the displacement of an object?The displacement of an object is the change in the position of an object.
Mathematically, the formula for the displacement of an object is given as;
Δx = xf - xi
where;
xf is the final position of the objectxi is the initial position of the objectIf Sue walks home, her displacement if her home is the origin is calculated as;
Δx = xf - xi
Δx = 0 mi - 2 mi
Δx = - 2mi
If Sue walks home, her displacement if the cinema is the origin is calculated as;
Δx = xf - xi
Δx = 0 mi - (2 mi + 3.2 mi )
Δx = 0 mi - 5.2 mi
Δx = -5.2 mi
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7. A pendulum consists of a ball of mass m suspended at the end of a massless cord of length L as shown. The pendulum is drawn aside through an angle of 60° with the vertical and released. At the low point of its swing, the speed of the pendulum ball is
(A) gL
(B) 2gL
(C) 1/2gL
(D) gL
The speed of the pendulum ball is determined as √ (gL).
option A is the correct answer.
What is the speed of the pendulum ball?
The speed of the pendulum ball is calculated by applying the law of conservation of energy as shown below.
Potential energy of the ball at top = Kinetic energy of the ball at bottom
U = K.E
mgh = ¹/₂mv²
v = √ ( 2gh)
where;
g is acceleration due to gravityh is the change in height of the pendulum ballThe change in height of the pendulum ball is given as;
h = L - Lcosθ
where;
θ is the angle of inclination of the pendulumh = L - Lcos(60)
h = L - ¹/₂L
h = ¹/₂L
The speed of the pendulum ball is calculated as;
v = √ (2g x ¹/₂L)
v = √ (gL)
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A ladder, length L, with mass M, leans against a frictionless wall at an angle of θ=70° as shown.
1) If the ladder is in static equilibrium,
The net force is zero but the net torque is not.
The net torque is zero but the net force is not.
The net force and net torque are both zero.
Neither net force nor net torque is zero.
2) Which of these free body diagrams best represents the forces on the ladder?
3) At which of the following locations can we put the rotation axis we use when calculating torques?
Only at the center of the ladder.
Only at the bottom left end of the ladder.
Only at the top right end of the ladder.
We can choose any of these locations for the rotation axis.
4) For the rest of these problems, we're using the top right end of the ladder as our pivot point. What is the magnitude of the torque from the force of gravity, around this point?
L* M g* sin (θ)
L* M g* cos (θ)
(L/ 2)* Mg g* sin (θ)
(L/ 2)* M g* cos (θ)
Which statement correctly compares sound and light waves?Both light and sound waves need matter to carry energy from one place to another.Neither light nor sound waves need matter to carry energy from one place to another.Light waves carry energy parallel to the motion of the wave, while sound waves carry energy perpendicular to it.Sound waves carry energy parallel to the motion of the wave, while light waves carry energy perpendicular to it.
Sound waves carry energy parallel to the motion of the wave, while light waves carry energy perpendicular to it.
What is energy parallel?Energy parallel is a type of energy efficiency strategy that seeks to reduce the amount of energy used in a building or facility by utilizing multiple energy sources instead of relying solely on one. This type of energy efficiency strategy works by drawing energy from multiple sources, such as solar, geothermal, wind, and water energy, and combining them to power a single building or facility. By utilizing multiple energy sources, energy parallel helps to reduce the overall amount of energy used in a building or facility, thus improving its overall energy efficiency. Additionally, this type of energy efficiency strategy helps to reduce the amount of energy that is wasted or lost by utilizing energy sources that are renewable and more sustainable.
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The times in this problem are given using metric prefixes on the base SI unit of time: the second (s). Give the times without the metric prefixes. For example, the metric prefix T (tera) stands for 1012, so 47 Ts would be written as 4.7×1013s.
a) 966 Ps
b) 966 fs
c) 48 ns
d) 640 μs
( a ) 966 Ps is expressed in SI unit as 9.66 x 10⁻¹⁰ s
( b ) 966 fs is expressed in SI unit as 9.66 x 10⁻¹³ s
( c ) 48 ns is expressed in SI unit as 4.8 x 10⁻⁸ s
( d ) 640 μsis expressed in SI unit as 6.4 x 10⁻⁴ s
What is the expression of the SI unit in standard form?
A standard way of expressing a derived quantity or fundamental quantity in terms of the SI unit is always in power of 10.
The standard form of the given quantity is calculated as follows;
( a ) 966 Ps = 966 x 10⁻¹² s = 9.66 x 10⁻¹⁰ s
( b ) 966 fs = 966 x 10⁻¹⁵ s = 9.66 x 10⁻¹³ s
( c ) 48 ns = 48 x 10⁻⁹ s = 4.8 x 10⁻⁸ s
( d) 640 μs = 640 x 10⁻⁶ s = 6.4 x 10⁻⁴ s
Thus, the standard form of a quantity in SI unit involves the power of 10.
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5 example proximodistal patterns development
1. The proximodistal pattern of development in the development of motor skills in infants involves the development of control and coordination of the head, neck, and trunk before control and coordination of the limbs. For example, an infant may first learn to lift their head and control its movements before learning to reach for and grasp objects with their hands.
2. The proximodistal pattern of development can also be seen in the development of language skills in children. Children typically learn to produce single words before they learn to put words together in simple phrases and sentences.
3. In the development of cognitive skills, the proximodistal pattern involves the development of more basic skills, such as perception and attention, before more complex skills, such as memory and problem-solving. For example, a child may first learn to identify basic shapes and colors before learning to solve more complex puzzles and games.
4. The proximodistal pattern of development can also be observed in the development of social and emotional skills in children. Children may first learn to express basic emotions, such as happiness and anger, before learning to recognize and understand the emotions of others.
5. In the development of sensory and perceptual abilities, the proximodistal pattern involves the development of more basic abilities, such as visual acuity and auditory sensitivity, before more complex abilities, such as spatial awareness and depth perception. For example, a child may first learn to focus their eyes on objects close to them before being able to see objects in the distance.
A speed-time graph is shown below:
What is the average acceleration of the object represented
in the graph above over the eight seconds?
01.0 cm/s²
01.5 cm/s²
Speed vs. Time
O2.0 cm/s²
Time (s)
The average acceleration of the object represented in the given graph above over eight seconds is equal to 0.5 m/s².
What is acceleration?Acceleration can be defined as the rate change of velocity with respect to time. The acceleration is a vector parameter with both magnitudes as well as directions.
Acceleration can be determined as the first derivative of the velocity of an object w.r.t. time.
[tex]\displaystyle a =\frac{v_f-v_o}{t}[/tex]
From Newton's 2 law of motion, acceleration can be determined as:
a = F/m
Given, the initial velocity at time t = 0 is v = 0 m/s
The final velocity at time t = 8 is v = 4 m/s
[tex]\displaystyle a =\frac{4-0}{8}[/tex]
a = 0.5 m/s²
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1kg of lead and 1 kg of aluminium are each made into a spherical ball . which one will occupy more space? explain step by step how you arrived at your answer take the density of aluminium to be 27000 kg per metre cubed and that of lad to be 11300kg per meter squared
The aluminum ball has a higher density and contains more matter and would fill more space than the lead ball.
What is the density?We know that in science, we can be able to define the density as the ratio of the mass per unit volume of the substance. The density is how we know the amount of material that is presence.
The fact that a substance has the greater density would have to mean that there is a lot more mass in the substance as we can see it and this is very important to the discussion that is going on here.
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1. Would a cart that has four solid disks for wheels have a final speed that is greater than, less than, or equal to the final speed of a single disc that has the same mass as the cart and
wheels? Explain.
2. Suppose a cart with four wheels and a disk whose mass is equal to the total mass of the cart roll down the ramp. Which, if either, has more gravitational potential energy at the top?
3. Which of those objects has more kinetic energy at the bottom? Why?
4. Imagine the disk just spinning in place instead of rolling, would it have kinetic energy? Why?
5. Why does the cart have more speed at the bottom even though it doesn't have more kinetic energy than the disk?
The final speed would be equal because they don't depend on the mass or the radius.
What variables affect kinetic and potential energy, respectively?The mass, gravitational pull, and height above the earth all affect how much potential energy an item has. This energy is transformed into kinetic or indeed the change in momentum, when you fall the thing. An object's mass and speed affect its kinetic energy.
What three variables determine kinetic energy?The quantity of work performed on an object as well as its velocity following an inertia moment caused by external forces are two aspects that affect the overall kinetic energy about an object. The most crucial variables that affect kinetic energy are the motion calculated in terms of the object's mass and velocity.
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Anne exerts a force of 34.1 N to pitch a softball. She moves the ball 1.8 meters before releasing it. What amount of work did Anne do on the ball?
Formula for work:
[tex]w=Fd[/tex]
work(measured in joules) = force(measured in newtons) * distance(measured in meters)
__________________________________________________________
Given:
[tex]F=34.1N[/tex]
[tex]d=1.8m[/tex]
[tex]w=?[/tex]
__________________________________________________________
Finding work:
[tex]w=Fd[/tex]
[tex]w=34.1\times1.8[/tex]
__________________________________________________________
Answer:
[tex]\fbox{w = 61.38 Joules}[/tex]
Both carts start from rest, their change in momentum will be equal to their final momentum. according to newton's second law, the same force applied to the two carts results in for the plastic cart compared to the lead cart, which means the plastic cart will travel the distance of 1 m in time interval compared to the lead cart. therefore, from the momentum principle the plastic cart will have final momentum, compared to the lead cart.
The impulses and changes in momentum are identical because equal forces are applied over equal periods of time.
The momenta of the two carts are identical since they both begin at rest and experience equal changes in momentum. We are aware that force is the same as mass multiplied by acceleration. Due to the initial resting state of both carts, u = 0 m/s, and the plastic cart moves 1 m. Newton's second law states that when the same force is applied to the two carts, the plastic cart will have more final momentum than the lead cart because of the momentum principle. Newton's third law states that every object feels the same force for the same length of time, which results in the same impulse and consequent change in momentum.
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Due to equivalent forces being delivered over equal times, the impulses and changes in momentum are identical.
What occurs to the cart's acceleration when the force being applied to it is doubled?The acceleration is determined by dividing the net force by the mass. An object's acceleration doubles if the net force exerted on it also doubles. Increased mass will result in a halving of acceleration.
What is the second law of Newton?Second Law of Motion: Force In accordance with his second law, a force is defined as the change in momentum (mass times velocity) per change in time. The definition of momentum is the product of the mass m and the velocity V of an object.
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(b)
The aorta transports blood from the heart to the body.
In a person at rest:
blood travels at a mean speed of 10 cm/s in the aorta
blood travels at a mean speed of 0.5 mm/s in the capillaries
the speed of blood decreases at a rate of 0.4 cm/s² as blood travels from the
aorta to the capillaries.
Calculate the time it takes for blood to travel from the aorta to the capillaries.
Assume that the speed of blood decreases at a constant rate.
Use the equation:
rate of decrease in speed=
Give your answer to 2 significant figures.
change in speed
time
The time it takes for blood to travel from the aorta to the capillaries is 20 seconds. This can be calculated using the equation: t = v₁ - v₂ / a , where v₁ is the initial velocity (10 cm/s), v₂ is the final velocity (0.5 mm/s), and a is the acceleration (0.4 cm/s²). Therefore, t = 10 cm/s - 0.5 mm/s / 0.4 cm/s² = 20 s.
A ball of mass m is fastened to a string. the ball swings at constant speed in a vertical circle of radius r with the other end of the string held fixed. neglecting air resistance, what is the difference between the string's tension at the bottom of the circle and at the top of the circle? (note: a vertical circle means the ball is moving up and down as it goes in a circle - this means that gravity must be considered.)
The difference between the string's tension at the bottom of the circle and at the top of the circle is 2mg.
Given the mass of the ball is m
radius of circle = r and constant speed is maintained = v
At the top of the circle, ΣF = FT + mg = mv^2/r, where F is the force acting on the string, T is tension, m is mass and g is gravitational acceleration.
Here as the ball moves in circle it carries centripetal force = mv^2/r.
Then FT = mv^2/r – mg.
At the bottom of the circle, ΣF = FT – mg = mv^2/r, So
FT = mv^2/r + mg
By comparing these two equations we get:
The difference is (mv^2/r + mg) – (mv^2/r – mg) = 2mg.
Hence the required difference is 2mg.
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There is a 2mg difference in string tension between the circle's bottom and top points.
Calculation:the mass of the ball is m
radius of circle = r and constant speed is maintained = v
At the top of the circle, ΣF = FT + mg = mv^2/r, where F is the force acting on the string, T is tension, m is mass and g is gravitational acceleration.
Here as the ball moves in circle it carries centripetal force = mv^2/r.
Then FT = mv^2/r – mg.
At the bottom of the circle, ΣF = FT – mg = mv^2/r, So
FT = mv^2/r + mg
By comparing these two equations we get:
The difference is (mv^2/r + mg) – (mv^2/r – mg) = 2mg.
Hence the required difference is 2mg.
Why does the top of a circle have zero tension?When the centripetal force and the gravitational force are exactly equal at the peak of the swing, the minimum speed will occur. The tension would then be exactly zero, and the ball would hardly be able to keep rolling in a circle.
Why is the bottom where stress is greatest?The weight of the body operates vertically downward while the centrifugal force acts vertically downward at the lowest position. As a result, the string's tension is at its highest. The weight of the body acts vertically downward and the centrifugal force acts vertically upward at the highest point.
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what happens to a vector when it is multiplied by a negative number that is not equal to negative one?
A. only the magnitude changes
B. The vector does not change
C. Both magnitude and direction change
D. Only the direction changes
The thing that happens to a vector when it is multiplied by a negative number that is not equal to negative one is A. only the magnitude changes
What happens if you multiply a vector by a negative number?except that the vector's arrow will point in the other direction when multiplied by a negative integer. A vector, for instance, will become half as long in the same direction when multiplied by 1/2, whereas it will become twice as long but directed when multiplied by 2.
A vector's direction is reversed but the magnitude is left unchanged when multiplied by a negative one. The direction and magnitude of the vector are reversed when multiplied by any other negative quantity.
Therefore, option A is correct.
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