Final answer:
To find the speed of the bullet before striking the block, we can use the law of conservation of momentum. By setting the initial momentum equal to the final momentum, we can solve for the initial velocity of the bullet.
Explanation:
To solve this problem, we can use the law of conservation of momentum. Momentum is defined as the product of an object's mass and velocity. In this case, we know the mass and velocity of the wooden block and bullet after the collision, and we want to find the velocity of the bullet before the collision.
Using the law of conservation of momentum, we have:
Initial momentum = Final momentum
Mass of bullet * Initial velocity of bullet + Mass of block * Initial velocity of block = Mass of bullet * Final velocity of bullet + Mass of block * Final velocity of block
Substituting the given values, we have:
(0.0107 kg)(Initial velocity of bullet) + (4.588 kg)(0 m/s) = (0.0107 kg)(1.74 m/s) + (4.588 kg)(1.74 m/s)
Simplifying the equation and solving for the initial velocity of the bullet, we get:
Initial velocity of bullet = 1.74 m/s - (4.588 kg)(1.74 m/s) / 0.0107 kg
Calculating the value, we find that the initial velocity of the bullet was 271.36 m/s.
Ball 1, with a mass of 150 g and traveling at 15 m/s , collides head on with ball 2, which has a mass of 350 g and is initially at rest.A) What are the final velocities of each ball if the collision is perfectly elastic?B) What are the final velocities of each ball if the collision is perfectly inelastic?
Answer: A. Vb1 = -6m/s , Vb2 = 9m/s.
B. Vb1 = 4.5m/s , Vb2 = 4.5m/s
Explanation: A. In a perfectly elastic collision the objects involved moved with a different velocity after collision. Also kenitic energy is conserved. In other to get the different velocity of ball 1 (Vb1) and ball 2 (Vb2) after collision, we apply the following formula
Vb1 = {{m1 - m2}*V1}/{m1 +m2}
Vb2 = {{2m1}*V1}/{m1 + m2}
Where V1 = velocity of ball 1 before collision=15m/s
m1 = mass of ball 1
m2 = mass of ball 2.
Substituting in the above equation:
Vb1 = {{0.15kg - 0.35kg}*15}/{0.15 + 0.35}
= {{-0.2}*15}/0.5
= -3/0.5
= -6m/s
Also,
Vb2 = {{2*0.15kg}*15m/s}/{0.15kg + 0.35kg}
={0.3kg*15m/s}/0.5kg
=4.5/0.5
=9m/s
B. In a perfectly inelastic collision the object involved move with a common velocity after collision.
We have that ,
m1*V1 + m2*v2 = {m1 + m2} V¹
Where V¹ is the final velocity of both balls after a perfectly inelastic collision.
NOTE: v2 here is 0m/s since ball 2 was at rest before collision.
So we have,
0.15kg*15m/s + 0.35kg*0m/s = {0.15kg + 0.35kg}*V¹
2.25 kgm/s = 0.5kg* V¹
Making V¹ subject of formula we have,
V¹ = 2.25kgm per sec/0.5kg
=4.5m/s. vb1 = Vb2 = V¹
NOTE also that the mass of the balls from the question were given in gram hence we converted to kilogram the standard unit for mass by dividing by 1000.
Answer:
For both ball 1 and ball 2, the change in velocity is less in an inelastic collision.
Explanation:
a short simple answer
Why do most aircraft tire manufacturers recommend that the tubes in newly installed tires be first inflated, fully deflated, and then reinflated to the correct pressure?
Answer:
1. This is to allow the tube of the tire to position itself properly inside the tire.
2. Inflating,deflating and reinflating aircraft tires help to eliminate all the air between the tube and the inside of the tire.
3. It helps to test the entire tube and tire assembly for any leaks.
Explanation:
A ball that is thrown upwards from the ground will eventually reach its highest point and fall back to the ground. Which of the following quantities will be constant over the course of this up and down motion?
a. The ball's position.b. The ball's speed.c. The ball's acceleration.d. Nonsense! None of these are constant.
Answer:
option (c)
Explanation:
When an object thrown upwards, the value of acceleration acting on the object is acceleration due to gravity which is always acting towards the earth.
As it falls downwards, the acceleration is again equal to the acceleration due to gravity.
So, the ball's acceleration is constant.
Final answer:
The acceleration of the ball remains constant throughout its up and down motion since it is solely influenced by gravity, which provides an acceleration of approximately 9.81 m/s² downward
Explanation:
When a ball is thrown upwards from the ground and then falls back down, the acceleration of the ball is what remains constant throughout its motion. This is due to gravity, which acts downward on the ball with an acceleration denoted as "g". While the ball's position and speed are changing throughout the motion, its acceleration due to gravity remains constant at approximately 9.81 m/s2 (on Earth), regardless of its state of motion. Therefore, the quantity that remains constant over the course of this up and down motion is the ball's acceleration.
On Mars gravity is one-third that on Earth. What would be the mass on Mars of a person who has a mass of 90 kilograms (kg) on Earth?
Answer: The person will still have a mass of 90kg on Mars
Explanation: The Truth is, the mass of a body remains constant from place to place. It is the weight which is equal to {mass of body * acceleration due to gravity{g}} that varies from place to place since it is dependent on {g}.
In this case the person will have a Weight of 90*9.8 = 882N on Earth.
{ "g" on Earth is 9.8m/s²}
And a Weight of 90*3.3 = 297N on Mars.
{ From the question "g" on Mars is {9.8m/s²}/3 which is 3.3m/s²}
From this analysis you notice that the WEIGHT of the person Varies but the MASS remained Constant at 90kg.
A 3-kg object is moving at 5.0 m/s. An 12-N force is applied in the direction of motion and then removed after the object has traveled an additional 6.0 m. What is the work done by this force?
Answer:
The work done by the force is 109.5 Joules.
Explanation:
It is given that,
Mass of the object, m = 3 kg
Speed of the object, v = 5 m/s
Force applied on the object, F = 12 N
Distance covered by the object, d = 6 m
The work done by this force is given by the sum of kinetic energy and potential energy as per work energy theorem as :
[tex]W=K+P[/tex]
[tex]W= \dfrac{1}{2}mv^2+Fd[/tex]
[tex]W=\dfrac{1}{2}\times 3\times (5)^2+12\times 6[/tex]
W = 109.5 Joules
So, the work done by the force is 109.5 Joules. Hence, this is the required solution.
If a child starts from rest at point A and lands in the water at point B, a horizontal distance L = 2.52 m from the base of the slide, determine the height h (in m) of the water slide.
Answer:
The height of the water slide is 0.878 m
Explanation:
Given that,
Distance = 2.52 m
Suppose Children slide down a friction less water slide that ends at a height of 1.80 m above the pool.
We need to calculate the time
Using equation of motion
[tex]s=ut+\dfrac{1}{2}gt^2[/tex]
Put the value in the equation
[tex]1.80=0+\dfrac{1}{2}\times9.8\times t^2[/tex]
[tex]t^2=\dfrac{1.80\times2}{9.8}[/tex]
[tex]t=\sqrt{\dfrac{1.80\times2}{9.8}}[/tex]
[tex]t=0.606\ sec[/tex]
We need to calculate the velocity
Using formula of velocity
[tex]v = \dfrac{d}{t}[/tex]
Put the value into the formula
[tex]v=\dfrac{2.52}{0.606}[/tex]
[tex]v=4.15\ m/s[/tex]
We need to calculate height
Using conservation of energy
[tex]\dfrac{1}{2}mv^2=mgh[/tex]
[tex]h=\dfrac{v^2}{2g}[/tex]
Put the value into the formula
[tex]h=\dfrac{4.15^2}{2\times9.8}[/tex]
[tex]h=0.878\ m[/tex]
Hence, The height of the water slide is 0.878 m.
One drawback of dams is that they can flood land upstream from the dam and reduce water flow downstream from the dam. Question 2 options: True False
Answer:
True
Explanation:
It can cause flooding and destruction of habitat because of dammed rivers create large reservoirs upstream which can spill out to the surrounding during heavy rainfall causing flooding and destruction of natural habitat.
Because it implies royal status, the granary at the Conical tower and circular wall of Great Zimbabwe is most similar to what object?
Answer:
The Commemorative head of a king (Oba)
Explanation:
The commemorative head of a king is similar to the other features mentioned in the question due to their royal statuses. These features are idolized by the people in their respective societies. The 'Oba' for example is respected by the people of Benin and he makes the rules and regulations for the people. When he dies, his eldest son usually takes his position.
Answer:
The Commemorative head of a king (Oba)
Explanation:
I took the test B )
Speed is an important component of which of the following sports? A. tennis B. soccer C. swimming D. all of the above Please select the best answer from the choices provided. A B C D
Answer: D. all of the above
Explanation:
The speed is important in tennis, so you can win easily, speed is important in soccer to collect the ball quickly and reach the goal, speed is necessary for swimming as the first person wins the game so, option D is correct.
What is speed?A moving object's rate of change in distance traveled is measured as speed. Speed is a scalar, which implies it is a measurement with a magnitude but no direction.
A thing that moves quickly and with high speed, covering a lot of ground in a short time. On the other hand, a slow-moving object traveling at a low speed covers a comparatively small distance in the same amount of time. An object with zero speed does not move at all.
Speed shortens the time needed to complete a task or travel between two locations. The spare time can then be applied to other tasks. The Earth's orbit around the Sun is maintained by speed.
Thus, speed is important in all the games mentioned here.
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If a force of 2n does work at the rate of -2sqrt2 w on an object moving iwth a speed of 2m/s the ale between the fore and teh velocity vector must be ______
Answer:
The value of the angle theta = 135degree, which is option c.
Explanation :
These are the options given in the question
a) 45 degrees
b)120 degrees
c)135 degrees
d)150 degrees
e) it is impossible to deliver a negative power.
The concept of work done on an object is applied here.
work = Fd
F = ma
work = mad
Work is a form of energy transferred by an object after the application of a force that act on the object. A step by step explanation is as attached below.
What is the estimated fraction of total energy used in the production and manufacturing of materials by the manufacturing industry in the United States?
Answer: 1/2
Explanation:
The total energy consumption in the United States of America has been estimated to be about 101.3quadrillion Btu( British thermal unit). The United States of America uses a mix energy source for energy Production which includes PRIMARY, SECONDARY, RENEWABLE,FOSSIL FUELS.
Five basic energy consumption sectors have been categorized in the United States,which includes ELECTRIC POWER, INDUSTRIAL, COMMERCIAL, RESIDENTIAL AND TRANSPORTATION. Of the estimated 101.3(quads) about 1/2 of 101.3(quads) are used for the production and manufacturing of materials by the manufacturing industry.
Practice entering numbers that include a power of 10 by entering the diameter of a hydrogen atom in its ground state, dH = 1.06 × 10⁻¹⁰m, into the answer box.
Express the diameter of a ground-state hydrogen atom in meters using a power of 10.
Answer:
[tex]1.06085\times 10^{-10}\ m[/tex]
Explanation:
h = Planck's constant = [tex]6.626\times 10^{-34}\ m^2kg/s[/tex]
m = Mass of electron = [tex]9.11\times 10^{-31}\ kg[/tex]
k = Coulomb constant = [tex]8.99\times 10^{9}\ Nm^2/C^2[/tex]
e = Charge of electron = [tex]1.6\times 10^{-19}\ C[/tex]
n = 1 (ground state)
Angular momentum is given by
[tex]L=mvr[/tex]
From Bohr's atomic model we have
[tex]L=\dfrac{nh}{2\pi}[/tex]
[tex]mvr=\dfrac{nh}{2\pi}\\\Rightarrow v=\dfrac{nh}{2\pi mr}[/tex]
The centripetal force will balance the electrostatic force
[tex]\dfrac{ke^2}{r^2}=\dfrac{mv^2}{r}\\\Rightarrow \dfrac{ke^2}{r}=mv^2\\\Rightarrow \dfrac{ke^2}{r}=m(\dfrac{nh}{2\pi mr})^2\\\Rightarrow r=\dfrac{n^2h^2}{4\pi^2mke^2}\\\Rightarrow r=\dfrac{1^2\times (6.626\times 10^{-34})^2}{4\pi^2 \times 9.11\times 10^{-31}\times 8.99\times 10^{9}\times (1.6\times 10^{-19})^2}\\\Rightarrow r=5.30426\times 10^{-11}\ m[/tex]
The diameter is [tex]2\times 5.30426\times 10^{-11}=1.06085\times 10^{-10}\ m[/tex]
Use Newton’s Universal Law of Gravitation to calculate the magnitude of the gravitational force between a 200 kg refrigerator and a 70 kg person that is 0.5 meters from the refrigerator.
Answer:
3.735×10⁻⁶ N
Explanation:
From newton' s law of universal gravitation,
F = Gmm'/r² .............................. Equation 1
Where F = Gravitational force between the person and the refrigerator, m = mass of the person, m' = mass of the refrigerator, r = distance between the person and the refrigerator. G = gravitational universal constant.
Given: m = 70 kg, m' = 200 kg, r = 0.5 m
Constant: G = 6.67×10⁻¹¹ Nm²/kg².
F = (6.67×10⁻¹¹×70×200)/0.5²
F = 93380×10⁻¹¹/0.25
F = 373520×10⁻¹¹
F = 3.735×10⁻⁶ N
Hence the force between the person and the refrigerator = 3.735×10⁻⁶ N
Sound travels at a speed of about 344 m/s in air. You see a distant flash of lighting and hear the thunder arrive 7.6 seconds later. How many miles away was the lighting strike? (assume the light takes essentially no time to reach you.)
Express your answer to two significant figures and include the appropriate units.
Answer:
0.056 miles away
Explanation:
From sound wave,
v = 2x/t .................................. Equation 1
Where v = velocity of sound in air, x = distance of echo, t = time.
making x the subject of the equation,
x = 2v/t........................... Equation 2.
Given: v = 344 m/s, t = 7.6 s.
Substituting into equation 2
x = 2(344)/7.6
x = 90.53 m.
x = 90.53/1609.344
x = 0.056 mile.
Thus the lighting strike 0.056 miles away
What mass of a material with density rho is required to make a hollow spherical shell having inner radius r1 and outer radius r2? (Use any variable or symbol stated above as necessary.)'
Answer:
[tex]m=\rho\times \frac{4}{3} \times \pi \times(r_2^3-r_1^3 )[/tex]
Explanation:
We have to make a hollow sphere of inner radius [tex]r_1[/tex] and outer radius [tex]r_2[/tex].Then the mass of the material required to make such a sphere would be calculated as:
Total volume of the spherical shell:
[tex]V_t=\frac{4}{3} \pi.r_2^3[/tex]
And the volume of the hollow space in the sphere:
[tex]V_h=\frac{4}{3} \pi.r_1^3[/tex]
Therefore the net volume of material required to make the sphere:
[tex]V=V_t-V_h[/tex]
[tex]V=\frac{4}{3} \pi(r_2^3-r_1^3)[/tex]
Now let the density of the of the material be [tex]\rho[/tex].Then the mass of the material used is:
[tex]m=\rho.V[/tex]
[tex]m=\rho\times \frac{4}{3} \times \pi \times(r_2^3-r_1^3 )[/tex]
"determine the resultant internal loadings acting at the cross sections at points f and g of the frame. set θ = 27º and t = 178 lb."
Hi you didn't provide any images to solve the question, hence I am going to solve a different question of same concept so you can have an idea how to tackle such types of questions.(please refer to the attachment for question)
Answer:
Please refer to the attachment for answers and explanation
Explanation:
Please refer to the attachment for answers and explanation
To determine the resultant internal loadings at the cross sections, we need to consider the external and internal forces. Trigonometric principles can be used to calculate the magnitudes and directions of the loadings. More information about the frame is needed for a precise analysis.
In order to determine the resultant internal loadings acting at the cross sections at points F and G of the frame, we need to consider the external forces applied to the frame, as well as the internal forces generated within the frame due to those external forces. These internal forces include axial forces, shear forces, and bending moments.
Given that θ = 27º and t = 178 lb, we can use trigonometric principles to determine the magnitudes and directions of the internal loadings at points F and G.
For a more specific and accurate analysis, it would be helpful to have more information about the frame, such as its shape, structural elements, and boundary conditions. Without that information, it is not possible to provide a more detailed answer at this time.
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Diamond and graphite are both composed entirely of carbon yet graphite is soft and diamond is one of the hardest substances known. Explain the difference between these substances in terms of intermolecular forces.
Explanation:
This difference is because of the difference in arrangement of carbon atoms both graphite and Diamond.
Carbon atoms in graphite are arranged in layered form in an infinite array of layers. These layers are held together by a weaker force of attraction called vander waal's force of attraction such that layer's can slip over one another. Whereas in diamond carbon atoms are arranged tetrahedrally. Each carbon atom is attached to four carbon atoms with a bond angle of 109.5°. It is strong rigid three dimensional structure that results in infinite array atoms. This accounts for hardness of the diamond.
Final answer:
Diamond and graphite exhibit vastly different physical properties due to their respective carbon atom structures: diamond's strong three-dimensional covalent bonds make it extremely hard, while graphite's layered structure with weak interlayer forces makes it soft and slippery.
Explanation:
Diamond and graphite are two forms of the same element, carbon, but they have vastly different physical properties due to the way their atoms are bonded together. In diamond, each carbon atom is tetrahedrally bonded to four other carbon atoms in a strong three-dimensional network, which is what makes diamonds so hard and durable. This covalent bonding extends throughout the crystal, making it an excellent insulator but very hard to break.
Conversely, graphite is composed of layers of carbon atoms bonded in a hexagonal pattern, with weaker interlayer attractions known as London dispersion forces. This allows the layers to slide past each other easily, which is why graphite can be used as a lubricant and as the 'lead' in pencils – rubbing off onto paper with ease. The strong covalent bonds within the layers give graphite its high melting point, but the weak interactions between layers contribute to its softness.
Furthermore, graphite's structure enables it to conduct electricity parallel to the planes due to delocalized π (pi) bonds, while diamond does not conduct electricity. Graphite's black color results from the absorption of light by its delocalized electrons, whereas pure diamond is colorless.
A floating ball normally weighs 5.5 N. The acceleration of gravity is 9.8 m/s 2 . What is the size of the buoyant force that acts on it?
Answer:
5.5 N
Explanation:
Weigh of floating ball=5.5 N
Acceleration due to gravity=9.8 [tex]m/s^2[/tex]
We have to find the size of the buoyant force that acts on it.
We know that
Buoyant force is that force which act in upward direction and exert by fluid and opposes the weight of an immersed object.
Therefore,
Buoyant force=Weight of ball
Buoyant force=5.5 N
Hence, the size of buoyant force acts on the ball=5.5 N
Given the ball's weight of 5.5 N, the buoyant force is also 5.5 N.
To determine the buoyant force acting on a floating ball, we can use the principles of buoyancy and the given information about the ball's weight. The ball's weight in air is 5.5 N, and we know the acceleration due to gravity (g) is 9.8 m/s².
For a floating object, the buoyant force (Fb) is equal to the weight of the object when it is floating. Therefore, since the ball is floating, the buoyant force must equal the weight of the ball:
Buoyant force Fb = Weight of the ball
Given that the weight of the ball is 5.5 N, the buoyant force acting on the ball is:
Fb = 5.5 N
This force is what keeps the ball afloat in the fluid.
Energizer batteries would be classified as which type of product? a. Shopping b. Convenience c. Industrial service d. Unsought e. Specialty
Answer:
i believe it would be classified as A shopping
A 0.71 W point source emits sound waves isotropically. Assuming that the energy of the waves is conserved, find the intensity (a)1.4 m from the source and (b)2.6 m from the source.
Answer:
(a) 2.88×10⁻² W/m²
(b) 8.36×10⁻³ W/m²
Explanation:
The intensity of sound from an isotropic point source, with distance L is given as
I = P/(4πL²) .................................... Equation 1
Where I = intensity of sound, P = Power from the source, L = length, π = pie.
(a)
1.4 m from the source.
I = P/(4πL²)
Given: P = 0.71 W, L = 1.4 m, π = 3.14.
Substitute into equation 1
I = 0.71/(4×3.14×1.4²)
I = 0.71/24.6176
I = 0.0288 W/m².
I = 2.88×10⁻² W/m²
(b) 2.6 m from the source.
Given: P = 0.71 W, L = 2.6 m, π = 3.14
Substitute into equation 1
I = 0.71/(4×3.14×2.6²)
I = 0.71/84.9056
I = 0.00836 W/m²
I = 8.36×10⁻³ W/m²
Two identical speakers, with the same phase constant, are arranged along a 1D track. One speaker remains at the origin. The other speaker can slide along the track to any position x. You are on the track at x=10 m. You hear interference maxima when the adjustable speaker's position is 0.6 m and 1.2 m and at no points in between. What is the frequency of the sound from the speakers in Hz?
Answer:
[tex]f=571.67\ Hz[/tex]
Explanation:
Given:
Two identical speakers have the same phase constant.One of the speaker remains origin.The other speaker moves linearly from origin to x=10mposition of maxima of the interference, [tex]x_1=0.6\ m[/tex]position of next maxima of the interference, [tex]x_2=1.2\ m[/tex]Therefore we have the wavelength of the wave as the distance between the two consecutive maxima:
[tex]\lambda=1.2-0.6[/tex]
[tex]\lambda=0.6\ m[/tex]
We have the speed of sound in the air as:
[tex]v=343\ m.s^{-1}[/tex]
Therefore the frequency of sound:
[tex]f=\frac{v}{\lambda}[/tex]
[tex]f=\frac{343}{0.6}[/tex]
[tex]f=571.67\ Hz[/tex]
The frequency of the sound from the speaker is 571.67 Hz.
How do you calculate the frequency?Given that the phase constant of speakers is the same, the position of one speaker is at origin, the position of another speaker from the origin is 10 m.
The position of maxima interference is at 0.6 m and 1.2 m. Hence the wavelength of the wave is equivalent to the difference between the two consecutive maxima interference.
[tex]\lambda = 1.2 - 0.6[/tex]
[tex]\lambda = 0.6 \;\rm m[/tex]
We know that the speed v of the sound in the air is 343 m/s. Hence the frequency of the sound is calculated as given below.
[tex]f = \dfrac {v}{\lambda}[/tex]
[tex]f = \dfrac { 343}{0.6}[/tex]
[tex]f = 571.67\;\rm Hz[/tex]
Hence we can conclude that the frequency of the sound from the speaker is 571.67 Hz.
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A 5 kg box is sliding across a level floor. The box is acted upon by a force of 27 newtons east and a frictional force of 17 newtons west. What is the magnitude of the acceleration of the box? Type only numbers. Do not include the units of m/s2.
Answer:
The acceleration of the box is 2.
Explanation:
According to Newton's second law of motion, the acceleration of any object will be directly proportional to the net unbalanced force acting on the object and inversely proportional to the mass of the object.
Net force = Mass × Acceleration
So [tex]Acceleration = \frac{Net force}{Mass}[/tex]
Since in this case, the box is experiencing a force from east of magnitude 27 N and resisting force of about 17 N from west. So the net force will be the difference of acting and reacting force.
Net force = 27-17 = 10 N.
Thus, [tex]Acceleration = \frac{10 N}{5 kg}[/tex]
So 2 [tex]m/s^{2}[/tex] is the acceleration of the box. Thus the magnitude of acceleration of the box is 2.
An egg is thrown nearly vertically upward from a point near the cornice of a tall building. It just misses the cornice on the way down and passes a point a distance 34.0 m below its starting point at a time 5.00 s after it leaves the thrower's hand. Air resistance may be ignored.
A) What is the initial speed of the egg?
B) How high does it rise above its starting point?
C) What is the magnitude of its velocity at the highest point?
E) What are the magnitude and direction of its acceleration at the highest point?
Part A. The initial speed of the egg is 17.7 m/s.
Part B. The maximum height of the egg is 15.98 m.
Part C. The magnitude of the velocity at its highest point is 0 m/s.
Part E. The magnitude and direction of the acceleration in the upward direction is 9.8 m/s2.
Velocity and AccelerationGiven that the distance traveled by the egg is 34 m in time 5 seconds.
The distance at its initial point will be zero.
Part A
The initial speed of the egg can be calculated by the position equation of the egg.
[tex]x = x_0 + v_0t + \dfrac {1}{2}at^2[/tex]
Where x is the initial position of the egg that is 0 m, x_0 is the final position that is 34 m in time t = 5 s, v_0 is the initial speed and a is the acceleration. Since the egg is thrown vertically, hence the acceleration of the egg is similar to the gravitational acceleration.
[tex]0 = 34 + v\times 5 + \dfrac {1}{2}\times(- 9.8)\times 5^2[/tex]
[tex]v = \dfrac {122.5 - 34}{5}[/tex]
[tex]v = 17.7 \;\rm m/s[/tex]
The initial speed of the egg is 17.7 m/s.
Part BThe maximum height for the egg can be calculated by the equation given below.
[tex]v^2 = v_0^2 + 2gh[/tex]
For the highest point, the final speed v will be zero and the initial speed v_0 is 17.7 m/s. Hence,
[tex]0 = (17.7)^2 + 2\times (-9.8)\times h[/tex]
[tex]19.6 h = 313.29[/tex]
[tex]h = 15.98 \;\rm m[/tex]
The maximum height of the egg will be 15.98 m.
Part CThe velocity of the object thrown at a height will be zero at its highest point. Hence the velocity of the egg will be zero at its highest point.
Velocity [tex]v_h[/tex] = 0 m/s
Part EThe egg is thrown vertically upward, hence its acceleration is similar to the gravitational acceleration.
Acceleration a = 9.8 m/s2
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An electron and a proton are each placed at rest in an electric field of 490 N/C. Calculate the speed (and indicate the direction) of each particle 54.0 ns after being released.
Answer
given,
Electric field,E = 490 N/C
time, t = 54 ns
for electron
Mass of electron me = 9.1 x 10⁻³¹ kg
Charge of electron e = -1.6 x 10⁻¹⁹ C
electrostatic force
F = E q
F = 490 x 1.6 x 10⁻¹⁹
F = 784 x 10⁻¹⁹ N
now, using newton second law
[tex]a = \dfrac{784\times 10^{-19}}{9.1\times 10^{-31}}[/tex]
a = 8.62 x 10¹² m/s²
using equation of motion
v = u + a t
v = 0 + 8.62 x 10¹² x 54 x 10⁻⁹
v = 4.65 x 10⁵ m/s
velocity of electron is equal to v = 4.65 x 10⁵ m/s
For Proton
Mass mp = 1.67 x 10⁻²⁷ kg
Charge p = 1.6 x 10⁻¹⁹ C
Electric field E = 490 V/C
from above solution
F = 784 x 10⁻¹⁹ N
now, acceleration
[tex]a = \dfrac{784\times 10^{-19}}{1.67\times 10^{-27}}[/tex]
a = 4.69 x 10¹⁰ m/s²
using equation of motion
v = u + a t
v = 0 + 4.69 x 10¹⁰ x 54 x 10⁻⁹
v = 4.65 x 10³ m/s
velocity of electron is equal to v = 4.65 x 10³ m/s
Answer:
Explanation:
Electric field, E = 490 N/C
mass of electron, me = 9.1 x 10^-31 kg
mass of proton, mp = 1.67 x 10^-27 kg
charge of electron or proton = 1.6 x 10^-19 C
time, t = 54 ns = 54 x 10^-9 s
initial velocity, u = 0 m/s
Force on each particle, F = q E = 1.6 x 10^-19 x 490 = 7.84 x 10^-17 N
acceleration of electron = Force / mass of electron
ae = (7.84 x 10^-17) / ( 9.1 x 10^-31) = 8.6 x 10^13 m/s²
Let the velocity of electron is ve.
use first equation of motion
ve = u + ae x t
ve = 0 + 8.6 x 10^13 x 54 x 10^-9
ve = 4.65 x 10^6 m/s
acceleration of proton = Force / mass of proton
ap = (7.84 x 10^-17) / ( 1.67 x 10^-27) = 4.69 x 10^10 m/s²
Let the velocity of electron is vp.
use first equation of motion
vp = u + ap x t
vp = 0 + 4.69 x 10^10 x 54 x 10^-9
ve = 2535.1 m/s
Particle 1 carrying -4.0 μC of charge is fixed at the origin of an xy coordinate system, particle 2 carrying +8.0 μC of charge is located on the x axis at x = 4.0 m , and particle 3, identical to particle 2, is located on the x axis at x = -4.0 m . What is the vector sum of the electric forces exerted on particle 3? Determine the x and y components of the vector sum.
To find the vector sum of the electric forces exerted on particle 3, calculate the electric forces exerted by particle 1 and particle 2 and add them as vectors. Use Coulomb's law to find the electric forces. Add the x and y components of the forces to get the vector sum.
Explanation:To find the vector sum of the electric forces exerted on particle 3, we need to calculate the electric forces exerted on particle 3 by particle 1 and particle 2 and then add them together as vectors. The electric force exerted on particle 3 by particle 1 can be found using Coulomb's law, which states that electric force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
Calculate the electric force exerted on particle 3 by particle 1 using Coulomb's law: F1 = (k * q1 * q3) / r13^2Next, calculate the electric force exerted on particle 3 by particle 2 using Coulomb's law: F2 = (k * q2 * q3) / r23^2Add the x-components and y-components of the electric forces to get the vector sum: Fx = F1x + F2x and Fy = F1y + F2yBy substituting the given values into the equations, you can calculate the x and y components of the vector sum of the electric forces exerted on particle 3.
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Final answer:
To find the vector sum of the electric forces exerted on particle 3, we need to calculate the electric force between particle 3 and both particle 1 and particle 2. The electric force between two charges is given by Coulomb's Law. By plugging in the charges and distances, we can calculate the electric forces and find the vector sum.
Explanation:
To find the vector sum of the electric forces exerted on particle 3, we need to calculate the electric force between particle 3 and both particle 1 and particle 2. The electric force between two charges is given by Coulomb's Law:
F = k * (|q1| * |q2|) / r^2
Where F is the electric force, k is the electrostatic constant, q1 and q2 are the charges, and r is the distance between the charges. Since particle 1 is fixed at the origin, the distance between particle 3 and particle 1 is |-4.0 m| = 4.0 m. Similarly, the distance between particle 3 and particle 2 is |4.0 m - (-4.0 m)| = 8.0 m. Plugging in the values, we can calculate the electric forces between particle 3 and both particle 1 and particle 2.
Let's calculate:
F3-1 = (9 * 10^9 N.m^2/C^2) * (|-4.0 μC| * |8.0 μC|) / (4.0 m)^2
F3-2 = (9 * 10^9 N.m^2/C^2) * (|-4.0 μC| * |8.0 μC|) / (8.0 m)^2
Now, we can find the vector sum of the electric forces by adding the x-components and the y-components of both forces.
If you very lightly touch a guitar string at its midpoint, you can hear a tone that is one octave above the fundamental for that string.Explain?
Answer:
Change, increase in note frequency of the sound that comes as a result of the reduction in the vibrating length (wavelength) when the string movement is slightly restricted at its midpoint
Explanation:
When the midpoint of a vibrating guitar string is lightly touched it reduces the wavelength of the guitar string sound, halving it and such increases the the frequency inversely by a factor of 2
The relationship
f = vw/λ, for sound wave where vw is the speed of sound, frequency, f and λ is the wavelength
Frequency varies inversely with wavelength
An Octave
is the frequency vibration of sound-wave twice that of its lower note
Which of the following are core capabilities for a response?
a. Cybersecurity; community resilience; and housing
b. Forensics and attribution; physical protective measures; and economic recovery
c. Interdiction and disruption; access control; and threats/hazards identification
d. Critical transportation; situation assessment; and mass care services
Answer:
d. Critical transportation; situation assessment; and mass care services
Explanation:
The correct answer is option d which is Critical transportation: Situation assessment and mass care services are core capabilities for response.
As we know that critical transportation are very important factor which control capability for responses. Due to fast transportation a life can be saved, people can be out of danger in the situation of natural calamity.
Suppose an electron is moving with a constant velocity until it encounters a positively charged sphere on its right. How does the sphere alter the trajectory of the electron?
a. It has no effect on the trajectory of the electron
b. It deflects the electron to the right.
c. It deflects the electron to the left.
d. Impossible to tell
Answer:
b. It deflects the electron to the right.
Explanation:
Since the sphere is positively charged and electron has negative charge, it will be attracted toward the sphere and hence,
The electron is deflected to the right as the positively charged sphere on its right
So, the 2nd option is correct.
Floating in deep space, you find yourself at rest next to a small asteroid. You reach out and tap the asteroid with a hammer. What happens to you in this process?
Answer:
There is a force that has the same magnitude as that of the hammer applied on the astronaut and with direction away from the asteroid, movement is given by
F_hammer - F_Gravitation = m a
Explanation:
For this exercise we will propose its solution from Newton's third law, which states that every action has a reaction of equal magnitude, but felt different.
As it is in space, we must assume that it is not subject to the gravitational attraction of nearby bodies, except the asteroid that attracts it. When he extends his hand and hits the asteroid, he exerts a force on him, by Newton's third law he responds with a force of equal magnitude applied to the astronaut, therefore without the two they are not united they could separate if this force is greater than the force of universal attraction between the two.
In summary There is a force that has the same magnitude as that of the hammer applied on the astronaut and with direction away from the asteroid, movement is given by
F_hammer - F_Gravitation = m a
An electrical engineer wants to build an electrical circuit with a 3-volt battery connected in series to a light bulb with a resistance of 6 ohms. How much current will be flowing through the light bulb if this circuit is built?
Answer:
0.5A
Explanation:
GIVEN THAT:
V = 3 V
R =6 ohms
V=IR
I =V/R
I = 3/6 =0.5 A