Answer:
To investigate the relationship between how far the spring is stretched and how much elastic potential energy is stored in the system, we can conduct the following experiment:
Materials:
Spring
Meter stick
Weights of different masses
Stopwatch
Triple beam balance
Retort stand
Clamp
Procedure:
Set up a retort stand and attach a clamp to it.
Attach the spring to the clamp.
Place a meter stick vertically next to the spring to measure the distance it is stretched.
Measure and record the natural length of the spring (when no weight is attached).
Add a known mass to the end of the spring and record the new length of the spring.
Calculate the difference between the stretched length and the natural length of the spring.
Repeat steps 5 and 6 for different masses.
Record the time taken for the spring to stretch when the mass is added.
Calculate the elastic potential energy stored in the spring for each mass added, using the formula:
Elastic potential energy = 1/2 x k x (distance stretched)^2
where k is the spring constant of the spring.
Plot a graph of the elastic potential energy stored against the distance stretched for each mass added.
Analyze the relationship between the distance stretched and the elastic potential energy stored.
By measuring the distance stretched and the time taken for the spring to stretch, we can calculate the velocity of the mass and use this to determine the elastic potential energy stored in the spring. By repeating this process for different masses and plotting a graph, we can determine if there is a linear relationship between the distance stretched and the elastic potential energy stored. This investigation will help to better understand the concept of elasticity and its relationship to potential energy.
Earth is closer to the sun in December than it is in July. What happens to the orbital speed of the planet between July and December? Explain your answer
The Earth's orbital speed increases slightly as it gets closer to the Sun, reaching its fastest speed in December, and decreases slightly as it moves away from the Sun, reaching its slowest speed at aphelion in July.
What is orbital speed?
The orbital speed of the Earth changes slightly as it moves around the Sun due to changes in its distance from the Sun. As the Earth gets closer to the Sun, it experiences a stronger gravitational pull, which increases its speed, and as it moves farther away from the Sun, the gravitational pull decreases, causing the speed to decrease.
In July, the Earth is at aphelion, which is the farthest point in its orbit from the Sun. At this point, the Earth is about 94.5 million miles away from the Sun. In December, the Earth is at perihelion, which is the closest point in its orbit to the Sun. At this point, the Earth is about 91.5 million miles away from the Sun. Therefore, the Earth is about 3 million miles closer to the Sun in December than it is in July.
As the Earth gets closer to the Sun, its orbital speed increases due to the stronger gravitational pull from the Sun. Therefore, in December, the Earth is moving faster in its orbit around the Sun than it is in July. This increase in speed is not noticeable to us on Earth, but it is a measurable change in the velocity of the Earth's orbit. In fact, the Earth's speed at perihelion is about 30 km/s (18.64 mi/s) compared to about 29.29 km/s (18.21 mi/s) at aphelion.
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2. For timet> 0 in seconds, a police car is patrolling a local street. The position along
the straight, flat road is given in meters by the function P(t)=25t. Directly ahead
of the police car, a bank robber's getaway car begins to speed up to leave the scene
of the crime. The getaway car's position along the road is given in meters by the
function G(t)=75+2.5. Graph the functions P and G on the same set of axes. What
conclusion can you draw? Does the police car catch the getaway car? Determine the
time at which the police car intersects the getaway car, or determine how close the
police car gets to the getaway car before the bank robber evades capture.
Answer:
The position of the police car along the road is given by the function P(t) = 25t. The position of the getaway car along the road is given by the function G(t) = 75 + 2.5t.
To determine if and when the police car intersects with the getaway car, we can set P(t) equal to G(t) and solve for t: P(t) = G(t) 25t = 75 + 2.5t 22.5t = 75 t = 3.33 seconds
So, after approximately 3.33 seconds, the police car will intersect with the getaway car.
Seafloor spreading occurs because ____.
Select one:
a.
new material is being added to the asthenosphere
b.
earthquakes break apart the ocean floor
c.
sediments accumulate at the area of spreading
d.
molten material beneath Earth's crust rises to the surface
Answer:
Seafloor spreading occurs because earthquakes break apart the ocean floor.
What is the seafloor spreading theory?
Seafloor spreading is a geologic process where there is a gradual addition of new oceanic crust in the ocean floor through a volcanic activity while moving the older rocks away from the mid-oceanic ridge. The mid-ocean ridge is where the seafloor spreading occurs, in which tectonic plates—large slabs of Earth’s Lithosphere—split apart from each other.
Seafloor spreading was proposed by an American geophysicist, Harry H. Hess in 1960. By the use of the sonar, Hess was able to map the ocean floor and discovered the mid-Atlantic ridge (mid-ocean ridge). He also found out that the temperature near to the mid-Atlantic ridge was warmer than the surface away from it. He believed that the high temperature was due to the magma that leaked out from the ridge. The Continental Drift Theory of Alfred Wegener in 1912 is supported by this hypothesis on the shift position of the earth’s surface.
The Process of Sea Floor SpreadingThe mid-ocean ridge is the region where new oceanic crust is created. The oceanic crust is composed of rocks that move away from the ridge as new crust is being formed. The formation of the new crust is due to the rising of the molten material (magma) from the mantle by convection current. When the molten magma reaches the oceanic crust, it cools and pushes away the existing rocks from the ridge equally in both directions.
A younger oceanic crust is then formed, causing the spread of the ocean floor. The new rock is dense but not as dense as the old rock that moves away from the ridge. As the rock moves, further, it becomes colder and denser until it reaches an ocean trench or continues spreading.
It is believed that the successive movement of the rocks from the ridge progressively increases the ocean depth and have greater depths in the ocean trenches. Seafloor spreading leads to the renewal of the ocean floor in every 200 million years, a period of time for building a mid-ocean ridge, moving away across the ocean and subduction into a trench.
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how are absorption and emission lines produced in a stellar spectrum? what information might absorption lines in the spectrum of a star reveal about a cloud of cool gas lying between us and the star?
Absorption and emission lines are produced in a stellar spectrum due to the interaction of light with the atoms and molecules present in the stellar atmosphere or in an intervening gas cloud.
Explanation:
1. When light from a star passes through its outer layers (the atmosphere), certain wavelengths of light are absorbed by the atoms and molecules present. This causes the creation of absorption lines in the spectrum, which are dark lines at specific wavelengths.
2. Conversely, when atoms and molecules in the star's atmosphere get excited due to various processes (e.g., collisions, heat), they can emit light at specific wavelengths. This leads to the formation of emission lines, which appear as bright lines in the spectrum.
Absorption lines in the spectrum of a star can reveal information about a cloud of cool gas lying between us and the star. By studying these lines, we can determine:
1. The composition of the gas cloud: Different elements and molecules absorb light at specific wavelengths, so the presence of certain absorption lines can indicate which elements or molecules are present in the cloud.
2. The temperature of the gas cloud: The relative strength and width of the absorption lines can give us information about the temperature of the cloud, as the population of excited atoms and molecules depends on temperature.
3. The motion of the gas cloud: If the absorption lines are shifted from their expected positions, this can indicate the motion of the cloud relative to us (the observer) due to the Doppler effect. This can reveal information about the cloud's velocity and direction of motion.
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what is the direction of the net momentum? express your answer in degrees measured clockwise from the north to the west.
Make sure your calculator is in degree mode.
The direction of the net momentum is θ degrees measured clockwise from the north to the west.
To determine the direction of the net momentum, follow these steps:
Step 1: Identify the momentum components
Since the question does not provide specific information about the magnitudes or directions of the individual momenta, let's assume that we have two momenta: momentum A pointing north, and momentum B pointing west.
We can represent them as vector quantities A and B, respectively.
Step 2: Find the horizontal (westward) and vertical (northward) components of the net momentum
The horizontal component of the net momentum is the westward momentum (momentum B).
The vertical component of the net momentum is the northward momentum (momentum A).
Step 3: Use the Pythagorean theorem to find the magnitude of the net momentum
The magnitude of the net momentum (C) can be found by using the Pythagorean theorem: [tex]C^2 = A^2 + B^2.[/tex]
Take the square root of both sides to find the magnitude of the net momentum: [tex]C = sqrt(A^2 + B^2).[/tex]
Step 4: Use trigonometry to find the direction of the net momentum
To find the direction of the net momentum, we need to calculate the angle between the net momentum and the north direction, measured clockwise.
We can use the tangent function in trigonometry for this purpose: tan(θ) = B/A,
where θ is the angle between the net momentum and the north direction.
Step 5: Calculate the angle in degrees
To find the angle in degrees, take the inverse tangent (arctan) of the ratio B/A: θ = arctan(B/A).
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what is the moment of inertia of the object starting from rest if it has a final velocity of 5.5 m/s? express the moment of inertia as a multiple of mr2 , where m is the mass of the object and r is its radius.
The moment of inertia of an object starting from rest and reaching a final velocity of 5.5 m/s depends on the object's mass, shape, and distribution of mass.
The moment of inertia can be expressed as a multiple of mr², where m is the mass of the object and r is its radius. This is known as the moment of inertia for a solid sphere or cylinder, which have a uniform mass distribution. For example, the moment of inertia for a solid sphere is 2/5mr², while the moment of inertia for a solid cylinder rotating about its central axis is 1/2mr².
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in what is known as ___, jupiter and venus appeared close together in the night sky.
In what is known as a conjunction, Jupiter and Venus appear to be passing each other quite close together in the night sky.
In Los Angeles In what is known as a conjunction, Jupiter and Venus appear to be passing each other quite close together in the night sky.
The amount of light reflected by each planet varies. Certain planets' composition and atmosphere prevent them from reflecting a significant amount of light. Yet, extremely dense clouds of gases and sulfuric acid surround Venus. Sunlight easily reflects off of these clouds, causing them to reflect light. Almost 75% of the sunlight that hits Venus' surface is reflected.
In addition, Venus is quite visible because it is so close to the Earth. It is in a good location for reflecting sunlight towards the earth and being quite visible because it is somewhat close to the Sun (although Mercury is closest to the Sun).
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a closed-loop system has sustained oscillations (i.e. constant amplitude) with a period of 66 seconds when the gains are: proportional
A closed-loop system has sustained oscillations (i.e., constant amplitude) with a period of 66 seconds when the gains are proportional and integral.
A closed-loop system is a type of control system in which the output is fed back into the system to regulate the input. In this way, the output controls the input. A closed-loop system is a type of feedback control system that includes a controller, a plant, and a sensor. The closed-loop system's sustained oscillations occur due to the interaction between the plant, sensor, and controller. The oscillations are a result of the feedback loop's positive feedback, which amplifies the input and causes it to oscillate.
In a closed-loop system, the gains of the controller play a critical role in determining the oscillations' characteristics. The period of oscillation in a closed-loop system is the time taken for one complete cycle of oscillation. The period of oscillation is measured in seconds. The question states that the closed-loop system has a period of 66 seconds, which implies that it takes 66 seconds to complete one cycle of oscillation. Proportional and integral gains are the two types of gains utilized in a closed-loop system's controller. Proportional gain is the direct relationship between the output and the input. Integral gain, on the other hand, is the error signal's integral over time.
By adding these two gains, the controller may regulate the plant to create the desired output. The fact that the closed-loop system has sustained oscillations with a period of 66 seconds when the gains are proportional and integral implies that the system's feedback loop is stable. In other words, the feedback loop is generating constant oscillations with a fixed period, which is a sign of a stable system.
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what are 2 ways that an unbalanced force can change the motion of an object
Answer:
Unbalanced forces can lead to a change in direction, a change in speed, or both a change in direction and in speed.
Explanation:
How is electric force related to charge?
A. Inversely related to charge
B. Directly related to charge
C. Weaker when closer to a sphere
D. Conservative
Electric force is directly related to charge.
According to Coulomb's law, the electric force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. This means that if the charge on one of the objects increases, the electric force between them will also increase proportionally, assuming the distance between them remains the same.
Therefore, the correct answer is:
B. Directly related to charge.
[tex] \: [/tex]
Helium has a density
of 0.179 kg/L. If 0.098
kg of helium is added to
each of these small
balloons. how much volume will
each have?
Answer:
The volume of each balloon can be calculated using the formula: Volume = Mass / Density.
If 0.098 kg of helium is added to each balloon and helium has a density of 0.179 kg/L, then the volume of each balloon will be:
Volume = 0.098 kg / 0.179 kg/L
Volume ≈ 0.547 L
So each balloon will have a volume of approximately 0.547 liters.
Each balloon will have a volume of approximately 0.547 liters when filled with 0.098 kg of helium. This is calculated using the formula for density: Density = Mass / Volume, and rearranging it to find Volume = Mass / Density.
Explanation:This question involves using the formula for density, which is Density = Mass / Volume. In this situation, we know the density of helium (0.179 kg/L), and we have the mass (0.098 kg). We rearrange the formula to find the volume: Volume = Mass / Density. Therefore, the volume of the helium in the balloon is 0.098 kg / 0.179 kg/L = 0.547 L. This means that each balloon will have a volume of approximately 0.547 liters when filled with 0.098 kg of helium.
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when the capacitor is connected to a battery with voltage 500.0 v , the electric field between the plates is 83 % of the dielectric strength. what is the area of each plate if the capacitor stores 0.250 mj of energy under these conditions? express your answer with the appropriate units.
The area of each plate if the capacitor stores 0.250 mJ of energy under these conditions is 3.82 x 10^-4 m^2.
When the capacitor is connected to a battery with voltage 500.0 V, the electric field between the plates is 83% of the dielectric strength. The area of each plate if the capacitor stores 0.250 mJ of energy under these conditions can be calculated as follows: Voltage V = 500V, Electric field E = 83% of dielectric strength, Energy stored E = 0.250 mJ. We know that the Energy stored by a capacitor is given by ,E = 1/2 CV²Where C is the capacitance of the capacitor, V is the voltage across the capacitor.
Area of the plate of the capacitor is given by, A = C / ε0Where ε0 is the permittivity of free space. Substituting E = 1/2 CV², we get0.25 × 10⁻³ J = 1/2 C × (500 V)²C = (2 × 0.25 × 10⁻³) / (500)²F. Now, the capacitance C is given as C = Aεr / d, Where A is the area of the plates, εr is the relative permittivity, and d is the distance between the plates.
Substituting the value of capacitance in the above equation, we get A = C d / εrε0
Substituting the values of C, E, and d in the above equation we get, A = (3.85 × 10⁻¹² × (1.5 × 10⁻³)) / (83/100 × 8.85 × 10⁻¹²)
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2. Calculate the IMA of a compound machine made of a lever with an input arm of 9 cm and an output arm of 3 cm and an inclined plane with length 6 m and height 0.5 m.
The output force to the input force of a compound machine is the IMA (Ideal Mechanical Advantage), assuming no energy losses from friction.
What is the inclined plane show's IMA?The run-to-rise ratio, also known as the ideal mechanical advantage (IMA) of an inclined plane, is the length of the inclination divided by the vertical rise. When the slope of the incline reduces, the mechanical advantage grows, but the weight must be transported over a longer distance.
IMA lever equals input arm length minus output arm length (9 cm minus 3 cm equals three).
6 metres divided by 0.5 metres yields 12 in the formula for the IMA inclined plane.
Assume we have a 100 N object in our possession. We can calculate the force necessary to raise the object up the inclined plane using the IMA of the lever:
100 N / 3 = 33.33 N force lever = weight of item / IMA lever
IMA inclined plane = 33.33 N / 12 = 2.78 N, where force inclined plane = force lever
Force lever: 100 N / 33.33 N = 3 IMA compound machine: output force / input force / weight of item
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astronauts on the first trip to mars take along a pendulum that has a period on earth of 1.50 s . the period on mars turns out to be 2.45 s. What is the free-fall acceleration onMars? gmars= m/s2
Astronaut on the first trip to mars take along a pendulum that has different period on earth and mars and the free fall acceleration on mars is 3.67m/s².
given:
period on earth T₁ = 1.50 secperiod on mars T₂ = 2.45sec
To calculate free fall acceleration on mars (g₂),
where g₁ free fall acceleration on earth and g₂ free fall acceleration on mars.
The period of the pendulum on the earth is obtained by the equation:
T₁ = 2π√(L/g₁)
The period of the pendulum on the mars is obtained by the equation:
T₂ = 2π√(L/g₂)
On dividing the above equation we get;
T₁/T₂ = √(g₂/g1)
On squaring both the sides,
T₁²/T₂² = g₂/g₁
(1.50)²/(2.45)² = g₂/g₁
g₂ = 2.25/6.0025(9.8)
g₂ = 3.67m/s²
The free fall acceleration g₂ on mars is obtained 3.67m/s².
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Think about tug of war. Team X has three members who pull with the following forces: +180 N, +200 N, and +190 N. Team Y has three members who pull with the following forces: -200 N, -180 N, and -191 N. Which team would win?
In tug of war, the team that pulls with the greater force wins. The net force acting on each team is the sum of the forces acting on each member of the team. In this case,
Team X has a net force of +570 N (180 N + 200 N + 190 N), while Team Y has a net force of -571 N (-200 N - 180 N - 191 N). Since Team X has a net force in the positive direction and Team Y has a net force in the negative direction, it means that Team X would win the tug of war. The difference between the net forces of the two teams is 1 N, which means that Team X would win by a very small margin. Therefore, the team with the greater net force wins, regardless of the number of members on each team. Team X has three members who pull with the following forces: +180 N, +200 N,
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The picture above shows a sound wave. If the distance from A to B was increased, the pitch of the sound would
The sound's pitch would decrease as the distance from point A to point B increased.
What does a sound's pitch mean?When a sound is played, its pitch—how high or low it is—is known.A sound with a high pitch is known as a high sound, and a sound with a low pitch is known as a low sound. In the illustration above, as the distance grows, the pitch will decrease.How does a sound wave change as the pitch rises?Pitch and frequency are connected, therefore as pitch rises, so does frequency, which reduces wavelength. Hence, the relationship between wave frequency and wave velocity is straightforward. Raising the pitch raises.For more information on sound wave kindly visit to
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what is the correct relation if the standard heat solution of calcium chloride CaCI2 salt equals -120 kJ/mol
The correct relation for the standard heat solution of calcium chloride CaCl2 salt can be expressed as:
ΔH°soln(CaCl₂) = -120 kJ/mol
Here, ΔH°soln(CaCl₂) represents the standard heat of solution of calcium chloride, which is the amount of heat absorbed or released when one MOLE of calcium chloride is dissolved in water under standard conditions (25°C and 1 atm pressure). The negative sign indicates that the process is exothermic, meaning that heat is released when the salt dissolves in water. The value of -120 kJ/mol represents the magnitude of the heat released per mole of CaCl₂ dissolved in water.
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what volume of 0.455 m koh solution is needed to neutralize 82.0 ml of 0.150 m solution of nitrous acid?
The correct option is C, volume of 0.455 m KOH solution is needed to neutralize 82.0 ml of 0.150 m solution of nitrous acid is 27.0ml.
The reaction between KOH and HNO2 is,
[tex]KOH_{(aq)} + HNO_2_{(aq)}[/tex] ⇒ [tex]KNO_2_{(aq)} + H_2_{(l)}[/tex]
It is 1:1 stochiomily betweeen KOH & [tex]HNO_2[/tex]
So, Volume of [tex]HNO_2[/tex]= V1 = 82.0 ml
Molarity of [tex]HNO_2[/tex] = M1 = 0.150M
Volume of KOH=?
Molarity of KOH = M2 = 0.455M.
We have,
[tex](M_1V_1)_{HNO_2}[/tex] = [tex](M_2V_2)_{KOH}[/tex]
[tex]V_2[/tex] = [tex]\frac{M_1V_1}{M_2}[/tex] = [tex]\frac{(82) (0.150)}{0.455}[/tex]
V2 = 27.03 ml
ie. Volume of KOH needed = 27-0 ml.
Nitrous acid is a weak, colorless, and unstable acid with the chemical formula HNO2. It is formed by the reaction of nitric oxide (NO) with water and can exist as both a solid and a liquid. In its pure form, nitrous acid is a pale blue liquid that decomposes rapidly at room temperature, releasing nitrogen dioxide (NO2) and water vapor.
Nitrous acid is an important intermediate in the industrial synthesis of many chemicals, including dyes, pharmaceuticals, and pesticides. It is also used as a bleaching agent and in wastewater treatment. In the atmosphere, nitrous acid plays a key role in the formation of nitrogen oxides, which contribute to the formation of acid rain and smog.
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Complete Question: -
What volume of 0.455 M KOH solution is needed to neutralize 82.0 mL of 0.150 M solution of nitrous acid?
a. 249 ml
b.41.0 mL
с. 27.0 mL
d. 82.0 mL
In 1924, Prince Louis de Broglie suggested that all moving particles demonstrate wave-like
behaviour.
a) State the de Broglie equation and define all the symbols.
b) Neutrons may be used to study the atomic structure of matter. Diffraction effects are
noticeable when the de Broglie wavelength of the neutrons is comparable to the spacing
between the atoms. This spacing is typically 2.6 x 10-10 m.
i. Suggest why using neutrons may be preferable to using electrons when investigating
matter.
ii.
Calculate the speed (v) of a neutron having a de Broglie wavelength of
2.6 x 10-¹0 m. The mass of a neutron is 1.7 x 10-27 kg.
a) The de Broglie equation is λ = h/mv, where λ is the wavelength of a particle, h is Planck's constant (6.626 x 10^-34 J s), m is the mass of the particle, and v is its velocity.
b) Neutrons may be preferable to electrons when investigating matter because neutrons have a higher penetrating power than electrons and can pass through thicker samples. Neutrons also interact differently with matter than electrons, allowing them to provide unique information about the atomic structure of materials.
To calculate the speed of a neutron with a de Broglie wavelength of 2.6 x 10^-10 m, we can rearrange the de Broglie equation to solve for v:
v = h/(mλ)
Plugging in the values, we get:
v = (6.626 x 10^-34 J s) / (1.7 x 10^-27 kg x 2.6 x 10^-10 m)
v = 1.56 x 10^3 m/s
Therefore, the speed of the neutron is approximately 1.56 x 10^3 m/s.
During take off, a plane leaves the ground and
travels in a straight line until it reaches a
height of 10 km. The distance the plane flies
during take off should be in the range 57 km
to 62 km.
What is the smallest possible angle that the
path of the plane could make with the ground?
Give your answer in degrees to 1 d.p.
Not drawn accurately
Explanation:
please mark as brainliest answer
The smallest possible angle that the path of the plane could make with the ground is 18.9 degrees.
We are given that the plane travels a distance of 57 km to 62 km during take off, and that it reaches a height of 10 km. We want to find the smallest possible angle that the path of the plane could make with the ground.
The smallest possible angle will occur when the plane travels the maximum distance of 62 km..
To calculate the angle, we can use the following formula:
sin(theta) = opposite / hypotenuse
sin(theta) = 10 / 62
theta = sin⁻¹(10/62) = 18.9 degrees
As a result, the least conceivable angle that the plane's path might create with the ground is 18.9 degrees.
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an angry rhino with a mass of 2400 kg charges directly toward you with a speed of 4.80 m/s. before you start running, as a distraction, you throw a 0.180 kg rubber ball directly at the rhino with a speed of 7.90 m/s. determine the speed of the ball (in m/s) after it bounces back elastically toward you.
The speed of the ball after it bounces back elastically toward you when throwing a 0.180 kg rubber ball directly at the rhino with a speed of 7.90 m/s is 7.90 m/s.
The formula for elastic collisions is m1v1 + m2v2 = m1v1' + m2v2' where m is the mass, v is the initial velocity, and v' is the final velocity after the collision. In this case, the rhino is massive and the ball is light, so we will assume that the rhino does not change speed after the collision.
We are given:
m1 = 0.180 kgInitial Velocity1 = 7.90 m/sm2 = 2400 kgInitial Velocity2 = 4.80 m/sWe can then solve for the final velocity of the ball:
= m1v1 + m2v2 = m1v1' + m2v2'
⇒ (2400 kg)(4.8 m/s) + (0.18 kg)(7.9 m/s) = (2400 kg)(4.8 m/s) + (0.18 kg)(v2')
⇒ 11,520 kg·m/s + 1.422 kg·m/s = 11,520 kg·m/s + 0.18 kg·v2'
⇒ v2' = (11,520 kg·m/s + 1.422 kg·m/s - 11,520 kg·m/s) / 0.18 kg = 7.90 m/s
Therefore, the speed of the ball after it bounces back elastically toward you is 7.90 m/s.
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find the rotational kinetic energy of a spinning (not rolling) bowling ball that has a mass of 10 kg and a radius of 0.09 m moving at 15 m/s.
The rotational kinetic energy of the bowling ball is 506.25 J.
The formula for rotational kinetic energy is:
Rotational kinetic energy = [tex]\frac{1}{2} I w^2[/tex]
where I is the moment of inertia and w is the angular velocity.
To calculate the moment of inertia for a solid sphere, we use the formula:
[tex]I = (2/5) m r^2[/tex]
where m is the mass and r is the radius of the sphere.
Plugging in the given values, we get:
[tex]I = (2/5) * 10 kg * (0.09 m)^2 = 0.081 kg m^2[/tex]
Next, we need to calculate the angular velocity. Since the ball is not rolling, we can assume that the angular velocity is equal to the tangential velocity divided by the radius of the ball. So, the angular velocity is:
w = v / r = 15 m/s / 0.09 m = 166.67 rad/s
Finally, we can plug in the values for I and w into the formula for rotational kinetic energy:
Rotational kinetic energy =[tex]1/2 * I * w^2 = 1/2 * 0.081 kg m^2 * (166.67 rad/s)^2 = 506.25 J[/tex]
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at this date and time, the four moons of jupiter appear in the order of their distances from jupiter. which moon will take the least time to orbit jupiter?
While the other moons have periods ranging from 3 to 16 days, Io completes one full orbit of Jupiter in less than 2 days.
Which of Jupiter's moons is the largest and how many of them are Class 3?Jupiter has 67 satellites. A few of them go unnamed. After Galileo Galilei, the four primary groupings of moons are known as the Galilean moons: Europa, Lo, Ganymede, and Callisto. Ganymede is the biggest moon in the solar system.
Why can we see only four of Jupiter's moons?If you only see three or four moons, one of them may be behind or in front of Jupiter. Since the orbits are nearly edge-on when viewed from Earth, the satellites appear to be arranged in a line.
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aaer the switch has been closed for a long ;me, someone comes along and quickly opens the switch. a large (and dangerous!) spark is observed across the contacts of the switch. why does this occur?
When a switch has been closed for a long time, and someone comes along and quickly opens the switch, a large and dangerous spark is observed across the contacts of the switch because: the inductance of the circuit does not change immediately.
The inductance of the circuit opposes the change in current, and it takes time for the current to drop to zero, which causes a large and dangerous spark across the contacts of the switch when it is turned off quickly after being turned on for a long time.
What is an inductor?An inductor is a passive component of an electrical circuit that stores energy in the form of a magnetic field. An inductor is typically composed of a coil of wire, although it can be produced in other forms, such as a spiral or a toroidal (donut-shaped) coil.
Inductors are used in a variety of applications, including tuning circuits, filters, and power supplies.
What is the effect of inductance?Inductance is the capability of a circuit to store energy in a magnetic field that surrounds the coil. The current in the coil produces a magnetic field that resists variations in current. When the circuit is turned off, the inductance of the circuit prevents the current from dropping to zero instantaneously.
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Assume the motions and currents mentioned are along the x axis and fields are in the y direction.(a) Does an electric field exert a force on a stationary charged object? Yes/No(b) Does a magnetic field do so? Yes/No
Yes, an electric field exerts a force on a stationary charged object. This is because the electric field is composed of electric lines of force that travel in a straight line and exert a force upon the stationary charged object.
The magnitude of the force depends on the strength of the electric field and the charge on the object. No, a magnetic field does not exert a force on a stationary charged object. This is because a magnetic field is composed of magnetic lines of force that travel in circles and therefore do not exert a force on a stationary object.
However, a magnetic field does exert a force on a moving charged object, such as a current-carrying wire. This force is known as the Lorentz force, which is a combination of both electric and magnetic forces.
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Measurements that are closely grouped around the mean are __________. What one word completes this sentence?
Measurements that are closely grouped around the mean are precise.
What is consistency of measurements?When measurements are closely grouped around the mean, it means that the data points are clustered together and are not spread out widely.
This indicates that the measurements are consistent and that the values are similar to one another. This consistency in the measurements is what we refer to as precision.
In other words, precision refers to the degree of closeness of individual measurements to each other. The more precise the measurements, the less variation there is between the individual data points.
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Answer:"precise"
Explanation:
Precision is different from accuracy. Measurements that are very close to each other, but not close to the true value would be precise, but not accurate.
a 2.30-m-long pole is balanced vertically on its tip. it starts to fall and its lower end does not slip. what will be the speed of the upper end of the pole just before it hits the ground?
When the lower end of a 2.30-m-long pole that is vertically balanced on its tip begins to fall, and the lower end does not slip, the speed of the upper end of the pole just before it hits the ground will be approximately 8.8 m/s.
The pole's motion can be divided into two parts: a rotational and a translational part.
Rotational motion: The pole starts to rotate as soon as it starts to fall. Its center of mass is continuously moving downward, but it rotates about its point of contact with the ground.
Translational motion: Since the lower end of the pole is in contact with the ground, it is subjected to a frictional force that opposes its movement, resulting in the pole's center of mass moving downward. The pole's velocity is determined by the total energy that it possesses before it begins to fall.
The speed of the upper end of the pole just before it hits the ground can be determined using the conservation of energy. The velocity of the pole just before it hits the ground can be determined by equating the potential energy of the pole with its kinetic energy, which is obtained by multiplying its mass by its final velocity squared, and dividing by two. Potential energy can be defined as mgh, where m is the pole's mass, g is the acceleration due to gravity, and h is the height from which it falls.
Assuming that the pole does not have any initial speed, the total energy of the system is equal to the gravitational potential energy at the time of the pole’s release. At the time of the pole’s contact with the ground, the total energy of the system is equal to its kinetic energy.
Thus, the speed of the upper end of the pole just before it hits the ground is determined by the following equation:
[tex]v^2 = 2gH[/tex]
Where v is the velocity of the upper end of the pole just before it hits the ground, g is the acceleration due to gravity, and H is the height of the pole.
Therefore, the speed of the upper end of the pole just before it hits the ground is:
v = √2gH
Plugging in the known values for g ([tex]9.8 m/s^2[/tex]) and H (2.30 m) gives a speed of 8.38 m/s.
Thus, the speed of the upper end of the pole just before it hits the ground will be determined by calculating the velocity of its center of mass, which will be found by equating the pole's potential energy to its kinetic energy. The speed of the upper end of the pole just before it hits the ground will be approximately 8.8 m/s.
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An electric motor lifts a roller coaster car that weighs 10,000 N to the top of the first hill that is 20 m above the ground. To add suspense, the ride up to the top takes 150 seconds.
Calculate the work done by the motor.
Explanation:
Work = F * d
= 10000 N * 20 m = 200 000 J
Time to top is not needed unless you want to calculate POWER watts
for a satellite to be in a circular orbit 850 km above the surface of the earth, what orbital speed must it be given?
the orbital speed of the satellite in a circular orbit 850 km above the surface of the Earth is approximately 7,663 m/s.
To determine the orbital speed of a satellite in a circular orbit, we can use the following formula:
v = √(GM/r)
Where v is the orbital speed, G is the gravitational constant[tex](6.674 x 10^-11 m^3/kg*s^2)[/tex], M is the mass of the Earth [tex](5.97 * 10^24 kg)[/tex], and r is the distance from the center of the Earth to the satellite (850 km + the radius of the Earth, which is approximately 6,378 km).
First, we need to convert the distance to meters:
r = 850,000 m + 6,378,000 m = 7,228,000 m
Plugging in the values, we get:
v = √[tex]((6.674 * 10^-11 m^3/kg*s^2) * (5.97 * 10^24 kg) / (7,228,000 m))[/tex]
Simplifying the equation, we get:
v = 7,663 m/s
Therefore, the orbital speed of the satellite in a circular orbit 850 km above the surface of the Earth is approximately 7,663 m/s.
This high speed is necessary to keep the satellite in orbit, as it must balance the force of gravity with its own centrifugal force. If the satellite were traveling too slowly, it would be pulled back towards the Earth by gravity, and if it were traveling too quickly, it would escape Earth's gravitational pull and fly off into space.
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for a given incident energy of an electromagne;c wave, why is the radia;on pressure on a perfectly reflec;ng surface twice as great as that on a perfectly absorbing surface?
The radiation pressure on a perfectly reflecting surface is twice as great as that on a perfectly absorbing surface because the reflection of an electromagnetic wave causes its momentum to double.
Electromagnetic waves are transverse waves consisting of mutually orthogonal electric and magnetic fields that oscillate with a time-varying amplitude and frequency as they travel through space. EM waves are generated by vibrating charged particles and are propagated through space at the speed of light in a vacuum.
Radiation pressure refers to the pressure exerted on a surface due to the impact of electromagnetic radiation. It is an expression of the momentum transfer of photons to a surface. Incident energy refers to the energy carried by an electromagnetic wave that strikes a surface or object. It is proportional to the amplitude of the wave and the duration of the pulse.
The radiation pressure on a perfectly reflecting surface is twice as great as that on a perfectly absorbing surface for a given incident energy of an electromagnetic wave because the reflection of an electromagnetic wave causes its momentum to double. When an EM wave is absorbed by a surface, the momentum of its photons is entirely transferred to the surface, resulting in the exertion of a force on the surface equivalent to the momentum of the photons.
The reflection of an EM wave, on the other hand, doubles the momentum of the wave, resulting in a greater force being exerted on the surface. Hence, the radiation pressure on a perfectly reflecting surface is twice as great as that on a perfectly absorbing surface.
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