A bullet with a mass of 7.91 g and a speed of 352 m/s penetrates a tree horizontally to a depth of 4.86 cm. What is the frictional force?
The frictional force acting on the bullet is 16.08 N. The force produced when two surfaces slide past one another and make contact is known as frictional force.
How does frictional force work?Friction is a force that prevents two solid objects from rolling or sliding over one another. Although frictional forces, such as the traction required to walk without slipping, may be advantageous, they can provide a significant amount of resistance to motion.
we need to use the equation for work done by friction.
The work done by friction is:
W = F_friction * d
F_friction = W / d
where F_friction is the frictional force.
To find the work done by friction, we need to use the kinetic energy equation:
KE = 1/2 * m * v^2
where KE = kinetic energy of the bullet, m = mass of the bullet, and v = velocity of the bullet.
W = KE
Substituting the values,
KE = 1/2 * m * v^2
KE = 1/2 * 0.00791 kg * (352 m/s)^2
KE = 0.782 J
So, the work done by friction is 0.782 J.
Now, we can use the given depth of penetration to find the distance over which the frictional force acts:
d = 0.0486 m
we can use the equation for the frictional force,
F_friction = W / d
F_friction = 0.782 J / 0.0486 m
F_friction = 16.08 N
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Two bar magnets are placed on the table a few inches apart. Then a compass is placed near them, as shown below. Draw an arrow on the compass that represents the direction the needle will point because of the magnetic field between the magnets. Explain what would cause the compass needle to point in that direction using the terms magnetic force and magnetic field.
Answer:
Explanation:
The reson that the north of the compas pin points in that direction is because ,that is Earth magnetic south pole is and that is where they attract
an iron rod is 2.58m long at 0°c. calculate the length of a brass rod at 0°c if the difference between the length of the two rods must remain the same at all temperatures. ( linear expansivity of iron= 1.2 ×10^-5k^-1, linear expansivity of brass= 1.9 × 10^-5k^-1)
Answer:
1.63 m
Explanation:
difference between the length of iron rod and brass rod must remain same, writing it in the equation form
[tex]l_{iron} - l_{brass} = C[/tex]
where C is a constant, differentiation both sides with respect to temperature([tex]\theta[/tex]),
[tex]\dfrac{dl_{iron}}{d\theta} - \dfrac{dl_{brass}}{d\theta} = 0[/tex] ... (1)
According to linear expansion equation,
[tex]\dfrac{dl}{d\theta} = \alpha l_0[/tex]
where [tex]l_0[/tex] is the length at 0 degree Celsius.
Now,
substituting values in equation 1 we get,
[tex]\alpha_{iron}. l_{iron} - \alpha_{brass} . l_{brass} = 0[/tex]
substituting the values of respective coefficient and length of iron at 0 degree Celsius we get,
[tex]l_{brass} = 1.63[/tex] m
Hopefully, this answer helped you solve the question!
A conductor of square with sides of length 2d, carries a current I uniformly distributed throughout its cross-sectional area.
The current in the conductor is directed out of the screen.
Ampère’s law is applied along the circle that touches the four sides of the conductor.
Select the expression that correctly represents the magnitude of the integral around the circle.
Group of answer choices
µ0(πd2I)
µ0(2πdI)
µ0(πI/4)
µ0(4I/π)
If you cut a wire directly and squarely across its width, the end will look like a circle. The cross sectional is the area of that end.
What is a conductor's cross sectional area?If you cut a wire directly and squarely across its width, the end will look like a circle. The cross sectionarea is Pi x r2, which is the area of that end. When the wire type is the same, a larger cross section area results in lower resistance per foot.
What is the relationship between conductor length and cross section area?It is assumed that the cross's length and area The conductor's section is doubled. This means that the new length and cross sectional area are both 2l and 2A. As a result, the new resistance of the conductor is R′=2l2A=lA.
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Consider the diagram of a pendulum's motion shown above. A pendulum can be used to model the change from potential energy to kinetic energy and back to potential energy. If you pull the bob back to point A and release it, potential energy is converted to kinetic energy. What do you think happens to the energy at point C?
A Potential energy is converted to kinetic energy.
B Potential energy decreases.
C Kinetic energy increases.
D Kinetic energy is converted to potential energy.
The correct answer is A. Potential energy is converted to kinetic energy.
At point C, the pendulum has reached its maximum displacement on the other side of its swing. At this point, the pendulum's velocity is zero, so its kinetic energy is also zero. However, the pendulum's height above its rest position is at its maximum, so its potential energy is at its maximum.
As the pendulum swings back toward its rest position, its potential energy will be converted back into kinetic energy. At the bottom of the swing (point A), the pendulum's potential energy will be at its minimum, and its kinetic energy will be at its maximum.
Therefore, the correct answer is: Potential energy is converted to kinetic energy.
What is Potential energy?
Potential energy is a form of energy that an object possesses due to its position or state. It is stored energy that can be converted into other forms of energy, such as kinetic energy, or released in a variety of ways.
What is kinetic energy?
Kinetic energy is a form of energy that an object possesses due to its motion. It is the energy an object has because of its motion, mass, and velocity. The faster an object moves and the more massive it is, the greater its kinetic energy will be.
The formula for kinetic energy is:
KE = 1/2 * m * v^2
where KE is kinetic energy, m is the mass of the object, and v is the velocity of the object.
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See Figure 1. What was the average yearly ice loss in 1980 versus 2010?
Between 1980 and 2010, there were significant differences in the average annual ice loss of glacial mass balance between different glaciers and geographical areas. This suggests that ice loss has risen since the 1980s.
What was the glacier mass balance's average annual ice loss between 1980 and 2010?The average annual mass balance of reference glaciers globally between 1980 and 1999 was -0.50 m water equivalent (w.e.) per year, while between 2000 and 2017 it was -0.69 m w.e. per year, according to the World Glacier Monitoring Service. This shows a pattern of higher ice loss compared to the 1980s and 1990s in recent years. It's crucial to remember that this figure represents an average across a significant number of glaciers.
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Look carefully at this telescopic photo of the Moon. All the following statements are true. Which one is proved by the fact that the line dividing the dark and bright regions is not perfectly straight?
The Moon's surface is not perfectly smooth but rather has mountains and valleys.
Answer:
Yes you're correct
Explanation:
The Moon's surface is not perfectly smooth but rather has mountains and valleys. Imagine looking at a sponge at a certain angle and put a dim flashlight behind the sponge. You can see that the grooves make it so its not a perfectly straight shadow.
The fact that the line dividing the dark and bright regions of the Moon is not perfectly straight proves that the Moon's surface is not perfectly smooth but rather has mountains and valleys.This is because the terrain of the Moon is comprised of mountains, craters, and valleys, meaning that the line separating the dark and bright regions will not be completely straight.
The irregularities of the terrain cause the line to appear wavy, and thus not completely straight. This tells us that the surface of the Moon is far from perfectly smooth.
To illustrate this further, a comparison can be drawn between the Moon and a billiard ball. If the Moon's surface were perfectly smooth, the line separating the dark and bright regions would be perfectly straight, just as if a billiard ball had been sliced in half. However, since the surface of the Moon is not perfectly smooth, the line appears wavy due to the irregularities of the terrain.
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assume you have two objects of the same mass m and radius r. one object is a thin hoop, and the other object is a solid cylinder. which object has a larger moment of inertia i?
For two objects of the same mass and radius, the one with more mass concentrated farther away from the axis of rotation will have a larger moment of inertia. Therefore, the moment of inertia of a solid cylinder is greater than that of a thin hoop of the same mass and radius.
The moment of inertia of a thin hoop of mass m and radius r is given by:
I_{hoop} = mr²
The moment of inertia of a solid cylinder of mass m and radius r is given by:
I_{cylinder} = (1/2)mr²
From these equations, the moment of inertia of a solid cylinder is greater than that of a thin hoop of the same mass and radius.
Therefore, a solid cylinder has a larger moment of inertia compared to a thin hoop.
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what is the biggest state? (this has nothing to do with school im testing people)
maybe a meme
The biggest state in the United States by land area is Alaska also what the meme
**s. O. P** (statement of the problem) need ngayon hehe thank youu!! Cleansing surface spots: an alternative to nylon-based cleaning brushes derived from coconut husk
An excellent green, eco-friendly substitute is coconut coir, a byproduct of coconuts. Due to its ability to clean without endangering the ecosystem, coir is becoming increasingly popular and adopted.
The shell of the coconut is known as coco coir. It is immersed in water for a few weeks after extraction to help it loosen and soften. The husk is then dried, brushed, and turned into a product that resembles fibre but is much stronger. Because of the product's durability, stretching or compressing it in any way won't harm it.
Fine brushes, ropes, beds, upholstery, and fishnets are all made from white coco coir, which is extracted from unripe coconuts.
Brown coco coir is pressed from ripe coconuts and used to create mats, pots, and scrubbers that resemble discs for cleaning kitchen surfaces and utensils. In the kitchen, these naturally antimicrobial items are preferable to plastic scrubbers. When they begin, they can be recycled as an organic planting substrate because they are not toxic.
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A negatively charged rod is brought near a metal can and the can attracts to the rod. Then additional negative charges are added to the rod and the experiment is repeated. How will the electrostatic and gravitational force between the rod and can change?
The electrostatic force between the negatively charged rod and the metal can will increase when additional negative charges are added to the rod, while the gravitational force between them will remain the same.
This is because the electrostatic force between the rod and the can is proportional to the charge on the rod and the distance between them, according to Coulomb's law. Adding additional negative charges to the rod increases its total charge, which in turn increases the electrostatic force between the rod and the can.
On the other hand, the gravitational force between the rod and the can is determined by their masses and the distance between them, according to the law of gravitation. Since neither the mass nor the distance between the rod and can changes in this experiment, the gravitational force remains the same.
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How long would it take for 300 C of electric charge to pass through an aluminum wire if the current through it is 0. 6
500 seconds (or 8 minutes and 20 seconds) for 300 C of electric charge to pass through an aluminum wire if the current through it is 0.6 A.
To answer this question, we need to use the formula:
Q = I × t
where:
Q is the electric charge in Coulombs (C)
I is the current in Amperes (A)
t is the time in seconds (s)
We can rearrange this formula to solve for t:
t = Q / I
Substituting the given values, we get:
t = 300 C / 0.6 A
t = 500 seconds
Therefore, it would take 500 seconds (or 8 minutes and 20 seconds) for 300 C of electric charge to pass through an aluminum wire if the current through it is 0.6 A.
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A U-Shaped tube of constant cross-sectional area contains water of density 1000kg/m cubed. Bothe side of the tube are open to the atmosphere. The atmospheric pressure is 1. 00 x 10 to the power of 5. The left hand side is now connected to a gas supply using a length of rubber tubing. This causes the level of the water in the left hand side to drop by 0. 200m. Calculate the pressure of the gas supply. Give your answer to 3 significant figures
Answer:
If the water in the left side drops .2 m then the water on the right side rises by .2 m
The pressure on the gas is due to the height difference of the water on the two sides.
P = ρ g h
ρ g = 9.8 m/s^2 * 1000 kg / m^3 = 9800 N/m^3 weight density of water
P = 9800 N/m^3 * .4 m = 3920 N / m^2 = 3.92E3 N/m^2
Absolute pressure of gas = 3.92E3 / 1.01E5 = .0388 atmosphere
A block with a mass of 2 kg sitting at rest on ice is pulled by a rope. The block achieves a velocity of 3
m/s, 4 seconds later, at a point 6 meters to the right of its starting point. If the blockís acceleration
was constant and the friction between the ice and block is negligible, which of the following is the
amount of work done by the force of the rope as it pulled the block through the first 6 meters?
O 117.6 J
36 J
9J
12 J
The amount of work done by the force of the rope as it pulled the block through the 6 meters is 9J.
The kinetic energy of the block is given by the formula
K = [tex]\frac{1}{2}[/tex]m[tex]v^{2}[/tex]
where,
m = mass of the block
v = velocity
Initially, the block is at rest. After being pulled by rope for 4 seconds it has an initial velocity of 3 m/s. Therefore, its final initial velocity is
Kf = [tex]\frac{1}{2}[/tex](2 kg)[tex](3 m/s) ^{2}[/tex]= 9 J
change in kinetic energy
ΔK = Kf - Ki = 9 J - 0 J = 9 J
Therefore, The amount of work done by the force of the rope as it pulled the block through the 6 meters is 9J.
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Two metal balls with the same mass hang so that they are touching each other. The ball on the left is pulled to the side
and released. What will happen when it swings back and hits the ball on the right?
Both balls will swing to the left.
The ball on the left will stop, and the ball on the right will remain still
The ball on the right will swing to the right.
Both balls will swing to the right.
When the ball on the left is pulled to the side and released, it will swing back and hit the ball on the right. Upon impact, the momentum of the left ball will be transferred to the right ball, causing the right ball to start swinging to the right while the left ball will come to a stop.
Therefore, the correct answer is: "The ball on the right will swing to the right." Option C
What is momentum about?In physics, momentum is a property of moving objects that is determined by both their mass and velocity. It is defined as the product of an object's mass and velocity, and it is a vector quantity, which means it has both magnitude and direction.
Mathematically, momentum (p) is expressed as:
p = m * v
where m is the mass of the object and v is its velocity.
Momentum is conserved in a closed system, meaning that the total momentum of the system remains constant unless an external force acts on it. This is known as the law of conservation of momentum, which is a fundamental principle of physics. The law of conservation of momentum has many practical applications, from understanding the behavior of collisions in billiards or car accidents, to designing spacecraft trajectories, to studying the behavior of subatomic particles
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Why must the negative terminals of the batteries be connected on the same side of the parallel circuit and positive terminals on the other side
The negative terminals of batteries must be connected on the same side of a parallel circuit and positive terminals on the other side to ensure that the voltage across each branch of the circuit is the same and that the batteries share the load equally.
In a parallel circuit, each branch of the circuit provides a separate path for current to flow, and the voltage across each branch is the same. Connecting the negative terminals of the batteries on the same side and the positive terminals on the other side ensures that the voltage across each branch remains the same, as the voltage drop across each battery is identical.
If the batteries were connected with opposite polarity, the voltage across each branch would be different, and the battery with the higher voltage would take on a larger share of the load, leading to unequal discharge and potentially damaging the batteries. It is essential to connect the negative terminals of the batteries on the same side and the positive terminals on the other side to ensure that each battery shares the load equally.
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The motion of an object changes only when a(n) net force acts on it according to Newton’s first law.True or False
True, The motion of an object changes only when a(n) net force acts on it according to Newton’s first law.
What is Newton's first law of motion?Newton's first law of motion, also known as the law of inertia, states that an object at rest will remain at rest, and an object in motion will remain in motion with a constant velocity, unless acted upon by a net external force.
Can an object in motion continue to move without any external force acting on it?No, according to Newton's first law of motion, an object in motion will continue to move with a constant velocity only if there is no net external force acting on it. Any change in motion requires the application of a net force.
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Consider a collar of mass m sliding on a frictionless shaft, as depicted in figure[4]. The collar can slide along the shaft and is connected to a spring of spring constant k, the other end of which is connected to the pivot point o a distance l from the shaft. The unstretched length of the spring is l. (a) how many degrees of freedom are there in this problem? describe the constraints, though you do not have to use formal equations. (b) find the equation of motion for the collar. (c) find an expression for the normal force vector between the collar and shaft as a function of x
(a) There is only one degree of freedom in this problem since the collar can move along the shaft but cannot rotate. The constraints are that the distance between the collar and the pivot point is always equal to l, and the collar cannot move perpendicular to the shaft.
(b) The forces acting on the collar are the spring force and the gravitational force. Since the collar is sliding along a frictionless shaft, there is no frictional force. The equation of motion for the collar is given by:
m(d²x/dt²) = -k(x-l) - mg
where x is the displacement of the collar from its equilibrium position.
(c) The normal force between the collar and the shaft is perpendicular to the shaft and balances the component of the gravitational force that is perpendicular to the shaft. As the collar moves away from its equilibrium position, the spring force becomes unbalanced and the normal force changes accordingly. The normal force is given by:
N = mgcos(θ) + k(x-l)sin(θ)
where theta is the angle between the shaft and the vertical axis.
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when its 75 kw (100 hp) engine is generating full power, a small single-engine airplane with mass 700 kg gains altitude at a rate of 2.5 m/s ( 150 m/min, or 500 ft/min ) . what fraction of the engine power is being used to make the airplane climb? (the remainder is used to overcome the effects of air resistance and of inefficiencies in the propeller and engine.)
The fraction of the engine power used to make the airplane climb is 0.14.
The fraction of the engine power used to make the airplane climb can be determined by the equation Pclimb/Pengine = mgh/Pengine, where Pclimb is the power used to climb, m is the mass of the airplane, g is the acceleration due to gravity, and h is the rate of climb. In this case, Pclimb = 75 kW, m = 700 kg, g = 9.81 m/s2, and h = 2.5 m/s. Plugging these numbers in, we get:
Pclimb/Pengine = (700 kg)(9.81 m/s2)(2.5 m/s)/75 kW
Pclimb/Pengine = 0.14
Therefore, the fraction of the engine power used to make the airplane climb is 0.14.
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Why does the Doppler effect detect only radial velocity?
a. For objects moving perpendicular to the line of sight, the wavelength shift can be measured only with a great error.
b. In space all bodies either converge or retreat, therefore they have only radial velocity.
c. Motion of a wave source perpendicular to the line of sight cannot cause a wavelength shift because such motion doesn't make peaks of waves closer together or farther apart.
d. Only objects moving directly toward or away from the observer can emit waves that can be detected
The correct answer is C i.e, . motion of a wave source perpendicular to the line of sight cannot cause a wavelength shift because such motion doesn't make peaks of waves closer together or farther apart.
The Doppler effect is the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. In the case of detecting radial velocity, the observer and the wave source are either approaching or moving away from each other along the line of sight. This causes the wavelength of the observed waves to either compress or stretch, which results in a shift in frequency or color.
Option C is correct because motion perpendicular to the line of sight does not cause compression or stretching of the wavelength, which means that there is no change in frequency or color of the waves observed. Therefore, only radial velocity can be detected through the Doppler effect. Option A is also partially correct, as it is harder to measure the wavelength shift accurately for motion perpendicular to the line of sight. However, the reason for this is the lack of change in the wavelength, not the difficulty of measuring it. Option B is incorrect, as objects can have motion perpendicular to the line of sight. Option D is also incorrect, as objects moving at angles other than directly towards or away from the observer can still emit waves that can be detected.
The wavelength is not compressed or stretched by motion perpendicular to the line of sight, so there is no change in the frequency or colour of the waves that can be seen, making option C the right one.
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Consider the following electrical circuit diagram in which nine identical
resistors of 3 Ω each are connected as shown. If the reading of the
ammeter A1 is 1 ampere, answer the following questions:
a) What is the relationship between the readings of A1 and A3? Give reason
b) What is the relationship between the readings A1 & A3?
c) determine the reading of the voltmeter V1 (or) find the total resistance of the circuit.
a) In a series circuit, the current remains the same throughout, so the current in the ammeter A1 is the same as the current in the ammeter A3. Therefore, the readings of A1 and A3 should be the same.
b) As mentioned in the previously, the readings of A1 and A3 should be the same since they are measuring the same current.
How to determine voltmeter reading?c) To determine the reading of the voltmeter V1, we need to know the current passing through it and the resistance between its two points. Since the circuit contains only resistors, we can apply Ohm's law to calculate the total resistance of the circuit.
The total resistance of the circuit can be calculated as follows:
Total Resistance = 9 x 3Ω (since there are nine 3Ω resistors connected in series)
Total Resistance = 27Ω
Since the current in the ammeter A1 is 1 ampere, the voltage across the voltmeter V1 can be calculated using Ohm's law:
V1 = I x R
V1 = 1 x 27
V1 = 27 volts
Therefore, the reading of the voltmeter V1 should be 27 volts.
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Suppose an electron is described by the wavefunction for , and zero otherwise, with 2 nm. Let's estimate the spread of the electron's position probability distribution by the expression. 1)what is for this wavefunctions?
The wavefunction number for the specified function is:Ψ(x) = [tex][2/(\alpha (1 - e^{(-4nm/\alpha )))}]e^{(-x/\alpha )}[/tex]
The wavefunction given is:
Ψ(x) = A[tex]e^{(-x/\alpha )}[/tex]
where Ψ(x) is the wavefunction, A is a constant, x is the position of the electron and α is a constant with units of length.
The normalization condition is:
∫|Ψ(x)|² dx = 1
Since Ψ(x) is zero outside the range (0, 2nm), the integral can be simplified to:
∫[tex]0^(2nm)|Ae^{(-x/\alpha )}|[/tex] ²dx = 1
Simplifying the integral further:
[tex]|A|^{2} (-\alpha /2) (e^{(-4nm/\alpha ) - 1)} = 1[/tex]
Since the wavefunction is normalized, |A|² is equal to the inverse of the integral above. Solving for |A|², we get:
|A|² = [tex][-2/(\alpha (e^{(-4nm/α) - 1))}][/tex]
Thus, the wavefunction is:
Ψ(x) = [tex][2/(\alpha (1 - e^{(-4nm/\alpha )))}]e^{(-x/\alpha )}[/tex]
So, the value of the wavefunction for this given function is:
[tex][2/(\alpha (1 - e^{(-4nm/\alpha )))}]e^{(-x/\alpha )}[/tex]
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what is work in physics
Please help with this, Im a little stuck!!
Answer:
Jwbsbsbdjeiskbsj3kabajj2jjj1jj2j2j3jkkkk3j3j2
Calculate how far a ball would be hit if it was hit at an angle of 25° and a velocity of 80 mph.
The ball would be hit if it was hit at an angle of 25° and a velocity of 80 mph, it will travel 1-8m.
What is velοcity ?The definitiοn οf velοcity is the rate at which a bοdy mοves in a particular directiοn. Velοcity is the rate at which a distance changes in relatiοn tο time. A vectοr quantity with bοth magnitude and directiοn is velοcity.
What is mass ?The amοunt οf matter in a bοdy is referred tο as its mass. The kilοgramme is the kilοgrams, which is the SI unit οf mass (kg). Mass is defined as: Mass = Density/Vοlume.
Therefοre, ball wοuld be hit if it was hit at an angle οf 25° and a velοcity οf 80 mph, it will travel 1-8m.
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If ocean water did not move it would be hot in the _ region and frigid in the _ region
If ocean water did not move, it would be hot in the equatorial region and frigid in the polar regions.
Ocean currents are responsible for redistributing heat around the planet. Without these currents, the equatorial region would receive more sunlight and heat than it loses, resulting in an accumulation of heat in the water. On the other hand, the polar regions would lose more heat than they receive, resulting in frigid temperatures.
The rotation of the Earth also influences the movement of ocean water through the Coriolis effect. Without this effect, ocean currents would be less predictable, and their impact on climate and temperature distribution would be more severe. Therefore, ocean currents play a crucial role in regulating Earth's climate, and their disruption could have significant consequences for both marine life and global weather patterns.
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what would be the mass of a truck if it is accelerating at a rate of 5 m/s^2 and hits a parked car with a force of 14,000N
If the the dolphin produces sound waves of wavelength of 5 cm determine by the means of calculations whether the frequency produced by dolphin can be heard by human ear the speed of sound is water is 1480 m. S-1
If the the dolphin produces sound waves of wavelength of 5 cm determine by the means of calculations whether the frequency produced by dolphin can be heard by human ear the speed of sound is water is 1480 m. S-1
To determine whether the frequency produced by the dolphin can be heard by the human ear, we can use the formula:
v = f x λ
where v is the velocity of sound in water, f is the frequency of the sound wave, and λ is the wavelength of the sound wave.
Given v = 1480 m/s, λ = 5 cm = 0.05 m, we can rearrange the formula to solve for f:
f = v / λ
Plugging in the values, we get:
f = 1480 m/s / 0.05 m
f = 29600 Hz
Therefore, the frequency produced by the dolphin is 29600 Hz.
The human ear can typically hear frequencies ranging from 20 Hz to 20,000 Hz, with some variation among individuals. Therefore, the frequency produced by the dolphin is well beyond the range of human hearing.
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a student applies a horizontal force of 20.0 n to the top of a steering wheel. the steering wheel has a radius of 18 cm and a rotational inertia of 0.097 kgm2 . assuming the friction and any opposing torques are negligible, what is the initial angular acceleration of the steering wheel?
The initial angular acceleration of the steering wheel is 3.67 rad by s2.
The initial angular acceleration of the steering wheel can be calculated using the formula alpha = (F * R) by I, where F is the applied force, R is the radius of the wheel, and I is the rotational inertia.
In this case, F = 20.0 N, R = 0.18 m, and I = 0.097 kgm2. Substituting these values into the formula gives:
alpha = (20.0 N * 0.18 m) by 0.097 kgm2 = 3.67 rad by s2
Therefore, the initial angular acceleration of the steering wheel is 3.67 rad by s2.
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how fast, in meters per second, is object a moving at the end of the ramp if it's mass is 115 g, it's radius 17 cm, and the height of the beginning of the ramp is 14 cm?
The required object A is moving at a speed of 2.62846 m/s at the end of the ramp.
To determine the speed of object A at the end of the ramp, we can use the principles of conservation of energy and rotational motion.
Given:
Mass of object A (m) = 115 g = 0.115 kgRadius of the ramp (r) = 17 cm = 0.17 mHeight of the beginning of the ramp (h) = 14 cm = 0.14 mFirst, let's calculate the potential energy (PE) of object A at the beginning of the ramp. The potential energy can be given by:
PE = m * g * h,
PE = 0.115 * 9.8 * 0.14 = 0.1628 J
At the end of the ramp, the potential energy is fully converted into kinetic energy (KE). The kinetic energy can be given by:
KE = (1/2) * I * ω²,
For a solid sphere rolling without slipping, the moment of inertia (I) can be given by:
I = (2/5) * m * r²,
I = (2/5) * 0.115 kg * (0.17 m)² = 0.00132 kg·m²
Now, we can relate the linear speed (v) and the angular velocity (ω) of the rolling object. For a solid sphere rolling without slipping, the relationship is:
v = ω * r,
ω = v / r.
Next, we equate the potential energy at the beginning of the ramp to the kinetic energy at the end of the ramp:
PE = KE
m * g * h = (1/2) * I * ω²
0.115 * 9.8 * 0.14 = (1/2) * 0.00132 * (v / r)²
0.115 * 9.8 * 0.14 = 0.00132/2 * (v / 0.17 )²
v = 2.62846
Therefore, object A is moving at a speed of 2.62846 m/s at the end of the ramp.
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