Yes, the ball will move with a constant speed. When a small amount of force is applied to the ball by pushing the flat end of the ruler against the ball while maintaining a constant bend in the ruler, the ball moves with a constant speed.
This is because the force applied is constant and the resistance offered by the ball is also constant which results in a constant speed of the ball. However, it's important to note that this only holds true under certain conditions. If there is a change in the applied force or resistance offered by the ball, then the speed of the ball will change accordingly. Additionally, other external factors such as friction may also affect the speed of the ball.
Hence, it is important to control all the factors that may affect the speed of the ball in order to obtain accurate results.
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you use the doppler method to discover a planet around a nearby star that is very similar to the sun; the velocity curve that has a period of 6 months. what can you conclude about the planet's orbital distance?
The Doppler method is used to discover a planet around a nearby star that is similar to the Sun; the velocity curve has a period of 6 months. We can conclude that the planet's orbital distance is 1 AU.
The Doppler method is a technique for discovering planets that orbit other stars. The Doppler method, also known as the radial velocity method, involves measuring the movement of a star towards or away from the observer. As a planet orbits a star, it pulls the star in a small, regular circle around the center of mass of the planet-star system.The period of the velocity curve can be used to determine the planet's orbital period and distance.
If the velocity curve has a period of 6 months, the planet's orbital period is also 6 months. Kepler's third law can then be used to determine the planet's orbital distance.
According to Kepler's third law, the square of a planet's orbital period is proportional to the cube of its orbital distance. P² α a³ where P is the orbital period and a is the orbital distance.
Thus, a² ∝ P²/3a² = 1 AU (since P = 6 months).
Therefore, we can conclude that the planet's orbital distance is 1 AU.
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15. The diagram shows an electric circuit including a photocell.
The photocell contains a metal plate X that is exposed to
electromagnetic radiation. Photoelectrons emitted from the
surface of the metal are accelerated towards the positive
electrode Y. A sensitive ammeter measures the current in the
circuit due to the photoelectrons emitted by the metal plate
X. The metal plate X has a work function of 2.2 eV. The
maximum kinetic energy of an emitted photoelectron from
this plate is 0.3eV.
5
KE/10-19 J
4
2
a) Calculate the energy of a single photon in eV and in joules.
b) Calculate the frequency of the incident electromagnetic radiation.
c) Deduce the effect on the current if the radiation has the same intensity, but the frequency is
greater than in (b).
16. A negatively charged metal plate is exposed to electromagnetic radiation of frequency (f). The
diagram below shows the variation with (f) of the maximum kinetic energy KEmax of the
photoelectrons emitted from the surface.
1
0-
0
2
6
a) Define the threshold frequency of a metal.
b)
+
8
Electroma
10
radiation
vacuum
12
f/10¹4 Hz
14
i. Explain how the graph shows that the threshold frequency of this metal is
5.0 x 10¹4 Hz.
ii. Calculate the work function of this metal in joules.
Answer:
15.
a) The energy of a single photon can be calculated using the equation: E = hf, where h is Planck's constant (6.63 x 10^-34 J s) and f is the frequency of the radiation. Thus, E = (6.63 x 10^-34 J s)(c/λ), where c is the speed of light (3.00 x 10^8 m/s) and λ is the wavelength of the radiation. Using the maximum kinetic energy of an emitted photoelectron (0.3 eV) and the work function of the metal plate (2.2 eV), we can find the energy of a single photon: E = 2.5 eV = 4.0 x 10^-19 J.
b) The maximum kinetic energy of a photoelectron can be related to the frequency of the radiation by the equation: KEmax = hf - Φ, where Φ is the work function. Thus, f = (KEmax + Φ)/h. Substituting the given values, we get: f = (0.3 + 2.2) eV/(6.63 x 10^-34 J s) = 3.4 x 10^14 Hz.
c) If the frequency of the radiation is increased, more photoelectrons will be emitted per unit time, so the current in the circuit will increase.
16. a) The threshold frequency of a metal is the minimum frequency of radiation required to emit photoelectrons from the surface of the metal.
i. The graph shows that the kinetic energy of the emitted photoelectrons is zero for frequencies below 5.0 x 10^14 Hz. This means that the photoelectrons are not emitted below this frequency, indicating that the threshold frequency is 5.0 x 10^14 Hz.
ii. The work function of the metal can be calculated using the equation: Φ = hf - KEmax, where h is Planck's constant and KEmax is the maximum kinetic energy of the emitted photoelectrons. At the threshold frequency, KEmax is zero, so Φ = hf. Substituting the given values, we get: Φ = (6.63 x 10^-34 J s)(5.0 x 10^14 Hz) = 3.32 x 10^-19 J.
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A group of students is given a loop of wire connected to a light bulb and a bar magnet. They are asked to make the light bulb light up. N S Which of the following would cause the light bulb to glow?
a) Leaving the magnet at rest beside the light bulb. b) Moving the magnet next to the light bulb. c) Moving the magnet through the coil of wire. d) Leaving the magnet at rest inside the coil of wire.
The following would cause the light bulb to glow : c) Moving the magnet through coil of wire.
What causes the light bulb to glow?When magnet moves through a coil of wire, it creates changing magnetic field that induces electric current in the wire. This current flows through light bulb, causing it to light up.
Bulbs work by sending electricity through curly tungsten filament. The long, twisting path increases electrical resistance faced by traveling electrons, heating filament to some 3000 K. At that temperature, filament glows with warm yellowish white light.
LED bulb as compared to halogen lamps or incandescent bulbs, has much higher resistance on count of integrated power supply unit. The serial connection of glow lamp clamps the circuit even when the switch is turned off.
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How do we know how much gravitational force objects have?
Answer:
understand Newton's second law of motion,F is equal to ma where F is the force ,m is the mass of the object,a is acceleration
what characteristic is shared by sunspots, solar flares, and coronal mass ejections? select the two correct responses.
The two correct responses that describe a characteristic shared by sunspots, solar flares, and coronal mass ejections are as follows:
They all are connected to the magnetic activity of the Sun.
They are all associated with the Sun's corona and solar atmosphere.
What are sunspots, solar flares, and coronal mass ejections?
Sunspots are dark areas on the surface of the sun. They have a cooler temperature than the surrounding area because they are regions where the magnetic fields prevent hot, plasma-carrying gases from moving in and out of the sun.
Solar flares are sudden, violent eruptions of energy on the sun's surface that release huge amounts of energy. They are also associated with the magnetic activity of the sun.
Coronal mass ejections (CMEs) are huge eruptions of plasma and magnetic fields from the sun's corona. They can have significant impacts on Earth's magnetosphere, and hence, on electrical power grids, satellite communications, and even GPS systems.
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What two properties change when light is refracted?
what is the strength of an electric field that will balance the weight of a proton? express your answer in newtons per coulomb to two significant figures.
The strength of an electric field that will balance the weight of a proton is 1.6 x 10^-18 N/C.
The strength of an electric field that will balance the weight of a proton is given by the Coulomb force formula which is F=Eq. Therefore, the electric field strength that balances the weight of a proton is given by:
E=qg
where E is the electric field strength, q is the charge of the proton, and g is the acceleration due to gravity.
Electric field strength (E) = qg
From the Coulomb's law, we know that, q = e = 1.60 x 10^-19 C
Also, the weight of the proton (F) is given by:
F = mg
where m is the mass of the proton and g is the acceleration due to gravity.
Therefore, the value of g is 9.81 m/s^2
Therefore,
F = m * g = (1.67 x 10^-27 kg) * (9.81 m/s^2) = 1.64 x 10^-26 N
Therefore, the electric field strength that balances the weight of a proton is:
E=qg = (1.60 x 10^-19 C) * (9.81 m/s^2) = 1.57 x 10^-18 N/C
Approximately, the electric field strength is 1.6 x 10^-18 N/C
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Defferentiate between vector and scalar quantity giving relevannt example in case
A scalar quantity is a quantity that just has magnitude and no direction. Scalars include things like length, mass, speed. But a physical quantity is referred to as a vector quantity if it includes both magnitude and direction.
A number of physical quantities that each express a unique meaning and significance in that context can be used to explain each scientific explanation. A physical quantity is a measurable, quantifiable physical property that carries specific information, according to the definition. Physical quantities can be divided into the scalar and vector categories depending on how dependent they are on direction. These two numbers are used to depict an object's motion.To know more about scalar quantity
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Three 21 ohm resistors are wired in parallel, what is the total resistance?
Answer:
7 Ω
Explanation:
Given:
R1 = 21 Ω
The connection is parallel
Since all 3 of the resistors have the same resistance, we can use this formula to find the total resistance of the circuit:
R = R1/n (R1 is the resistance of one resistor and n is the number of resistors)
R = 21/3 = 7 Ω
a tennis player hits a 0.1-kilogram tennis ball with her racket from the north end of a court. her racket was traveling at 65 kilometers per hour. the ball accelerated at a rate of 10 meters per second squared. the ball hits the floor on the south end of the tennis court. the floor sends the ball toward the tennis player's opponent with the same acceleration. how much force did the floor on the south end of the court exert on the ball?(1 point)
The force exerted by the racket on the south end on the ball is 1.2 N.
Mass of the ball , m = 0.1 kg, velocity of the ball, v₁ = 65 km/h = 18.06 m/s. Distance travelled by the ball, S = 23.78.
S = v₁t + 1/2at²
23.78 = 18.06t + 5t²
t = 1.7 s
F = ΔP
F = mv₂ /t, F = 0.1 x 20.83/1.7 and F = 1.2 N.
A push or a pull that an object experiences as a result of interacting with another item is known as a force. some forces are the result of contact interactions (normal, frictional, tensional, and applied forces are examples of contact forces), whilst other forces (gravitational, electrical, and magnetic forces) are the consequence of action-at-a-distance interactions.
Thus, The force exerted by the racket on the south end on the ball is 1.2 N.
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what is the current through a long straight wire if the magnetic field at a point 3.70 cm away is 1.70 t?
The current through the long straight wire is 45.7 A.
The magnetic field produced by a long straight wire carrying a current is given by the formula B = (μ0I)/(2πr), where B is the magnetic field, μ0 is the permeability of free space, I is the current, and r is the distance from the wire. Rearranging the formula to solve for I, we get I = (2πrB)/μ0.
Substituting the given values, we have B = 1.70 T and r = 0.0370 m. The permeability of free space μ0 is a constant equal to 4π × 10⁻⁷ T·m/A. Thus, we can calculate the current I as I = (2π0.0370 m1.70 T)/(4π × 10⁻⁷ T·m/A) = 45.7 A.
Therefore, the current through the long straight wire is 45.7 A.
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Two charged balloons, one black and one red, are separated by some distance r. The black balloon has 5 times the charge of the red balloon The black balloon exerts a force of F black-red on the red balloon, and the red balloon exerts a force of F red-black on the black balloon. How does the magnitude of F black-red compare to F red-black?
The magnitude of F black-red compared to F red-black 5 times greater.
Gravitational force problemThe force exerted between two charged objects is given by Coulomb's law:
F = k * (q1 * q2) / r^2
where F is the force, k is Coulomb's constant, q1 and q2 are the charges of the two objects, and r is the distance between them.Let's denote the charge on the red balloon as q_red and the charge on the black balloon as q_black. Since the black balloon has 5 times the charge of the red balloon, we can write:
q_black = 5 * q_red
Now let's consider the force exerted by the black balloon on the red balloon. According to Coulomb's law, this force is given by:
F_black-red = k * (q_black * q_red) / r^2
Substituting q_black = 5 * q_red, we get:
F_black-red = k * (5 * q_red * q_red) / r^2
Simplifying this expression, we get:
F_black-red = 5 * (k * q_red^2) / r^2
Similarly, the force exerted by the red balloon on the black balloon is given by:
F_red-black = k * (q_red * q_black) / r^2
Substituting q_black = 5 * q_red, we get:
F_red-black = k * (q_red * 5 * q_red) / r^2
Simplifying this expression, we get:
F_red-black = 5 * (k * q_red^2) / r^2
Comparing the two expressions, we can see that:
F_black-red = 5 * F_red-black
Therefore, the magnitude of the force exerted by the black balloon on the red balloon is 5 times greater than the magnitude of the force exerted by the red balloon on the black balloon.
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one end of a 3.0-m rope is tied to a tree; the other end is tied to a car stuck in the mud. the motorist pulls sideways on the midpoint of the rope, displacing it a distance of 0.25 m. if he exerts a force of 200.0 n under these conditions, determine the force exerted on the car.
The force exerted on the car when motorist is pulling on the midpoint of the 3.0-m rope is 400 N.
The question involves the determination of the force exerted on the car when one end of a 3.0-m rope is tied to a tree; the other end is tied to a car stuck in the mud.
The motorist pulls sideways on the midpoint of the rope, displacing it a distance of 0.25 m. If he exerts a force of 200.0 N. Under these conditions, the force exerted on the car can be calculated as follows;
Since the displacement of the rope is perpendicular to the direction of the applied force, the component of the force perpendicular to the rope's direction must be considered. We can calculate the force perpendicular to the direction of the applied force as follows;
F_perpendicular = F x sinθ
where, F is the force exerted, and θ is the angle between the force and the direction of the rope (90°).
Therefore,
F_perpendicular = 200 x sin(90°) = 200 x 1 = 200 N
The force acting on the car is the force in the direction of the rope, which is equal to two times the force perpendicular to the rope direction. Therefore,
F_car = 2 x F_perpendicular
F_car = 2 x 200 N = 400 N
Therefore, the force exerted on the car is 400 N.
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What type of volcanic material indicates an eruption under water? a) AA flows b) Pyroclastic flows c) Pillow lavas d) Pahoehoe flows. e) Pillow lavas.
The type of volcanic material that indicates an eruption underwater is pillow lavas. So the correct answer is option C or E.
Pillow lavas are igneous rock formations that occur when magma extrudes from a volcano's vent and cools quickly under seawater or other bodies of water. When magma comes into contact with the water, it cools quickly and solidifies into what looks like a pile of stacked pillows. Pillow lavas are a clear indication of an underwater eruption. Pillow lavas are typically found in submarine basaltic volcanoes, which are located near mid-ocean ridges, and can be found in a variety of other underwater volcanic settings.
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a 70 n force pulls a box straight up 5 m above the ground. if the box is not moving after it is lifted, what type of energy does it now have? a. chemical b. elastic c. gravitational d. kinetic
The box has gravitational energy. Therefore, option c is correct.
Gravitational potential energy is the energy an object has due to its position in a gravitational field. When the box is lifted to a height of 5m above the ground, it gains an amount of gravitational potential energy equal to the work done on it, which is equal to the force (70N) multiplied by the distance (5m).
When a 70 N force pulls a box straight up 5 m above the ground, and the box is not moving after it is lifted, the type of energy it now has is gravitational energy. Gravitational potential energy is the potential energy stored in an object because of its height over the Earth's surface. An object that has been lifted above the ground has the ability to do work when it falls back to the ground. The work is generated by the object's gravitational potential energy, which is a function of its mass and height over the ground.
As a result, the option c, gravitational, is the correct answer.
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Physics is the branch of science that involves the study of physical phenomena in order to
establish patterns.
false
true
True. In order to develop patterns, the study of physical phenomena is considered to be a part of physics.
Is physics the scientific discipline that studies phenomena?The field of research known as physics studies the interactions between the underlying elements of the cosmos and the structure of matter. Quantum mechanics is used to study very small objects, and general relativity is used to study everything in the universe.
Does a field of physical science that focuses on heavenly phenomena and objects fall under the category of natural science?The study of celestial objects and space in general—basically, everything outside of Earth's atmosphere—is known as astronomy.
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Which fossil fuel has the highest heating value per pound?A) CoalB) OilC) Natural gas.
The correct answer is A) Coal. Coal has the highest heating value per pound compared to oil and natural gas.
This is due to the fact that coal has a higher carbon content and burns more slowly and steadily than other fossil fuels. To further explain, coal is a black or brown rock-like substance that is composed primarily of carbon.
It is formed over millions of years from the remains of ancient plants that were buried and subjected to high pressure and heat. Coal is typically burned to produce electricity and heat, and it is a primary energy source for many countries around the world.
Oil and natural gas are also fossil fuels, but they have lower heating values per pound than coal. Oil is a liquid petroleum product that is refined from crude oil and is used primarily as a transportation fuel.
Natural gas is a colorless, odorless gas that is primarily composed of methane and is used for heating, cooking, and electricity generation. While these fossil fuels are also important sources of energy, coal has the highest heating value per pound.
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at some distance away from a long, straight current carrying wire, in what direction does the magnetic field point?
At some distance away from a long, straight current carrying wire, the magnetic field points perpendicular to the wire. This is known as the right-hand rule, which is used to determine the direction of the magnetic field in relation to the direction of the current flow.
A long, straight current-carrying wire produces a magnetic field, and the direction of the field is determined by the right-hand rule. This rule states that if you wrap your right hand around the wire in such a way that your thumb points in the direction of the current, your fingers will point in the direction of the magnetic field.
The direction of the magnetic field can also be determined by the direction of the current flow. The field is perpendicular to the wire and circular around the wire. This means that the field lines of the magnetic field are circular around the wire, and they point in the direction of the current flow.
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A student places a transparent semicircular block on a sheet of paper and draws
around the block. She directs a ray of light at the centre of the flat edge of the block.
Figure 1 shows the path of the ray through the block.
Figure 1
incident ray
centre of the flat
edge of the block
transparent
semicircular block
emergent ray \ sheet of paper
[foya}(4] State why the emergent ray does not change direction as it leaves the block.
[1 mark]
Answer:incidence
Explanation: Because it depends on incident
The electric field in a region of space is Ex = -1000 xV/m, where x is in meters. What is the potential difference between xi = −30cm and xf = 60cm? I got -900 but it is wrong.
The potential difference between xi = -30 cm and xf = 60 cm for the given electric field is -135 V.
To find the potential difference follow these steps:
1. Convert the given positions from centimeters to meters: xi = -0.3 m and xf = 0.6 m.
2. Calculate the potential difference using the formula ΔV = -∫(E(x) dx) over the interval [xi, xf].
3. Integrate the electric field function, Ex = -1000 x, with respect to x: ∫(-1000 x dx) = -500 x² + C, where C is the integration constant.
4. Find the potential difference by evaluating the integral at the given points: ΔV = -500 (xf² - xi^2) = -500 (0.6² - (-0.3)^2) = -500 (0.36 - 0.09) = -500 (0.27).
5. Calculate the result: ΔV = -500 * 0.27 = -135 V.
The potential difference between xi = -30 cm and xf = 60 cm for the given electric field is -135 V.
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superman throws a boulder of weight 2200 n at an adversary. what horizontal force must superman apply to the boulder to give it a horizontal acceleration of 13.0 m/s2 ?
Superman must apply a horizontal force of 2918.5 N to the boulder to give it a horizontal acceleration of 13.0 m/s^2.
We can use Newton's second law, which states that force equals mass times acceleration. In this case, the mass of the boulder is not given, so we cannot directly calculate the force. However, we know that weight is equal to mass times the acceleration due to gravity (9.8 m/s^2), so we can use this relationship to determine the mass of the boulder.
[tex]2200 N = m * 9.8 m/s^2\\\Solving for mass, we get:\\\m = 224.5 kg[/tex]
We can use Newton's second law to find the horizontal force:
[tex]F = m * a = 224.5 kg * 13.0 m/s^{2 }= 2918.5 N[/tex]
Therefore, Superman must apply a horizontal force of 2918.5 N to the boulder to give it a horizontal acceleration of 13.0 m/s^2.
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the term we use to generally describe the total incoming solar energy from the sun to the earth is called
The term we use to generally describe the total incoming solar energy from the sun to the Earth is called solar radiation or solar insolation.
This refers to the electromagnetic radiation emitted by the sun, which includes visible light, ultraviolet (UV) radiation, and infrared (IR) radiation, among others. Solar radiation is the primary source of energy that drives many Earth systems, such as the atmosphere, oceans, and land surface. It is responsible for warming the Earth's surface and fuels photosynthesis in plants, among other important processes. The amount and distribution of solar radiation that reaches the Earth's surface depend on various factors, including latitude, time of day, season, and atmospheric conditions.
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---The complete question is, the term we use to generally describe the total incoming solar energy from the sun to the earth is called ___________.------
Which situations show examples of work occurring? Check all that apply
Examples of work taking place include options 1, 2, and 3.
Work is said to be done when a force causes a displacement in an object in the direction of the force. The following situations are examples of work occurring:
Lifting a box off the ground: The force of lifting the box causes a displacement in the box in the upward direction, which is the same direction as the force applied. Therefore, work is done on the box.
Pushing a car up a hill: The force of pushing the car causes a displacement in the car in the direction of the hill, which is the same direction as the force applied. Therefore, work is done on the car.
Carrying a backpack: Although the backpack may not be moving, work is still being done because the force of carrying the backpack causes a displacement in the person's body in the upward direction.
Holding a heavy object: If a person is holding a heavy object, but not moving it, no work is being done on the object because there is no displacement. However, the person's muscles are still working to maintain the position, which is an example of isometric work.
Therefore, options 1, 2, and 3 are examples of work occurring. Option 4 is not an example of work being done on the object, but it is an example of work being done by the person's muscles.
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What is the net force if two equal forces are acting in opposite directions on an object? [1MARK]
If two equal forces are acting in opposite directions on an object, the net force is zero.
The net force when two equal forces are acting in opposite directions on an object is zero. Here's a step-by-step explanation:
1. First, identify the magnitudes and directions of the two forces acting on the object. Let's say force F1 acts in the positive direction, and force [tex]F_2[/tex] acts in the negative direction.
2. Since the forces are equal in magnitude, we can represent them as [tex]F_1[/tex] = [tex]F_2[/tex]
3. Net force is the vector sum of all individual forces acting on the object.
In this case, we only have two forces: [tex]F_1[/tex] and [tex]F_2[/tex].
To calculate the net force, we can use the formula:
Net Force = [tex]F_1[/tex] + [tex]F_2[/tex]
4. As [tex]F_1[/tex] and [tex]F_1[/tex] are acting in opposite directions, we need to take into account their directions when calculating the net force.
As [tex]F_1[/tex] is in the positive direction and [tex]F_2[/tex] is in the negative direction, the formula becomes:
Net Force = [tex]F_1[/tex] - [tex]F_2[/tex]
5. Now, we can substitute the values of [tex]F_1[/tex] and [tex]F_2[/tex].
Since [tex]F_1[/tex] = [tex]F_2[/tex], the equation becomes:
Net Force = [tex]F_1[/tex] - [tex]F_1[/tex].
6. Finally, when we subtract [tex]F_1[/tex] from itself, the result is zero.
Therefore, the net force is zero when two equal forces are acting in opposite directions on an object.
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the current in an electromagnet connected to a 240 v line is 17.5 a. at what rate must cooling water pass over the coil if water temperature is to rise no more than 6.5 k?
To determine the rate at which cooling water must pass over the coil, we need to find the power of the electromagnet and then use the specific heat capacity of water to calculate the required mass flow rate.
Explanation:
Step 1: Calculate the power of the electromagnet.
Power = Voltage x Current
Power = 240 V x 17.5 A = 4200 W
Step 2: Determine the specific heat capacity of water.
The specific heat capacity of water is approximately 4.18 J/(g ·K).
Step 3: Calculate the required mass flow rate.
Power = mass_ flow_ rate x specific_ heat_ capacity x temperature_ rise
4200 W = mass_ flow_ rate x 4.18 J/(g ·K) x 6.5 K
Rearrange the formula to find the mass flow rate:
mass_ flow_ rate = 4200 W / (4.18 J/(g· K) x 6.5 K)
mass_ flow_ rate = 4200 W / (27.17 J/g) = 154.54 g/s
So, the cooling water must pass over the coil at a rate of 154.54 g/s to keep the water temperature rise no more than 6.5 K.
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you are riding in a train. since the train car is almost empty, you and your friend are pushing a cart (with almost no friction) back and forth between the front and rear of the car. the train is moving at a speed of 5.4m/s and each time you push the cart, the cart has a speed of 2.4m/s. what is the velocity of the cart relative to the ground when the cart is moving toward the front of the car
The relative velocity of the cart relative to the ground when the cart is moving toward the front of the car is 3 m/s.
Given Data:
Train's speed, v = 5.4 m/s
Cart's speed, u = 2.4 m/s
The relative velocity of the cart relative to the ground when the cart is moving toward the front of the car is to be determined. The velocity of an object in a moving frame is equal to the sum of the velocity of the object relative to the moving frame and the velocity of the moving frame. We know that the velocity of the train, v = 5.4 m/s
When the cart is moving forward, the velocity of the cart is the sum of the velocity of the train and the velocity of the cart relative to the train. Therefore, the velocity of the cart when it is moving toward the front is given as:
v = v_train + v_cart (towards the front)v_cart = v - v_trainv_cart = 5.4 - 2.4v_cart = 3 m/s
Therefore, the relative velocity of the cart relative to the ground when the cart is moving toward the front of the car is 3 m/s.
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a point mass of 1 grams located 5 centimeters to the left of the origin and a point mass of 3 grams located 7 centimeters to the right of the origin are connected by a thin, light rod. find the center of mass of the system.
The center of mass of the system is located 1.75 centimeters to the right of the origin.
The center of mass of the system can be found using the formula:
x_cm = (m1x1 + m2x2) / (m1 + m2)
Where x_cm is the center of mass, m1, and m2 are the masses of the two-point masses, and x1 and x2 are their respective positions.
Substituting the values given, we get:
x_cm = (1 gram * -5 cm + 3 grams * 7 cm) / (1 gram + 3 grams)
x_cm = (3 grams * 2 cm) / 4 grams
x_cm = 1.5 cm
Therefore, the center of mass of the system is located 1.5 centimeters to the right of the origin.
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What is the magnitude of the force per meter of length on a straight wire carrying a 7.30 A current when perpendicular to a 0.90 T uniform magnetic field? What if the angle between the wire and field is 34.5∘?
The magnitude of the force per meter of length on the wire is 6.57 N/m when the wire is perpendicular to the magnetic field. The magnitude of the force per meter of length on the wire is 3.77 N/m when the angle between the wire and field is 34.5∘.
The magnitude of the force per meter of length on a straight wire carrying a 7.30 a current when perpendicular to a 0.90 T uniform magnetic field can be calculated using the formula:
F = B * I * L
where F is the force, B is the magnetic field, I is the current, and L is the length of the wire.
Since we want to calculate the force per meter of length, L = 1 meter.
F = 0.90 T * 7.30 A * 1 m = 6.57 N/m
If the angle between the wire and field is 34.5°, we need to use the formula:
F = B * I * L * sin(θ)
where θ is the angle between the wire and the magnetic field.
F = 0.90 T * 7.30 A * 1 m * sin(34.5°) = 6.57 N/m * sin(34.5°) ≈ 3.77 N/m
So, the magnitude of the force per meter of length is 6.57 N/m when perpendicular, and 3.77 N/m when the angle is 34.5°.
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what are the radii of a symmetric converging plastic lens (i.e., two equally curved surfaces) that will form an image on the screen twice the height of the object? (take the index of refraction of plastic to be 1.59.)
The radii of a symmetric converging plastic lens that will form an image on the screen twice the height of the object is [tex]R_1[/tex] = 4.28 cm and [tex]R_2[/tex] = 2.1333 cm.
The index of refraction of plastic is 1.59.
The height of the object = h
The height of the image = 2h
We know that the magnification formula is M = -v/u,
where M = -2 (since the height of the image is twice the height of the object),
v is the distance between the image and the lens and
u is the distance between the object and the lens.
Therefore, -v/u = -2 ... (1)
We also know that the lens formula is [tex]\frac{1}{v} - \frac{1}{u} = \frac{1}{f}[/tex],
where f is the focal length of the lens.
Since the lens is symmetric, the radius of curvature of the two surfaces will be equal, which is the same as the focal length of the lens.
Therefore, f = R/2, where R is the radius of curvature of the lens surfaces.
Substituting f = R/2 in the lens formula and simplifying it,
we get, u = 2f/3 ... (2)
We can get the value of v by substituting equation (2) in equation (1) and solving for v.
We get v = -4f/3.
Substituting u and v values in the lens formula, we get,
[tex]\frac{1}{v} - \frac{1}{u} = \frac{1}{f}[/tex], Solving for f, we get
f = 1.0667 cm.
We also know that f = R/2, so R = 2f.
Substituting f value, we get R = 2(1.0667) = 2.1333 cm.
The radii of the two surfaces of the lens will be equal, so [tex]R_1 = R_2[/tex] = 2.1333 cm.
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an empty balloon sits 10 meters away from a golf ball. jamie wants to increase the gravitational force between the two objects by filling the balloon with a substance and holding it 10 meters away from the golf ball. which substance should jamie use to increase the gravitational force between the balloon and the golf ball the most?
Jamie should use Lead as the substance to increase the gravitational force between the balloon and golf ball the most.
The gravitational force between two objects is influenced by their masses and the separation between them. The gravitational force is calculated using the formula F = G × (m1 × m2) / r², where F is the gravitational force, G is the gravitational constant, m1, and m2 are the objects' masses, and r is the separation between them. Jamie has to either reduce the distance between the items or raise their masses in order to enhance the gravitational pull between the balloon and the golf ball.
The only way to increase the gravitational force since the separation is fixed at 10 meters is to increase the masses of the objects. As a result, Jamie ought to inflate the balloon with something heavy. Jamie may increase the balloon's mass and, as a result, the gravitational pull between the balloon and the golf ball by filling the balloon with lead.
Hence, Jamie should use Lead as the substance to increase the gravitational force between the balloon and golf ball the most.
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