The moment of inertia of the system can be calculated using the formula:
I = m₁ × r² + (2/5) × m₂ × r²
where m₁ is the mass of your arm, m₂ is the mass of the ball, and r is the length of your arm.
In this scenario, the ball is rotating your arm freely, so the arm is relaxed and not providing any resistance to the rotation. Therefore, we can assume that the moment of inertia of the arm is solely due to its own mass, and we can ignore any contribution from the muscles or bones.
The moment of inertia of a point mass (the ball) is given by I = m × r².
However, since the ball is not rotating around a fixed axis, we need to use the parallel axis theorem to calculate its moment of inertia relative to the center of mass of the arm.
The theorem states that the moment of inertia of a rigid body about any axis parallel to its center of mass is equal to the moment of inertia about a parallel axis through the center of mass plus the product of the body's mass and the square of the distance between the two axes.
Assuming that the center of mass of the arm is located at the elbow joint, the distance between the center of mass and the point where the ball is caught is equal to the length of the arm r.
Therefore, the moment of inertia of the ball relative to the center of mass of the arm is:
I(ball) = m₁ × r² + m₁ × r² = 2 × m× r²
Substituting this expression into the formula for the moment of inertia of the system, we get:
I = m₁ × r² + (2/5) × 2 × m₂ × r²
= m₁ × r² + (4/5) × m₂ × r²
Therefore, the moment of inertia of the system is equal to the sum of the moment of inertia of the arm and the moment of inertia of the ball relative to the center of mass of the arm.
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at 2:10 pm it reads 50 mi/h. show that at some time between 2:00 and 2:10 the acceleration is exactly 120 mi/h2.
The acceleration is exactly 120 mi/h² at 12.5 seconds past 2:00 pm.
What is acceleration?Acceleration is the rate at which an object's velocity changes over time. It is a vector quantity, meaning it has both a magnitude and a direction. Acceleration is the rate of change of velocity, or the rate at which an object's speed or velocity changes over time. It can be calculated by dividing the change in velocity by the change in time.
In this case, we have v₂ = 50 mi/h, v1 = 0 mi/h, x = 10 min and we need to find a. We can rearrange the equation to solve for a: a = (v₂ - v₁ / (2x)
Plugging in the values from the problem, we get a = (50 - 0) / (2*10) = 25 mi/h².
Now, to find the exact time at which the acceleration is 120 mi/h2, we need to use the equation for velocity again. This time, we know v₂ = 50 mi/h, a = 120 mi/h² and x = some time t between 2:00 and 2:10. We can rearrange the equation to solve for t: t = (v₂ - v₁) / (2a)
Plugging in the values from the problem, we get t = (50 - 0) / (2*120) = 0.2083333... minutes. This is approximately 12.5 seconds.
Therefore, the acceleration is exactly 120 mi/h² at 12.5 seconds past 2:00 pm.
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A brick is dragged across a concrete floor. The type of friction that acts between the brick and the floor is ________ friction.
rolling
kinetic
fluid
static
A brick is dragged across a concrete floor. The type of friction that acts between the brick and the floor is Static friction.
What is friction ?Friction is a force that opposes the relative motion of two objects that are in contact. It is the resistive force that acts in the opposite direction of the relative motion between two objects. Friction is a non-conservative force, meaning that the total work done by friction is not conserved. Friction is caused by the roughness of the surfaces of the two objects in contact. The amount of friction between two objects depends on the materials of the two objects, the force with which they are pressed together, and the area of contact between them. Friction can be beneficial and can be used to slow down motion, or it can be detrimental and cause objects to become stuck together.
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if you stand 2.0 m in front of a plane mirror, what is the distance between you and your mirror image?
if you stand 2.0 m in front of a plane mirror, 4.0 m is the distance between you and your mirror image.
When you stand 2.0 m in front of a plane mirror, your image is formed behind the mirror, also 2.0 m away from the mirror. Therefore, the total distance between you and your mirror image is 2.0 m (from you to the mirror) + 2.0 m (from the mirror to your image) = 4.0 m.
The distance between you and your mirror image is twice the distance between you and the mirror itself, which is 4.0 m.
When you stand in front of a plane mirror, your mirror image is formed behind the mirror at a distance that is twice the distance between you and the mirror.
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how long do you need to make an organe pipe whose fundamental frequency is a c sharp? the pipe is closed on one end and the seed of sound in air is 340 m/s
To calculate the length of an organ pipe that produces a fundamental frequency of C sharp (which has a frequency of 277 Hz), we can use the following formula:
Length of organ pipe = (wave speed in air) / (4 x frequency)
Plugging in the given values, we get:
Length of organ pipe = 340 m/s / (4 x 277 Hz)
Length of organ pipe = 0.307 m or 30.7 cm
Therefore, the length of the organ pipe needs to be approximately 30.7 cm to produce a fundamental frequency of C sharp. This assumes that the pipe is closed on one end and the speed of sound in air is 340 m/s.
To calculate the length of an organ pipe with a closed end and a fundamental frequency of C sharp, you can follow these steps:
1. Determine the frequency of C sharp. The standard pitch for A4 is 440 Hz, and C sharp is 4 semitones above A. To find the frequency of C sharp, you can use the formula:
Frequency of C sharp = 440 * 2^(n/12), where n = 4 semitones.
Frequency of C sharp = 440 * 2^(4/12) ≈ 554.37 Hz
2. Use the formula for the fundamental frequency of a closed pipe:
Frequency = (2n - 1) * (v / 4L), where n = 1 (first harmonic), v = speed of sound in air (340 m/s), and L = length of the pipe.
3. Solve for L:
554.37 Hz = (2*1 - 1) * (340 m/s / 4L)
554.37 Hz = (1) * (340 m/s / 4L)
4. Rearrange to find L:
L = 340 m/s / (4 * 554.37 Hz)
L ≈ 0.153 m or 15.3 cm
So, you need to make an organ pipe whose length is approximately 15.3 cm to produce a fundamental frequency of C sharp with one closed end.
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a ball player wishes to determine pitching speed by throwing a ball horizontally from an elevation 5 m above ground level. the ball lands 20 m downrange. the player's pitching speed is about
A ball player wishes to determine pitching speed by throwing a ball horizontally from an elevation 5 m. The player pitching speed will be 20 m/s .
Option C is correct.
Elaborating:Let the time required to land on ground be t
5 = 1/2 gt²
2 × 5 / 10 = t²
t = 15
let the pitching speed be v
vt = 20
v = 20 m/s
How fast is the pitch?The speed of a pitch is estimated by the distance the ball goes in the air, from the time it passes on the pitcher's hand to the time it arrives at the catcher's glove. The typical pitching speed for a MLB player is around 93 miles each hour. The typical speed range is between 90 and 100 miles per hour.
What exactly is a fast pitch?Pitchers throw the ball underhand at speeds of up to 105 miles per hour (169 kilometers per hour) for men and up to 77 miles per hour (124 kilometers per hour) for women. Fastpitch softball pitches differently than slowpitch softball pitches.
Incomplete question:
A ball player wishes to determine pitching speed by throwing a ball horizontally from a of 5 m above the ground. The player sees the ball land 20 m down range. The player's speed is about om an elevation wer's pitching
a. 5 m /s
b. 10 m/s
C. 20 m/s
d. 25 m/s
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Which measurement unit CANNOT be used to express power?
A) kg x m^2 x s^2
B) J x s^-1
C) ft x lb x s^-1
D) W
According to the given question, ft x lb x s^-1 cannot be used to express power.
What is power?Power is the ability or capacity to do or act, to effect change, or to produce a desired result. It can refer to the capacity to influence others, control resources, or exercise authority. Power can be seen as a means of gaining authority and control, as well as a way of achieving goals. In its most basic form, power is the ability to get things done and to bring about change. It can be used for good or ill, to bring about progress or destruction, depending on the user’s intentions. Power is the ability to make decisions, to shape and influence events, and to create and maintain systems of order. It is an essential element in the functioning of human societies, and its use can be both empowering and destructive.
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Assuming no air resistance, if you dropped a penny from a cliff and it fell for 12 seconds, during which second did the penny travel the greatest distance vertically (when did it fall the farthest?a) 1-2 seconds b) 3- 4 sec c) 9-10 sec d) 10-11 sec
the penny falls with constant acceleration, and the distance traveled increases quadratically with time. The greatest distance traveled vertically will be during the final second of its fall (between 11 and 12 seconds).
So the answer is option d) 10-11 seconds
The vertical distance travelled by the penny at any given time, t, may be stated as follows since it is dropped from rest:
d(t) = (1/2)gt^2
where g is the gravitational acceleration, which is around 9.81 m/s2.
We need to identify the time window that maximises d(t) in order to establish the second during which the penny covered the maximum vertical distance. Using d(t)'s derivative with regard to t, we may calculate:
d'(t) = gt
In order to determine the maximum, we set d'(t) to zero and obtain:
gt = 0
This happens at time t = 0, which corresponds to the penny's starting location after being dropped.
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4) Which one of the following quantities is the smallest unit of heat energy?
A) calorie
B) kilocalorie
C) Btu
D) joule
The smallest unit of heat energy is joule.
Joule is the SI unit of energy, and it is defined as the amount of energy required to perform work of one Newton meter (N*m). It is named after James Prescott Joule, who discovered the relationship between heat and mechanical work. The joule is used to measure various forms of energy, including thermal energy. In the context of thermal energy, the joule is used to measure the amount of heat energy transferred between two objects due to a temperature difference. The calorie and kilocalorie are non-SI units of energy commonly used in nutrition, while the Btu is a non-SI unit commonly used in the United States. However, the joule is the smallest unit of energy and is widely used in scientific and engineering applications.
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two waves are created in air and move toward outer space. wave x cannot travel in the vacuum of outer space, but wave y can. what types of waves are x and y ?
Wave X is a type of mechanical wave, such as sound, that requires a medium to travel. Since it cannot travel in a vacuum, it is likely a longitudinal wave, such as a compression wave.
What is vacuum?Vacuum is a space that contains no matter. It is an empty space that has been emptied of all matter and is often used as a reference point for other measurements. Vacuums can be artificially created in laboratories or found in nature. In the laboratory, vacuums are created by removing gas molecules from the atmosphere using a vacuum pump. In nature, vacuums may be found in space, such as between stars, or in areas where there is no atmosphere, such as the deep oceans. Vacuums may also be used to create an environment in which a certain experiment can take place without any interference from outside matter. Vacuums are essential to many scientific experiments, including those involving lasers, electrical components, and medical treatments.
Wave Y is a type of electromagnetic wave, such as radio waves, that can travel through a vacuum.
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The change in entropy equals the ______ divided by the temperature at which the heat flow occurs.
The change in entropy equals the heat transfer divided by the temperature at which the heat flow occurs.
What is temperature ?Temperature is a physical quantity that measures the degree of hotness or coldness of an object or environment. It is measured by the thermometer and is expressed in degrees Celsius (°C) or Fahrenheit (°F). Temperature is an important factor that affects the behavior of molecules, which in turn affects the state of matter, chemical reactions, and many other physical and biological processes. Temperature also plays a vital role in the Earth’s climate, helping to regulate the amount of energy released into the atmosphere. Temperature can also be used to measure the rate of heat transfer between objects, as well as its efficiency.
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To practice Problem-Solving Strategy 30.1: Inductors in Circuits. A circuit has a 5 V battery connected in series with a switch. When the switch is closed, the battery powers two paths in parallel, one of which has a resistor of resistance R1 = 85 Ω in series with an inductor of inductance L = 1.1Ã10â2 H , while the other has a resistor of resistance R2 = 270 Ω . What is the current supplied by the battery at a time t = 0.3 ms after the switch is closed?
What is the current i1 supplied by the battery a time t = 0.3 ms after the switch is closed?
The current supplied by the battery at a time t = 0.3 ms after the switch is closed is i1 = 0.0058 A.
What is current?Current is the flow of electric charge through a conductor. It is measured in amperes, which is a unit of electric current equal to one coulomb of charge passing a point in one second.
The current supplied by the battery at a time t = 0.3 ms after the switch is closed can be calculated using the equation i1 = V/R1 + (L/R1)×(di1/dt).
Since the battery is supplying a constant voltage of 5V and the initial current is 0, V = 5V and i1 = 0.
Plugging these values into the equation, we get i1 = 5V/(85 Ω) + (1.1Ã10â2 H / 85 Ω)×(di1/dt).
Differentiating both sides with respect to time, we get di1/dt = (5V/(85 Ω))/(1.1Ã10â2 H).
Substituting the value of di1/dt into the original equation and solving for i1, we get i1 = (5V/(85 Ω))×(1-e^(-t/(L/R1))).
Substituting the value of t = 0.3 ms and L/R1 = 1.1Ã10â2 H / 85 Ω, we get i1 = (5V/(85 Ω))×(1-e^(-0.3 ms/(1.1Ã10â2 H / 85 Ω)) = 0.0058 A.
Therefore, the current supplied by the battery at a time t = 0.3 ms after the switch is closed is i1 = 0.0058 A.
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the lowest energy level of a certain quantum harmonic oscillator is 5.00 ev. what is the energy of the next higher level?
The lowest energy level of a certain quantum harmonic oscillator is 5.00 ev. The energy of the next higher level of the quantum harmonic oscillator is 10.00 ev.
The energy levels of a quantum harmonic oscillator are quantized, meaning that they can only exist at certain discrete energy values. The energy difference between these levels is given by the equation E = (n + 1/2)hν, where E is the energy of the level, n is the quantum number, h is Planck's constant, and ν is the frequency of the oscillator.
In this case, we know that the lowest energy level has an energy of 5.00 ev. Using the equation above, we can solve for the energy of the next higher level by plugging in n = 1 (since we are looking for the next level), h = 4.136 × 10^-15 eV·s (Planck's constant), and ν = ? (unknown frequency).
Solving for E, we get:
E = (1 + 1/2)hν
E = 3/2 hν
Since we don't know the frequency, we can't solve for E directly. However, we do know that the energy of the next level must be twice that of the lowest level (since the energy difference between levels is constant). Therefore, the energy of the next level is:
E = 2 × 5.00 ev
E = 10.00 ev
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what value offf freactance qx could be added to make the total load seen by the generator purely resistive
To make the total load seen by the generator purely resistive, the reactive component of the load must be canceled out. This can be achieved by adding a reactance with the opposite sign and equal magnitude to that of the reactive component of the load.
Let's assume that the load has a resistance R and a reactance X. The total impedance of the load is then given by Z = R + jX, where j is the imaginary unit.
To cancel out the reactive component of the load, we need to add a reactance -X in series with the load, which gives a total impedance of Z' = R + jX - jX = R. This means that the total load seen by the generator is purely resistive, with no reactive component.
Therefore, to find the value of reactance Qx that needs to be added, we just need to find the magnitude of the reactive component of the load, which is |X|. So, Qx = |X|.
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during a power demand, the voltage output is reduced by 5.0%. by what percentage is the power on the resistor affected?
The power on the resistor is affected by a reduction of 9.75% (approximately). This can be calculated using the equation P = V^2/R, where P is power, V is voltage, and R is resistance. If the voltage output is reduced by 5.0%, the new voltage will be 0.95V (where V is the original voltage). Plugging this into the power equation and simplifying, we get:
P' = (0.95V)^2/R
P' = 0.9025V^2/R
To determine the percentage change in power, we can compare P' to the original power P:
% change = (P' - P)/P x 100%
% change = (0.9025V^2/R - V^2/R)/(V^2/R) x 100%
% change = (0.9025 - 1)/1 x 100%
% change = -0.0975 x 100%
% change = -9.75%
Therefore, the power on the resistor is reduced by approximately 9.75% during a power demand that causes a 5.0% reduction in voltage output.
During a power demand, when the voltage output is reduced by 5.0%, the power on the resistor is affected as follows:
The power (P) on a resistor can be calculated using Ohm's Law: P = V^2 / R, where V is the voltage and R is the resistance of the resistor. If the voltage is reduced by 5%, the new voltage is 0.95V.
Now, we can calculate the new power (P') with the reduced voltage: P' = (0.95V)^2 / R = 0.9025V^2 / R.
To find the percentage change in power, we can use the formula: percentage change = ((P' - P) / P) * 100%.
Plugging in the values, percentage change = ((0.9025V^2 / R - V^2 / R) / (V^2 / R)) * 100% = (0.9025 - 1) * 100% = -9.75%.
So, the power on the resistor is reduced by 9.75% when the voltage output is reduced by 5.0%.
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With two slits spaced 0.2 mm apart, and a screen at a distance of 1.0 m, the third bright fringe is found to be displayed at 7.5 mm from the
central fringe. Find the wavelength of the light use.
The wavelength of the light is 0.4 mm.
The wavelength of light can be calculated using the diffraction grating equation:
λ = 2dsin(θ/2)
Here λ is the wavelength, d is the spacing between adjacent slits, θ is the angle between the incident beam and the screen, and sin(θ/2) is the sine of half of the angle between the incident beam and the screen.
The wavelength of the light, we can substitute the given values into the diffraction grating equation as follows:
λ = 2dsin(θ/2)
here d = 0.2 mm, θ = arctan(7.5 mm / 1.0 m) = 41.5 degrees, and sin(θ/2) = 0.707.
Put these values into the diffraction grating equation, we can solve for λ as follows:
λ = 2(0.2 mm)sin(41.5 degrees)
λ = 0.4 mm
Therefore, the wavelength of the light is 0.4 mm.
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FILL IN THE BLANK. Saran Wrap has a larger electron affinity than Nylon. If Nylon is rubbed against Saran Wrap, which would end up with the excess negative charge? ____________ Explain.
If Nylon is rubbed against Saran Wrap, Saran Wrap would end up with the excess negative charge.
What is charge?Charge is an electrical property of matter that causes it to experience a force when placed in an electric field. Charges can be either positive or negative and they can be either static (unchanging over time) or dynamic (changing over time). Positive charges are attracted to negative charges, and negative charges are attracted to positive charges. Positive and negative charges can also cause repulsion, meaning that like charges will push each other away. Charges can be carried by particles such as electrons, protons or ions.
This is because Saran Wrap has a larger electron affinity, meaning it can more easily attract electrons from other materials. Nylon has a lower electron affinity, so it would be more likely to lose electrons to Saran Wrap.
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a 3.55 l helium ballon at 101 kpa is released at sea level and rises to a height where the pressure is 950 kpa. determine the final volume of the balloon and its gas law
To solve this problem, we need to use the combined gas law: (P1V1/T1) = (P2V2/T2), where P1, V1, and T1 are the initial pressure, volume, and temperature of the balloon, and P2, V2, and T2 are the final pressure, volume, and temperature of the balloon.
First, we need to convert the initial pressure of 101 kPa to 1 atm (101 kPa = 0.998 atm). We also know that the temperature of the balloon remains constant since it is released at sea level, where the temperature is roughly 15°C or 288 K.
Therefore, we can plug in the given values:
(0.998 atm)(3.55 L)/(288 K) = (950 kPa)(V2)/(288 K)
Simplifying the equation:
V2 = (0.998 atm)(3.55 L)(950 kPa)/(101 kPa)
V2 = 33.3 L
Therefore, the final volume of the balloon is 33.3 L. As for the gas law, since the temperature is constant, the gas law that applies is Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at constant temperature.
To determine the final volume of a 3.55 L helium balloon initially at 101 kPa that rises to a height where the pressure is 950 kPa, we can use Boyle's Law. Boyle's Law states that the product of the initial pressure and volume (P1V1) is equal to the product of the final pressure and volume (P2V2) for an isothermal process (constant temperature).
Step 1: Identify the initial pressure (P1), initial volume (V1), and final pressure (P2).
P1 = 101 kPa
V1 = 3.55 L
P2 = 950 kPa
Step 2: Apply Boyle's Law formula.
P1V1 = P2V2
Step 3: Solve for the final volume (V2).
V2 = P1V1 / P2
Step 4: Plug in the values and calculate V2.
V2 = (101 kPa × 3.55 L) / 950 kPa
Step 5: Calculate the final volume.
V2 ≈ 0.3768 L
The final volume of the helium balloon at 950 kPa is approximately 0.3768 L, and the gas law involved is Boyle's Law.
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suppose water is moving through a pipe. which of the following occurs as the water moves from a wide area (large radius) into a narrow area (small radius)?
A - The pressure decreases and the flow velocity increases. This phenomenon is known as the Bernoulli Principle. As the water flows from a wide area to a narrow area, the pressure decreases due to the decrease in area, while the velocity increases due to the conservation of energy.
What is Bernoulli Principle?The Bernoulli Principle, named after Swiss scientist Daniel Bernoulli, states that an increase in the speed of a fluid results in a decrease in the pressure of the fluid. This is because when a fluid moves faster, it has less time to interact with its environment and thus exert less pressure. This principle is widely used in aerodynamics, as when an aircraft moves through the air, its wings are designed to produce a decrease in pressure above the wing and an increase in pressure below the wing, which create lift. This is known as the Bernoulli Effect. Additionally, the Bernoulli Principle can be applied to the behavior of other fluids such as water and gas, and is used to explain phenomena like the Venturi effect.
This causes an increase in the kinetic energy of the water and a decrease in its potential energy, resulting in an overall increase in the flow velocity.
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Complete Question:
Suppose water is moving through a pipe. Which of the following occurs as the water moves from a wide area (large radius) into a narrow area (small radius)?
a- Both the pressure and flow velocity increase
b- Both the pressure and flow velocity decrease
c- The pressure increases and the flow velocity decreases
d- The pressure decreases and the flow velocity increases
Two conducting cylindrical wires are made out of the same material. Wire X has twice the length and twice the diameter of wire Y. What is the ratio Rx/Ry of their resistances?
A) 1/2
B) 1
C) 2
D) 4
Two conducting cylindrical wires are made out of the same material. Wire X has twice the length and twice the diameter of wire Y. The ratio of their resistances Rx/Ry is 1/2.
The resistance of a cylindrical wire depends on its length and cross-sectional area, and is given by the formula: R = (ρL) / A, where ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area. Since both wires are made of the same material, they have the same resistivity ρ.
Wire X has twice the length and twice the diameter of wire Y. The length of wire Y is L and its cross-sectional area is A. Therefore, the length of wire X is 2L and its cross-sectional area is 4A (since the diameter is doubled, the area is quadrupled).
Using the formula for resistance, the ratio of the resistances of the two wires is:
Rx/Ry = [(ρ x 2L) / (4A)] / [(ρ x L) / A] = 1/2
Therefore, the answer is A) 1/2.
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Which two parts must all electric circuits contain?.
All electric circuits must contain two essential parts: a source of electrical potential difference, also known as a voltage source, and a closed path, also known as a circuit, for the current to flow through.
The voltage source provides the electrical potential difference, which pushes the electrons in the circuit to flow from one point to another. This voltage can come from a variety of sources, such as batteries, generators, or power supplies. Without a voltage source, there is no electrical potential difference, and no current can flow through the circuit.
The closed path or circuit is necessary to provide a continuous path for the electrons to flow from the voltage source through the components in the circuit and back to the voltage source again. If the circuit is broken or open, the current cannot flow, and the circuit will not work. Therefore, the circuit must be a continuous loop of conductive material, such as wires or conductive tracks on a printed circuit board, that connects all of the components in the circuit.
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The positive point charges repel each other with force 0.36 N when their separation in 1.5 m. What force do they exert on each other when their separation is 1.0 m?
A) 0.81 N
B) 0.36 N
C) 0.24 N
D) 0.16 N
We can use Coulomb's law to solve this problem. Coulomb's law states that the 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.
Let's assume the two point charges have a charge of +q each. Using Coulomb's law, we can write:
F = k * (q1 * q2) / r^2
where F is the force between the charges, k is Coulomb's constant (9 x 10^9 Nm^2/C^2), q1 and q2 are the charges of the two point charges, and r is the distance between them.
When the separation between the charges is 1.5 m, the force between them is 0.36 N. Using this information, we can solve for the value of q:
0.36 = k * (q * q) / (1.5^2)
q^2 = (0.36 * 1.5^2) / k
q = 1.5 x 10^-6 C
Now, let's calculate the force when the separation between the charges is 1.0 m:
F = k * (q1 * q2) / r^2
F = (9 x 10^9) * (1.5 x 10^-6) * (1.5 x 10^-6) / (1^2)
F = 2.025 x 10^-15 N
Therefore, the answer is D) 0.16 N (rounded to two significant figures).
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A motorboat is driven across a river at 3.00 km/hr at right angles to a current that is flowing at 10.0 km/hr. What is the resulting speed of the motorboat?
The resulting speed of the motorboat is 10.4 km/hr.
To find the resulting speed of the motorboat, we can use the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the hypotenuse represents the resulting speed of the motorboat, and the other two sides represent the velocity of the motorboat and the velocity of the current.
Using this formula, we can calculate the resulting speed of the motorboat as follows:
Resulting speed = √(velocity of motorboat)^2 + (velocity of current)^2
Resulting speed = √(3.00 km/hr)^2 + (10.0 km/hr)^2
Resulting speed = √(9.00 km^2/hr^2 + 100.0 km^2/hr^2)
Resulting speed = √109 km^2/hr^2
Resulting speed = 10.4 km/hr (rounded to one decimal place)
Therefore, the resulting speed of the motorboat is 10.4 km/hr.
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draw a sketch showing the major parts of the grating spectrometer used in the experiment. describe their functions.
Monochromator, This is a device that uses a grating to separate a beam of light into its component wavelengths. It is used to select a particular wavelength from the spectrum of light and then send it to the detector.
What is wavelengths?Wavelengths are a measure of distance between two successive crests or troughs of a wave. Wavelengths can represent a variety of different wave forms, including sound waves, light waves, radio waves, and X-rays. Wavelengths are measured in various units, including meters (m), Angstroms (Å), nanometers (nm), and micrometers (μm). The wavelength of a wave is inversely proportional to its frequency; in other words, the higher the frequency, the shorter the wavelength. Wavelengths are an important factor in determining what type of wave is being emitted from a particular source.
The sketch of the grating spectrometer used in the experiment can be represented as follows:
1.Monochromator – This is a device that uses a grating to separate a beam of light into its component wavelengths. It is used to select a particular wavelength from the spectrum of light and then send it to the detector.
2. Slit – This is a narrow opening in the monochromator that limits the amount of light that can pass through.
3. Detector – This is the device that measures the intensity of the light at the selected wavelength.
4. Grating – This is a component of the monochromator that is used to separate the light into its component wavelengths.
5. Mirror – This is used to redirect the light beam onto the grating.
The functions of these components are as follows:
The monochromator is used to select a specific wavelength of light from the spectrum of light and send it to the detector. The slit is used to limit the amount of light that can pass through. The detector is used to measure the intensity of the light at the selected wavelength. The grating is used to split the light into its component wavelengths.
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A ball is thrown with an initial velocity of 20 m/s at an angle of 60° above the horizontal. If we can neglect air resistance, what is the horizontal component of its instantaneous velocity at the exact top of its trajectory?.
At the exact top of its trajectory, the ball's vertical component of velocity is zero. Therefore, the horizontal component of its instantaneous velocity is simply the same as its initial horizontal velocity, which can be found by using trigonometry to calculate the horizontal component of the initial velocity:
horizontal component of initial velocity = initial velocity * cos(θ)
where θ = 60°
Plugging in the values given:
horizontal component of initial velocity = 20 m/s * cos(60°)
= 10 m/s
Therefore, the horizontal component of the ball's instantaneous velocity at the exact top of its trajectory is 10 m/s.
The horizontal component of velocity remains constant throughout the trajectory, as there is no air resistance. At the top of its trajectory, the horizontal component of the ball's instantaneous velocity is 10 m/s.
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2. A small electronic device is rated at 0.25 W when connected to 120 V. What is the resistance of this device?
The resistance of the small electronic device is 576 ohms.
To find the resistance of the device, we can use Ohm's law, which states that resistance (R) is equal to voltage (V) divided by current (I). However, we don't know the current, so we need to use another equation: power (P) is equal to voltage (V) times current (I). We can rearrange this equation to solve for current: I = P/V.
To solve this problem, we can use the formula for power in terms of voltage and resistance, which is:
P = V^2 / R
where P is power, V is voltage, and R is resistance.
We are given that the power rating of the device is 0.25 W and the voltage is 120 V. Plugging these values into the formula, we get:
0.25 = 120^2 / R
To solve for R, we can rearrange the equation:
R = 120^2 / 0.25
R = 57,600 ohms
Therefore, the resistance of the device is 57,600 ohms.
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Athletes "follow through" when swinging because it helps increase the change of momentum of the ball the are swinging at. TrueFalse
Athletes "follow through" when swinging because it helps increase the change of momentum of the ball the are swinging. - True.
"Follow through" refers to the continuation of the motion of a sports movement after the ball or object has been hit. In sports such as golf, tennis, and baseball, athletes are often taught to follow through to help increase the change of momentum of the ball they are hitting. This is because the follow-through motion allows the athlete to transfer more energy from their body to the ball, resulting in a greater change in momentum of the ball.
In physics, momentum is defined as the product of mass and velocity, and it is conserved in a closed system. Therefore, increasing the momentum of the ball results in a greater force exerted on it, which can lead to a more powerful shot or hit. Additionally, the follow-through motion also helps the athlete maintain proper form and reduces the risk of injury.
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you are standing at the top of a tall building and drop a stone. you hear the sound of the stone hitting the street below 2.7 s later. if the speed of sound in air is 343 m/s, how high is the building?
The building is about 49.8 meters high. We can use the formula d=1/2gt², where d is the distance, g is the acceleration due to gravity (9.8 m/s²), and t is the time.
To solve this problem, we can use the fact that the time it takes for the sound to travel from the stone to the ground is equal to the time it takes for the stone to fall from the top of the building to the ground.
We can use the formula for the distance traveled by an object in free fall: d = 1/2 gt², where d is the distance, g is the acceleration due to gravity (9.8 m/s²), and t is the time.
In this case, the time for the stone to fall is the same as the time for the sound to travel up to the observer, so we can use the equation: d = 1/2 gt² = (343 m/s)(2.7 s)/2 = 49.8 meters. Therefore, the building is approximately 49.8 meters high.
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a comparison of asteroids and terrestrial planets would reveal that both are: group of answer choices located beyond the effect of solar heat and wind. large and dense, compared to the jovian planets. made primarily of gases. composed of chunks of ice surrounded by solid material. relatively rocky and small.
A comparison of asteroids and terrestrial planets would reveal that both are relatively rocky and small. Terrestrial planets, which include Mercury, Venus, Earth, and Mars, are primarily composed of rock and metal.
Similarly, asteroids are also made up of rock and metal, though they can have some amounts of ice and other materials.
Both asteroids and terrestrial planets are smaller and denser compared to the Jovian planets, which are large gas giants like Jupiter and Saturn.
While Jovian planets are made primarily of gases like hydrogen and helium, terrestrial planets and asteroids have a more solid composition.
The locations of terrestrial planets and asteroids differ, as terrestrial planets are situated closer to the Sun and are more affected by solar heat and wind.
Meanwhile, the Asteroid Belt, which contains most asteroids, is located between Mars and Jupiter, farther from the Sun's direct influence.
In summary, a comparison between asteroids and terrestrial planets would show that they are both relatively small and rocky, with a denser composition compared to the gas giants.
However, their locations in the solar system differ, with terrestrial planets being closer to the Sun and asteroids residing in the Asteroid Belt.
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Where would a brown dwarf be located on an h-r diagram?.
A brown dwarf would be located in the lower right corner of an H-R diagram, where it is cooler and less luminous than main sequence stars.
This is because brown dwarfs are objects that are not massive enough to sustain nuclear fusion in their cores, so they emit very little light and heat. In a direct and detailed answer, a brown dwarf would be located below the main sequence on the H-R diagram, closer to the bottom right corner where the temperature is cooler and luminosity is lower. This location reflects the fact that brown dwarfs are not true stars, but are more massive than planets, and have a unique place in the astronomical landscape.
A brown dwarf would be located on the lower right side of the H-R diagram. This position represents lower luminosity (brightness) and cooler temperatures, as brown dwarfs are not massive enough to sustain nuclear fusion in their cores like main sequence stars.
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the magnitutde of the resultant of 2 forces acting ona body is 12 n. which parid of forces acting ont he vody can combine to produce this resultant?
In order to determine which part of the forces acting on a body can combine to produce a resultant magnitude of 12 N, we need to first understand what is meant by the terms "magnitude" and "resultant".
Magnitude refers to the size or strength of a force. In this case, the magnitude of the resultant force is given as 12 N, which means that the total strength of the two forces acting on the body is equivalent to 12 N.
Resultant, on the other hand, refers to the net or overall effect of multiple forces acting on an object. It is the sum or combination of all the individual forces, taking into account their direction and magnitude.
So, to answer the question, we need to identify which part of the forces acting on the body can combine to give us a resultant magnitude of 12 N. This could be any combination of the two forces, as long as their magnitudes and directions are such that they add up to 12 N. For example, if one force is 8 N and the other is 4 N, and they are acting in opposite directions, then they could combine to give us a resultant of 12 N (8 N - 4 N = 12 N). Alternatively, if one force is 10 N and the other is 2 N, and they are acting in the same direction, then they could also combine to give us a resultant of 12 N (10 N + 2 N = 12 N).
In summary, any combination of the two forces acting on the body could potentially produce a resultant magnitude of 12 N, as long as their magnitudes and directions are such that they add up to that value.
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