a gearbox bru.
How will the element Ca + O bond ?
Answer:
Ionic bonding
Explanation:
Since Ca is a metal and O is a nonmetal, they will experience ionic bonding. This means that Ca will "donate" two of its valence electrons to O. This will give both Ca and O a complete octet.
Answer:
CaO
Explanation:
Depending on the element "a" stands for, there is not enough info to conclude how these elements would bond. however, if they are typed out correctly then one possible bond would be CaO. I am assuming that the C and O represent Carbon and Oxygen.
A soda bottle (m=0. 1 kg) filled with a flammable vapor is ignited and a rubber stopper (m=0. 01kg) is fired across the room at 100m/s. Find the recoil velocity of the soda bottle
The recoil velocity of the soda bottle is -10 m/s
To find the recoil velocity of the soda bottle, we'll need to use the conservation of momentum principle. The initial momentum of the system is zero since both the soda bottle and rubber stopper are initially at rest. The equation for conservation of momentum is:
m1v1 + m2v2 = 0
Where m1 and v1 are the mass and velocity of the soda bottle, and m2 and v2 are the mass and velocity of the rubber stopper. We know the masses and the velocity of the rubber stopper, so we can plug in those values:
(0.1 kg) * v1 + (0.01 kg) * (100 m/s) = 0
Now, solve for v1 (the recoil velocity of the soda bottle):
0.1 kg * v1 = -1 kg*m/s
v1 = -1 kg*m/s / 0.1 kg
v1 = -10 m/s
The recoil velocity of the soda bottle is -10 m/s, with the negative sign indicating that it moves in the opposite direction to the rubber stopper.
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Students push a swing with a hard push and a soft push. Each time the students count how many time the swing moves back and forth before stopping. What variable is tested in this investigation?
a. differences in pushes and pulls
b. force of the push
c. number of time the swing moves
d. distance the swing moves
A 2.00 m long string transmits
waves at 12.9 m/s. At what
frequency will it create standing
waves with 3 loops?
(Unit = Hz)
Answer:
The frequency at which the string will create a standing wave be with three loops is 8.6 Hz
Explanation:
The speed of the of the wave, v = 12.9 m/s
The number of loops of the standing wave = 3 loops
The length of the string = 2.00 m
Given that one loo = half of the wavelength, we have;
Three loops = 3 × half = One and half wavelength = 1.5·λ
The frequency of a wave = f = v/λ
Therefore, we have;
The frequency, f = 12.9/1.5 = 8.6 Hz
The frequency at which the string will create a standing wave be with three loops = 8.6 Hz.
Answer:
9.675
Explanation:
got it right on acellus
you are sitting at the center of a large turntable at an amusement park as it is set spinning freely. you decide to crawl towards the edge of the turntable. what does your action do to the rate of rotation of the turntable? explain
You are sitting at the center of a large turntable at an amusement park as it is set spinning freely. You decide to crawl towards the edge of the turntable. Rotational speed will decrease
There is no external torque
hence , the angular momentum of the table is conserved
L (initial) = L ( final)
since , L = m*v*r
where
m = mass
v = velocity
r = radius
If the person is crawled towards the outer rim, then the rotational inertia of the turntable will increase. In order to conserve the angular momentum , its rotational speed will decrease as mass and radius cannot be altered .
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Waves with __________ energy have a higher frequency?
Answer:
High
Explanation:
Waves with high energy have a higher frequency.
streams of protons and electrons emitted from the sun produce ________.
Streams of protons and electrons emitted from the Sun produce the solar wind. The Sun continuously emits a stream of charged particles, mainly protons and electrons, known as the solar wind.
These particles are accelerated by the Sun's intense heat and magnetic field. As they travel through space, the solar wind interacts with planetary magnetic fields and the Earth's magnetosphere, causing various effects such as auroras and geomagnetic storms. The solar wind also carries energy and plays a crucial role in shaping the space environment within our solar system. It has implications for space weather and can impact satellites, spacecraft, and other technological systems.
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g Let's use a diffraction grating to break up a laser beam into multiple beams. The laser has a wavelength of 589 nm, a screen is 10 meters away, and you need the spacing between spots there to be 22 cm. What is the line spacing you need for your diffraction grating (in lines/mm)?
The line spacing you need for your diffraction grating is approximately 45454.55 lines/mm.
To calculate the line spacing you need for your diffraction grating in lines/mm, you can use the formula:
Line spacing (in mm) = 1 / (number of lines per mm)
Given that the screen is 10 meters away and the spacing between spots there should be 22 cm, we need to convert the screen distance and spot spacing to meters.
Screen distance = 10 meters
Spot spacing = 22 cm = 0.22 meters
Now, let's calculate the number of lines per meter by dividing the screen distance by the spot spacing:
Number of lines per meter = Screen distance / Spot spacing
Number of lines per meter = 10 meters / 0.22 meters = 45.45 lines/meter
To convert the number of lines per meter to lines per millimeter, we need to multiply it by 1000:
Number of lines per mm = Number of lines per meter * 1000
Number of lines per mm = 45.45 lines/meter * 1000 = 45454.55 lines/mm
Therefore, the line spacing you need for your diffraction grating is approximately 45454.55 lines/mm.
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Usain Bolt accelerates at a rate of 3.7
m/s2 and his top speed is 12.7 m/s. How
long does it take for him to run the 100m
dash based on these numbers
Answer:
Explanation:
I think that you to run more than 12 miles
which of these galaxies is likely to be oldest? (a) a galaxy in the local group (b) a galaxy observed at a distance of 5 billion light-years (c) a galaxy observed at a distance of 10 billion light-years
The correct option is (a) i.e. a galaxy in the local group, galaxies is likely to be oldest.
A galaxy is a collection of stars, stellar remains, interstellar gas, dust, and dark matter that are gravitationally bonded together. The name comes from the Greek word galaxias, which means "milky" and refers to the Milky Way galaxy, which houses the Solar System. Galaxies, which contain an average of 100 million stars, range in size from dwarfs, which contain fewer than 100 million stars, to supergiants, which contain 100 trillion stars, all of which orbit the galaxy's center of mass. Only a small percentage of the mass in a normal galaxy is visible in the form of stars and nebulae; the majority of the galaxy's mass is dark matter. Supermassive black holes are a typical component of galaxy centers. According on their optical shape, galaxies are classified as elliptical, spiral, or irregular. It is believed that the nuclei of many of them contain supermassive black holes. Sagittarius A*, the name of the Milky Way's primary black hole, is four million times more massive than the Sun. GN-z11 is the oldest and furthest away galaxy as of March 2016. It can be seen as having existed only 400 million years after the Big Bang and is located 32 billion light-years away from Earth.
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Ratio of dimension of k.e and power
The proportion of kinetic energy to power in dimensions is [T].
The following determines the object's kinetic energy:
E = ½mv²
The mass formula in dimensions is [m] = [M].
The dimensional velocity formula is [v] = [LT-1].
Kinetic energy's dimensional formula is [K] = [ML2T-2].
Power is the amount of work completed each second. It comes from:
P = W / t
[W] = [ML2T-2] is the dimensional formula for work done.
The time dimension formula is [t] = [T].
The dimensionless power equation is [P] = [ML2T-3].
The kinetic energy to power ratio is [K]/[P] = [ML2T-2] / [ML2T-3].
[K] / [P] [T]
Therefore, [T] is the ratio of the dimensions of kinetic energy to power. This is the necessary remedy as a result.
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a simple harmonic oscillator has a mass of 5 kg and a spring constant of 250 n/m. what is its period and frequency?
The period of the oscillator is approximately 0.89 seconds and its frequency is approximately 1.12 Hz
To calculate the period and frequency of a simple harmonic oscillator with a mass of 5 kg and a spring constant of 250 N/m, we can use the following equations:
Period (T) = 2π√(m/k)
Frequency (f) = 1/T
where m is the mass of the oscillator and k is the spring constant.
Substituting the given values, we get:
T = 2π√(5/250) = 2π√(0.02) ≈ 0.89 seconds
f = 1/T = 1/0.89 ≈ 1.12 Hz
Therefore, the period of the oscillator is approximately 0.89 seconds and its frequency is approximately 1.12 Hz. These values represent the time and rate at which the oscillator will complete one full cycle of its motion. The simple harmonic oscillator is a fundamental concept in physics and is used to model a wide range of physical systems, including mechanical vibrations, electronic circuits, and quantum mechanical systems.
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Compared to an atom as a whole, an atomic nucleus is.
Answer:
The nucleus is very small compared to the size of the atom.
The radius of the atom is about 100,000 times the radius of the nucleus
using a ruler, measure the longest and shortest diameters of elliptical 1. the subtypes of ellipticial galaxies are based on these measurements. find the subtype of these galaxies with the following:
The subtype of Elliptical 1 is 5.
To find the subtype of Elliptical 1, we need to measure the longest and shortest diameters of the galaxy using a ruler. Let's assume that the longest diameter measures 8 centimeters and the shortest diameter measures 4 centimeters.
Subtype = 10 x (longest side - shortest side) / longest side
Substituting the measured values into the formula, we have:
Subtype = 10 x (8 - 4) / 8
Subtype = 10 x 4 / 8
Subtype = 40 / 8
Subtype = 5
Therefore, the subtype of Elliptical 1 is 5.
The subtype calculation formula given is used to categorize elliptical galaxies based on the elongation or roundness of their shape. The formula compares the difference between the longest and shortest sides of the galaxy and normalizes it by dividing it by the longest side. The resulting value, multiplied by 10, gives the subtype of the galaxy.
In this case, the subtype of 5 indicates that Elliptical 1 has a relatively moderate elongation. Subtypes range from 0 (perfectly round) to infinity (highly elongated). As the calculated subtype of 5 is a relatively low value, it suggests that Elliptical 1 is not highly elongated and likely exhibits a more rounded shape compared to highly elongated elliptical galaxies.
It's important to note that the measurements used in this example are arbitrary and for demonstration purposes. To obtain accurate subtype classifications, precise measurements of the longest and shortest diameters should be taken using appropriate astronomical techniques and instruments.
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in an exothermic reaction, chemical energy is converted to ____ energy.
FILL IN THE BLANK.
MECHANICAL OR THERMAL.
Answer:thermal energy
Explanation:
please mark this answer as brainliest
A 1500kg car moving at a speed of 20.1m/s comes toa stop after travelling a distance of 200m. What was the average force exerted by the breaks on the car?
Answer:
= -1515N
Explanation:
v^2=u^2+2as
0m/s
u=20.1m/s
0=(20.1)^2+(2xax200)
0=404.01+400a
-404.01=400a
-404.01÷400=a
a= -1.01m/s^s
its negative because the force is slowing down the car
Newton's second law of motion
F=ma
=1500×-1.01
F= -1515N
A force of 10 N works on a ball over a distance of 5 m. The force is perpendicular to the displacement of the ball. What is the total work done by the force?
Since the force is perpendicular to the displacement of the ball, the total work done by the force is 50 Nm.
Given the following data:
Force = 10 NewtonDistance = 5 metersTo find the total work done by the force:
The work done by an object is the product of the perpendicular force acting on the object and the distance it covers.
Mathematically, work done is given by the formula:
\(Work\;done = Force\) × \(distance\)
Substituting the given parameters into the formula, we have;
\(Work\;done = 10\) × \(5\)
Work done = 50 Nm.
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a hot pot of water is set on the counter to cool. after a few minutes it has lost 755 j of heat energy. how much heat energy has the surrounding air gained?
The heat energy the surrounding air gained is 755 j.
Energy is a quantitative property given to a body or physical system and can be identified as work being done in the form of heat and light. Energy is Conserved - The law of conservation of energy states that energy can be transformed into form, but cannot be created or destroyed. Energy is the ability to do work. It can exist in electrical, kinetic, thermal, electrical, chemical, nuclear, or other forms.
Concept:-
Since the energy is always conserved, the energy lost by the hot water is gained bt the surrounding
- energy lost = + energy gained by the surrounding
- 755 j = + 755 j
Energy exists in many forms. Examples include light energy, thermal energy, mechanical energy, gravitational energy, electrical energy, acoustic energy, chemical energy, and nuclear or atomic energy. Each form can be transformed or changed into other forms.
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which tissue provides medical strength plant
what's the answer to say
GUYS PLEASE HELPPPP
Q. A body is thrown at an angle of 30 degree with velocity of 30m/s downward, if the height of the tower is 15m find:
1) the time when body reaches the ground
2) displacement vector
3) angle when body hits the ground
4) max height?
1. To find the time when the body reaches the ground, we can use the vertical motion equation:
h = v₀y * t + (1/2) * g * t²
where:
h = height of the tower = 15m
v₀y = initial vertical velocity = v₀ * sin(θ) = 30m/s * sin(30°)
g = acceleration due to gravity = 9.8m/s²
t = time
Plugging in the values:
15 = (30 * sin(30°) * t) + (0.5 * 9.8 * t²)
Simplifying the equation:
15 = 15t * 0.5t² + 4.9t²
Combining like terms:
15 = 7.5t² + 4.9t²
Simplifying further:
15 = 12.4t²
Dividing both sides by 12.4:
t² = 15 / 12.4
Taking the square root of both sides:
t = √(15 / 12.4)
Calculating the value:
t ≈ 1.01 seconds
Therefore, the time it takes for the body to reach the ground is approximately 1.01 seconds.
2. To find the displacement vector, we need to calculate the horizontal and vertical components separately.
Horizontal component:
The horizontal displacement can be calculated using the formula:
x = v₀x * t
where:
v₀x = initial horizontal velocity = v₀ * cos(θ) = 30m/s * cos(30°)
t = time is taken to reach the ground (previously calculated as approximately 1.01 seconds)
Plugging in the values:
v₀x = 30m/s * cos(30°)
t = 1.01 seconds
Calculating the value:
v₀x ≈ 26.02 m/s
Vertical component:
The vertical displacement can be calculated using the formula:
y = v₀y * t + (1/2) * g * t²
where:
v₀y = initial vertical velocity = v₀ * sin(θ) = 30m/s * sin(30°)
g = acceleration due to gravity = 9.8m/s²
t = time is taken to reach the ground (previously calculated as approximately 1.01 seconds)
Plugging in the values:
v₀y = 30m/s * sin(30°)
t = 1.01 seconds
Calculating the value:
v₀y ≈ 15 m/s
Now we have the horizontal and vertical components of the displacement vector:
Horizontal component: x ≈ 26.02 m/s
Vertical component: y ≈ 15 m/s
Therefore, the displacement vector of the body is approximately (26.02 m/s, 15 m/s).
3. To find the angle when the body hits the ground, we can use the vertical and horizontal components of the velocity.
The horizontal component of the velocity, v₀x, can be calculated using the formula:
v₀x = v₀ * cos(θ)
where:
v₀ = initial velocity = 30m/s
θ = angle of projection = 30 degrees
Plugging in the values:
v₀x = 30m/s * cos(30°)
Calculating the value:
v₀x ≈ 26.02 m/s
The vertical component of the velocity, v₀y, can be calculated using the formula:
v₀y = v₀ * sin(θ)
where:
v₀ = initial velocity = 30m/s
θ = angle of projection = 30 degrees
Plugging in the values:
v₀y = 30m/s * sin(30°)
Calculating the value:
v₀y ≈ 15 m/s
Now, to find the angle when the body hits the ground, we can use the inverse tangent function:
θ = arctan(v₀y / v₀x)
Plugging in the values:
θ = arctan(15 m/s / 26.02 m/s)
Calculating the value:
θ ≈ 30.96 degrees
Therefore, the angle when the body hits the ground is approximately 30.96 degrees.
4. To find the maximum height, we can use the vertical motion equation:
h = v₀y² / (2 * g)
where:
h = maximum height
v₀y = initial vertical velocity = v₀ * sin(θ) = 30m/s * sin(30°)
g = acceleration due to gravity = 9.8m/s²
Plugging in the values:
h = (30 * sin(30°))² / (2 * 9.8)
Calculating the value:
h ≈ 27.55 meters
Therefore, the maximum height reached by the body is approximately 27.55 meters.
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. A marble sphere with a diameter of 1/4 inch is fully immersed in the oil of density 0.961 g/cm3 . Calculate the buoyant force exerted on the marble sphere by the oil.
Answer:
See below ( was it REALLY 1/4 INCH??)
Explanation:
Calculate the volume of the sphere
v = 4/3 pi r^3
this times the density of the oil will give g displacement
then f = ma
4/3 pi (.25 in * 2.54 cm/inch) ^3 * .961 = 1.0307 gm
1.0307 gm is .0010307 kg
f = ma = .0010307 * 9.8 = .0101 N
To test the integrity of the capacitor, researchers maintained a voltage of 50 mV across the parallel portion of the circuit for several minutes. During this time, how much energy was stored in the capacitor
To calculate the energy stored in the capacitor, you can use the formula:
Energy (E) = 0.5 * Capacitance (C) * Voltage (V)^2
To determine how much energy was stored in the capacitor during the time it was tested, you will need to know the capacitance value of the capacitor and the voltage across it. In this case, you mentioned the voltage across the parallel portion of the circuit is 50 mV. However, the capacitance value is not provided.
To calculate the energy stored in the capacitor, you can use the formula:
Energy (E) = 0.5 * Capacitance (C) * Voltage (V)^2
Assuming you have the capacitance value (in farads) and the voltage (in volts), you can plug in the values into the formula and find the energy stored in the capacitor (in joules).
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The study of electrons as it relates to their use in electric devices
Answer:
An electron is a component of the broader term, electricity. Generally electricity refers to the control, manipulation, and use of the movement of electrons to perform some kind of work (motion/rotation, light, heat, etc…).
Explanation:
Or
put this
The study of electrons as it relates to their use in electric devices is electricity.
But I will go with the first one
Shelby the Skater's rocket provides a forward force of
220 Newtons. Shelby has a mass of 60. kg. If friction
provides a resistive force of 30. Newtons, then at what
rate does Shelby accelerate? Show all work.
Answer:
\(a=3.17\ m/s^2\)
Explanation:
Given that,
Force force acting on the Skater's rocket is 220 N
Resistive force acting on it, F' = 30 N
Mass of Shelby, m = 60 kg
We need to find the acceleration of Shelby. Net force acting on Shelby is given by :
Net force = 220-30
= 190 N
The formula of net force is :
F = ma
a is acceleration of Shelby
\(a=\dfrac{F}{m}\\\\a=\dfrac{190}{60}\\\\a=3.17\ m/s^2\)
So, the acceleration of Shelby is \(3.17\ m/s^2\)
Elastic Collision in One DimensionBlock 1, of mass m1, moves across a frictionless surface with speed ui. It collides elastically with block 2, of mass m2, which is at rest (vi=0). After the collision, block 1 moves with speed uf, while block 22 moves with speed vf. Assume that m1>m2, so that after the collision, the two objects move off in the direction of the first object before the collision.Part AThis collision is elastic. What quantities, if any, are conserved in this collision?kinetic energy onlymomentum onlykinetic energy and momentumPart BWhat is the final speed uf of block 1? Express uf in terms of m1,m2, and uiuf =Part CWhat is the final speed vf of block 2?Express vf in terms of m1,m2, and ui.vf =
When an elastic collision happens, both the momentum and the kinetic energy are conserved. Therefore, in this collision, both the momentum and the kinetic energy are conserved. Thus, the correct option is:Kinetic energy and momentum are conserved.
What is the final speed uf of block 1? Express uf in terms of m1,m2, and uiThe initial momentum of the two objects is:m1uiBecause the two objects move in opposite directions after the collision, the momentum of the two objects can be written as:(m1 * uf) - (m2 * vf).
Because the collision is elastic, the kinetic energy of the two objects can be written as:1/2m1ui² = 1/2m1uf² + 1/2m2vf²Now the final speed of block 1 can be found by solving the above equation, which is:uf = √((2m1ui²)/(m1 + m2)). Part C. What is the final speed vf of block 2?Express vf in terms of m1,m2, and uiUsing the same above equations and solving for vf:vf = (m1/m2)ui - ufTherefore, the final speed of block 2 can be found by solving the above equation, which is:vf = ((m1 - m2)/(m1 + m2))ui.
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A boy runs on a circular path of radius R = 28 m with a constant speed u = 4 m/s. Another boy starts from the centre of the path to catch the first boy. The second boy always remains on the radius connecting the centre of the circle and the first boy and maintains magnitude of his velocity constant V = 4 m/s. If the time of chase is (10 + x) sec then
Answer:
We can solve this problem by using the concept of relative motion. Let's assume that the first boy is running in the clockwise direction and the second boy is chasing him in the counterclockwise direction.
Since the second boy always remains on the radius connecting the center of the circle and the first boy, the distance between them is always equal to the radius of the circle, which is 28 m.
Let's denote the distance covered by the first boy as S1 and the distance covered by the second boy as S2. We know that the first boy is running with a constant speed of 4 m/s, so we can write:
S1 = u*t1
where t1 is the time taken by the first boy to complete the chase.
The second boy is moving with a constant velocity of 4 m/s towards the first boy, so we can write:
S2 = V*t2
where t2 is the time taken by the second boy to catch up with the first boy.
Since the second boy is always moving on the radius connecting the center of the circle and the first boy, the distance covered by him is equal to the distance on the circumference of the circle covered by the first boy, minus the distance covered by the first boy along the radius. We can write:
S2 = S1 - 2*pi*R
where pi is the mathematical constant pi (approximately equal to 3.14).
Substituting the values of S1 and S2, we get:
u*t1 = V*t2 + 2*pi*R
Since the time of chase is (10 + x) sec, we can also write:
t1 + t2 = 10 + x
We have two equations and two unknowns (t1 and t2), so we can solve for them. First, we can solve for t2:
t2 = (u*t1 - 2*pi*R) / V
Substituting this in the second equation, we get:
t1 + (u*t1 - 2*pi*R) / V = 10 + x
Simplifying this equation, we get:
t1*(1 + u/V) = 10 + x + 2*pi*R/V
Finally, we can solve for t1:
t1 = (10 + x + 2*pi*R/V) / (1 + u/V)
Substituting the given values of R, u, and V, we get:
t1 = (10 + x + 56*pi) / 20
Simplifying this expression, we get:
t1 = 2.8*pi + 0.5*x + 2.8
Therefore, the time taken by the first boy to complete the chase is 2.8*pi + 0.5*x + 2.8 seconds.
Explanation:
this gives me nightmare
A flywheel with radius of 0.200 m starts from rest and accelerates with a constant angular acceleration of 0.600 rad/s2.
1) For a point on the rim of the flywheel, what is the magnitude of the tangential acceleration after 2.00 s of acceleration?
2) For a point on the rim of the flywheel, what is the magnitude of the radial acceleration after 2.00 s of acceleration?
3) What is the magnitude of the resulant acceleration for this point after 2.00 s of acceleration?
To determine the worth of each job by investigating the market value of the knowledge, skills, and requirements needed to perform it, HR managers should use _______.
To determine the worth of each job by investigating the market value of the knowledge, skills, and requirements needed to perform it, HR managers should use job evaluation methods. Job evaluation methods are systematic approaches used to assess the relative worth of different jobs within an organization.
One commonly used job evaluation method is the Point Factor System. This method involves breaking down each job into different factors, such as knowledge, skills, responsibility, and working conditions. Each factor is assigned a specific weight or points based on its importance to the job. HR managers then evaluate each job based on these factors and assign a total point value.
Another method is the Ranking Method, where HR managers compare jobs and arrange them in order of their value or importance to the organization. This method is relatively simple but can be subjective as it relies on the judgment of HR managers.
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The area vector of a square loop of 5 turns of a conductor each with side length of 0.2 m carrying a current of 2 A is antiparallel to a uniform magnetic field of 50.0 T in which it lies. Question 5. The magnitude and direction of the total magnetic moment is ……to the area vector.
Answer:
\(M= 0.4 Am^2\)
Explanation:
From the question we are told that:
Number of turns \(N=5\)\(N=5\)
Conductor each with side length \(L=0.2m\)
Current \(I=2A\)
Magnetic field \(B=50.0T\)
Generally the equation for the total magnetic moment M is mathematically given by
\(M = current * area\)
\(M= I * A\)
\(M = 2 * (5* 0.2*0.2)\)
\(M = 2 * 0.2\)
\(M= 0.4 Am^2\)
Zoe is setting up a track for a toy car. The track has a ramp that is 32° above horizontal. If Zoe wants the car to travel as a projectile for 1.0 seconds, how fast does the toy car need to be moving as it leaves the ramp?
Answer:
The toy car needs to be moving at approximately -8.2 m/s in the x direction and -4.9 m/s in the y direction as it leaves the ramp.
Explanation:
To solve this problem, you will need to use the equations of motion for a projectile. The equations are as follows:
x = x0 + v0x * t
y = y0 + v0y * t - (1/2) * g * t^2
where x and y are the horizontal and vertical positions of the projectile, x0 and y0 are the initial positions, v0x and v0y are the initial velocities in the x and y directions, t is the time, and g is the acceleration due to gravity (9.8 m/s^2).
In this case, we are given that the track has a ramp that is 32° above horizontal, and we want to find the initial velocity of the toy car. We can use the equation for y to solve for the initial velocity in the y direction (v0y). We are given that the toy car will be traveling as a projectile for 1.0 seconds, and we can assume that the initial position (y0) is 0 and the acceleration due to gravity (g) is 9.8 m/s^2. We can rearrange the equation to solve for v0y:
v0y = (y - y0 - (1/2) * g * t^2) / t
Substituting in the given values, we get:
v0y = (0 - 0 - (1/2) * 9.8 * 1^2) / 1
v0y = -4.9 m/s
Now that we have the initial velocity in the y direction, we can use the equation for x to solve for the initial velocity in the x direction (v0x). We are given that the ramp is 32° above horizontal, so we can use trigonometry to find the initial velocity in the x direction. The tangent of 32° is approximately 0.6, so we can use the following equation to solve for v0x:
v0x = v0y / tan(32°)
Substituting in the value for v0y that we found earlier, we get:
v0x = -4.9 / 0.6
v0x = -8.2 m/s
So, to answer the question, the toy car needs to be moving at approximately -8.2 m/s in the x direction and -4.9 m/s in the y direction as it leaves the ramp.