Answer:
√ [tex]\frac{3}{5} m[/tex]
Explanation:
Hope it helps!.
The change in the length of the spring will be 3.5 cm.Principal of the law of conservation of the momentum is applied in the problem.
What is the law of conservation of momentum?According to the law of conservation of momentum, the momentum of the body before the collision is always equal to the momentum of the body after the collision.
According to the law of conservation of momentum;
Momentum before collision =Momentum after collision
Speed after impact is;
[tex]\rm v = \frac{(1.50)(3.5)}{(1.50)+(3)} \\\\ v= 1.1666 \ m/sec[/tex]
From the law of conservation of energy:
[tex]\rm \frac{1}{2} kx^2= \frac{1}{2} (m+M)v^2 \\\\ x= \sqrt{\frac{M+m}{k} } \\\\ x=\sqrt{\frac{4.5}{5000 } }(1.1666)\\\\ x= 0.35 \ m \\\\ x=3.5 \ cm[/tex]
The change in the length of the spring will be 3.5 cm.
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Hi there! I'm not quite sure on how to solve this....
[tex]\frac{dx}{dt} = 2.5 \: \frac{cm}{sec} [/tex]
Explanation:
The volume of a cube is V = x^3. Taking the time derivative of this expression, we get
[tex] \frac{dV}{dt} = 3 {x}^{2} \frac{dx}{dt} [/tex]
or
[tex]\frac{dx}{dt} = \frac{1}{3 {x}^{2}} \frac{dV}{dt} [/tex]
We know that dV/dt = 30 cm^3/sec so the value of dx/dt when x = 2 cm is
[tex]\frac{dx}{dt} = \frac{1}{3 {(2 \: cm)}^{2}}(30 \: \frac{ {cm}^{3} }{sec} ) = 2.5 \: \frac{cm}{sec} [/tex]
Answer:
Explanation:
[tex]V=x^3\\\\\frac{dV}{dt}=3x^2\frac{dx}{dt}\\\\30\frac{cm^3}{s}=3x^2\frac{dx}{dt}\\\\\frac{dx}{dt}=\frac{30\frac{cm^3}{s}}{3x^2}~at~x=2cm,~\frac{dx}{dt}=\frac{30\frac{cm^3}{s}}{3*(2cm)^2}=\frac{5}{2}\frac{cm}{s}[/tex]
a metal of work function 1.8eV is illuminated by light of wavelength 3.0x*10-7,calculate the maximum kinetic energy
Complete question:
a metal of work function 1.8eV is illuminated by light of wavelength 3.0x*10-7 m,calculate the maximum kinetic energy of the emitted photons.
Answer:
the maximum kinetic energy of the emitted photons is 3.742 x 10⁻¹⁹ J
Explanation:
Given;
work function, Ф = 1.8 eV
wavelength of the light, λ = 3 x 10⁻⁷ m
The maximum kinetic energy of the emitted photons is calculated from photoelectric equation.
[tex]E = K.E_{max} + \phi\\\\KE_{max} = E- \phi\\\\where;\\\\E \ is \ the \ energy \ of \ the \ incident \ light\\\\E = hf = h \frac{c}{\lambda} \\\\where;\\\\c \ is \ speed \ of \ light = 3 \times 10^8 \ m/s\\\\h \ is \ Planck's \ constant = 6.626 \times 10^{-34} \ Js\\\\E = \frac{ (6.626 \times 10^{-34})\times ( 3 \times 10^8)}{3\times 10^{-7}} \\\\E = 6.626 \times 10^{-19} \ J[/tex]
[tex]K.E_{max} = E - \phi\\\\K.E_{max} = 6.626\times 10^{-19} \ J \ - \ (1.8 \times 1.602 \times 10^{-19} \ J)\\\\K.E_{max} = 6.626\times 10^{-19} \ J \ - \ 2.884 \times 10^{-19} \ J\\\\K.E_{max} =3.742 \times 10^{-19} \ J[/tex]
Therefore, the maximum kinetic energy of the emitted photons is 3.742 x 10⁻¹⁹ J
2. Is this an open or a closed circuit?
open circuit
closed circuit
Answer:
Open Circuit
Explanation:
This Picture represents an open circuit.
Answer: Closed Circuit
Explanation:
Use the following information for questions 18 - 21. A 0.13 kg disk is rotating at an angular speed of 57 rad/s. The disk has a radius of 0.25 m. The disk speeds up for 3 s. After the 3 s have passed, the edge of the disk is under a centripetal force of 312.13 N. What is the centripetal acceleration of the disk at this time
Answer:
[tex]a=2401m/s^2[/tex]
Explanation:
From the question we are told that:
Mass [tex]m=0.13kg[/tex]
Angular speed [tex]\omega=57rads/s[/tex]
Radius [tex]r=0.25m[/tex]
Time [tex]t=3s[/tex]
[tex]F=312.13N[/tex]
Generally the equation for centripetal acceleration is mathematically given by
[tex]a=\frac{f}{m}[/tex]
[tex]a=\frac{312.13}{0.13}[/tex]
[tex]a=2401m/s^2[/tex]
Two insects are at points 1 and 2. which
of the two insects has the greater kinetic energy of rotation
13. What type of lens bends light outwards and away from a point?
concave
Answer:
No,it isn't concave. The correct answer is convex lens.
Explanation:
A lens is a piece of transparent material bound by two surfaces of which at least one is curved. A lens bound by two spherical surfaces bulging outwards is called a bi-convex lens or simply a convex lens. A single piece of glass that curves outward and converges the light incident on it is also called a convex lens.
Convex lens is the answer.
See the attached diagram.
what is the velocity of a 1.3 kg puppy with a forward momentum of 6 kg m/s
Answer:
by using p = mv equation we can find v,
6 = 1.3 v
4.615 = v
Four 8.5-kg spheres are located at the corners of a square of side 0.90 m.
A. Calculate the magnitude of the gravitational force exerted on one sphere by the other three.
B. Calculate the direction of the gravitational force exerted on one sphere by the other three.
Explanation:
the answer is in the above image
Which describes the bending of light as it passes around or through a slit
Answer:
Diffraction
Explanation:
Hope that helps!!!
A 70-kg boy is surfing and catches a wave which gives him an initial speed of 1.6 m/s. He then drops through a height of 1.60 m, and ends with a speed of 8.5 m/s. How much nonconservative work (in kJ) was done on the boy
Answer:
3.6 KJ
Explanation: Given that a 70-kg boy is surfing and catches a wave which gives him an initial speed of 1.6 m/s. He then drops through a height of 1.60 m, and ends with a speed of 8.5 m/s. How much nonconservative work (in kJ) was done on the boy
The workdone = the energy.
There are two different energies in the scenario - the potential energy (P.E ) and the kinetic energy ( K.E )
P.E = mgh
P.E = 70 × 9.8 × 1.6
P.E = 1097.6 J
P.E = 1.098 KJ
K.E = 1/2mv^2
K.E = 1/2 × 70 × 8.5^2
K.E = 2528.75 J
K.E = 2.529 KJ
The non conservative workdone = K.E + P.E
Work done = 1.098 + 2.529
Work done = 3.63 KJ
Therefore, the non conservative workdone is 3.6 KJ approximately
the 200 g baseball has a horizontal velocity of 30 m/s when it is struck by the bat, B, weighing 900 g, moving at 47 m/s. during the impact with the bat, how many impules of importance are used to find the final velocity of the bat
Solution :
Given :
Mass of the baseball, m = 200 g
Velocity of the baseball, u = -30 m/s
Mass of the baseball after struck by the bat, M = 900 g
Velocity of the baseball after struck by the bat, v = 47 m/s
According to the conservation of momentum,
[tex]Mv+mu=Mv_1+mv_2[/tex]
(900 x 47) + (200 x -30) = (900 x [tex]v_1[/tex]) + (200 x [tex]v_2[/tex])
36300 = (900 x [tex]v_1[/tex]) + (200 x [tex]v_2[/tex])
[tex]9v_1 + 2v_2 = 363[/tex] ..............(i)
[tex]9v_1 = 363 - 2v_2[/tex]
[tex]v_1=\frac{363 - 2v_2}{9}[/tex]
The mathematical expression for the conservation of kinetic energy is
[tex]\frac{1}{2}Mv^2+\frac{1}{2}mu^2 = \frac{1}{2}Mv_1^2+\frac{1}{2}mv_2^2[/tex]
[tex]\frac{1}{2}(900)(47)^2+\frac{1}{2}(200)(-30)^2 = \frac{1}{2}(900)v_1^2+\frac{1}{2}(200)v_2^2[/tex] ................(ii)
[tex]$(9)(14)^2+(2)(-30)^2 = (9)v_1^2+2v_2^2$[/tex]
[tex]21681 = 9v_1^2+2v_2^2[/tex]
Substituting (i) in (ii)
[tex]21681= 9\left( \frac{363-2v_2}{9}\right)^2+2v_2^2[/tex]
[tex](363-2v_2)^2+18v_2^2=195129[/tex]
[tex](363)^2+18v_2^2-2(363)(2v_2)+(363)^2-195129=0[/tex]
[tex]22v_2^2-145v_2-63360=0[/tex]
Solving the equation, we get
[tex]v_2=96 \ m/s, -30 \ m/s[/tex]
The negative velocity is neglected.
Therefore, substituting 96 m/s for [tex]v_2[/tex] in (i), we get
[tex]v_1=\frac{363-(2 \times 96)}{9}[/tex]
= 19
Thus, only impulse of importance is used to find final velocity.
En un barrio un estudiante observa un roedor en medio de dos postes, los cuales están comunicados por un solo cable de fibra óptica, el cual calcula que tiene 50 m de longitud de poste a poste. Dicho roedor al estar apoyado pandea el cable 0.058 m. Si el estudiante intuye, que por sus clases de bilogía el roedor tiene aproximadamente 350gde masa, ¿Cuál será la tensión del cable debido a dicho suceso?
Answer:
7 Newton
Explanation:
Dado
Longitud de la cuerda = 50 m
El cable se dobla en 0,058 m.
Masa de roedor = 350 gramos = 0,35 kg
T = m * a + m × v2 / r
Sustituyendo los valores dados obtenemos
T = 0,35 (10 + 10)
T = 0,35 * 20
T = 7 Newton
Determine the tension in the string that connects M2 and M3.
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Two loops of wire are arranged so that a changing current in one will induce a current in the other. If the current in the first is increasing clockwise by one amp every second, the current in the second loop will
Answer:
The current in the second loop will stay constant
Explanation:
Since the induced emf in the second coil, ε due to the changing current i₁ in the first wire loop ε = -Mdi₁/dt where M = mutual inductance of the coils and di₁/dt = rate of change of current in the first coil = + 1 A/s (positive since it is clockwise)
Now ε = i₂R where i₂ = current in second wire loop and R = resistance of second wire loop.
So, i₂R = -Mdi₁/dt
i₂ = -Mdi₁/dt/R
Since di₁/dt = + 1 A/s,
i₂ = -Mdi₁/dt/R
i₂ = -M × + 1 A/s/R
i₂ = -M/R
Since M and R are constant, this implies that i₂ = constant
So, the current in the second wire loop will stay constant.
2. Ms. Evelyn lined up her students at recess on the soccer field. She told each student to kick a soccer ball as hard as they could. Then she measured how far each student kicked the soccer ball and marked the distance with a flag. After the activity she brought the class back inside and created a graph from the data. Did Ms. Evelyn's class do an experiment? A. Yes, because they did several tests with the soccer balls and recorded their observations. B. Yes, because every student kicked the same soccer ball. C. No, because they did not start with a hypothesis or a control group. This was an investigation. D. No, because all experiments require the use of a laboratory and scientists.
Answer
A. Yes, because they did several tests with the soccer balls and recorded their observations. B. Yes, because every student kicked
Explanation:
If the frequency of a sound wave is 250 hertz and its wavelength is 1.36 meters, what is the wave's velocity
OA. 250 meters/second
ОВ.
340 meters/second
O c.
200 meters/second
OD.
120 meters/second
Answer:
B
Explanation:
V=frequency*wavelength V=? W=1.36mF=250hertzAnswer:
B
Explanation:
Bc i say
negative effects of restricting roles in a democratic society
Answer:
it could lead to riot
it could lead to uncertainty of life and property
Answer:
Positive: has everybody informed on whats going on and where. Unadulterated media could let the people know the truth about their governments.
Negative: adulterated media could give people wrong ideas and leading to more unnecessary problems. Media who prioritise money over society would always do what gets them more money, thus their information is unreliable. Since most people believe what the media says, media has the power to alter the truth within an instance
what are two injuries that heal slowly and with difficulty
A golf ball is dropped from rest from a height of 8.40 m. It hits the pavement, then bounces back up, rising just 5.60 m before falling back down again. A boy then catches the ball when it is 1.40 m above the pavement. Ignoring air resistance, calculate the total amount of time that the ball is in the air, from drop to catch.
Answer:
t1= 8.40/10 =.84 s
t2 = 5.60/10 = .56s
t3= 1.4/10 = .14s
total time = 1.54 sec
A 55 kg person is in a head-on collision. The car's speed at impact is 12 m/s. Estimate the net force on the person if he or she is wearing a seat belt and if the air bag deploys.
Calculate the kinetic energy of a 100.0-kg meteor approaching the Earth at a speed of 10.0 km/s. Remember that 1 km = 1000 m.
5.00 × 109 J
10 × 107 J
50.0 × 108 J
1.00 × 108 J
A train starts from rest and accelerates uniformly until it has traveled 5.6 km and acquired a forward velocity of The train then moves at a constant velocity of for 420 s. The train then slows down uniformly at until it is brought to a halt. The acceleration during the first 5.6 km of travel is closest to which of the following?
a. 0.19 m/s^2
b. 0.14 m/s^2
c. 0.16 m/s^2
d. 0.20 m/s^2
e. 0.17 m/s^2
Answer:
The acceleration during the first 5.6 km of travel is closest to 0.16 m/s²
Option c) 0.16 m/s² is the correct answer.
Explanation:
Given the data in the question;
since the train starts from rest,
Initial velocity; u = 0 m/s
final velocity; v = 42 m/s
distance covered S = 5.6 km = ( 5.6 × 1000 )m = 5600 m
acceleration a = ?
From the third equation of motion;
v² = u² + 2as
we substitute in our values
( 42 )² = ( 0 )² + [ 2 × a × 5600 ]
1764 = 0 + [ 11200 × a ]
1764 = 11200 × a
a = 1764 / 11200
a = 0.1575 ≈ 0.16 m/s² { two decimal place }
Therefore, The acceleration during the first 5.6 km of travel is closest to 0.16 m/s²
Option c) 0.16 m/s² is the correct answer.
A police car in hot pursuit goes speeding past you. While the siren is approaching, the frequency of the sound you hear is 5500 Hz. When the siren is receding away from you, the frequency of the sound is 4500 Hz. Use the Doppler formula to determine the velocity of the police car. Use vsound=330 m/s.
What is the velocity v of the police car ?
When a police car in hot pursuit goes speeding past you, the velocity v of the police car is 33 m/s.
What is the Doppler formula?The formula is used when there exists a Doppler shift. The Doppler shift is due to the relative motion of sound waves between the source and observer.
The frequency increase by the Doppler effect is represented by the formula
f' = [tex]\dfrac{v-v_{o} }{v-v_{s} }[/tex]× f
Given the frequency of source f' is 5500 Hz . Velocity of the observer v₀ is 0.
Substituting the value into the equation will give us the velocity of the police car.
[tex]5500 = \dfrac{330}{330-v} \times f[/tex]...........(1)
When the car is receding, the frequency of the receiving signal f = 4500 Hz.
[tex]4500 = \dfrac{330}{330+v} \times f[/tex]..........(2)
Solving both equation, we get the velocity of a police car.
v = 33 m/s
Therefore, the velocity v of the police car is 33 m/s.
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g you hang an object of mass m on a spring with spring constant k and find that it has a period of T. If you change the spring to one that has a spring constant of 2 k, the new period is
Answer:
a) T = 2π [tex]\sqrt{\frac{m}{k} }[/tex], b) T ’= [tex]\frac{1}{\sqrt{2} } T[/tex]
Explanation:
a) A system formed by a mass and a spring has a simple harmonic motion with angular velocity
w² = k / m
angular velocity and period are related
w = 2π /T
we substitute
4π²/ T² = k / m
T = 2π [tex]\sqrt{\frac{m}{k} }[/tex]
b) We change the spring for another with k ’= 2 k, let's find the period
T ’= 2π [tex]\sqrt{\frac{m}{k'} }[/tex]
T ’= 2π [tex]\sqrt{ \frac{m}{2k} }[/tex]
T ’= [tex]\frac{1}{\sqrt{2} } T[/tex]
What is the law of conservation of energy
Electromagnetic waves from the sun carry what to the earth
Answer:
Solar radiation
Explanation:
Visible light, ultraviolet light, infrared, radio waves, X-rays, and gamma rays.
==> Energy
==> Radio noise, heat, visible light, ultraviolet radiation, X-rays, gamma rays
==> They carry all these kinds of energy wherever they go. Not only to the Earth.
Impervious surfaces prevent water from flowing through them.
True or false?
Answer: the answer is true
Explanation:
Increasing the surfactant concentration above the critical micellar concentration
will result in: Select one:
1.An increase in surface tension
2. A decrease in surface tension
3. No change in surface tension
4.None of the above
Answer:
Explanation:no change in surface tension
An increase in the surfactant concentration above the critical micellar concentration will result in no change in surface tension.
In water-gas interface, surfactant reduces the surface tension of water by adsorbing at the liquid–gas interface.
Also, in oil-water interface, surfactant reduces the interfacial tension between oil and water by adsorbing at the oil-water interface.
The concentration of the surfactant can increase to a level called critical micellar concentration, which is an important characteristic of a surfactant.
As the concentration of the surfactant increases before critical micellar concentration, the surface tension changes strongly with an increase in the concentration of the surfactant. After reaching the critical micellar concentration, any further increase in the concentration will result in no change of the surface tension, that is the surface tension will be constant.Thus, increasing the surfactant concentration above the critical micellar concentration will result in no change in surface tension.
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A 3.00-kg crate slides down a ramp. the ramp is 1.00 m in length and inclined at an angle of 30.08 as shown in the figure. The crate starts from rest at the top, experiences a constant friction force of magnitude 5.00 N, and continues to move a short distance on the horizontal floor after it leaves the ramp.
Answer:
2.55 m/s
Explanation:
A 3.00-kg crate slides down a ramp. the ramp is 1.00 m in length and inclined at an angle of 30° as shown in the figure. The crate starts from rest at the top, experiences a constant friction force of magnitude 5.00 N, and continues to move a short distance on the horizontal floor after it leaves the ramp. Use energy methods to determine the speed of the crate at the bottom of the ramp.
Solution:
The work done by friction is given as:
[tex]W_f=F_f\Delta S\\\\Where\ F_f\ is\ the \ frictional\ force=-5N(the\ negative \ sign\ because\ it\\acts\ opposite\ to \ direction\ of\ motion),\Delta S=slope\ length=1\ m\\\\W_f=F_f\Delta S=-5\ N*1\ m=-5J[/tex]
The work done by gravity is:
[tex]W_g=F_g*s*cos(\theta)\\\\F_g=force\ due\ to\ gravity=mass*acceleration\ due\ to\ gravity=3\ kg*9.81\\m/s^2, s=1\ m, \theta=angle\ between\ force\ and\ displacement=90-30=60^o\\\\W_g=3\ kg*9.81\ m/s^2*1\ m*cos(60)=14.72\ J\\\\The\ Kinetic\ energy(KE)=W_f+W_g=14.72\ J-5\ J=9.72\ J\\\\Also, KE=\frac{1}{2} mv^2\\\\9.72=\frac{1}{2} (3)v^2\\\\v=\sqrt{\frac{2*9.72}{3} } =2.55\ m/s[/tex]
A cart approaches a hill at an unknown velocity. It comes to rest at the top of the hill. Assume friction is negligible.
5.00 kg
10.0 m
Which is the best estimate for the amount of kinetic energy that the cart had at the bottom of the hill?
А
4.91 Joules
B
50.0 Joules
С
250 Joules
D
490 Joules