Answer:
a) The potential energy of the system is 1/9 of the total mechanical energy, when [tex]x= \frac{1}{3}\cdot A[/tex].
b) The fraction of the total mechanical energy that is kinetic if the displacement is 1/2 the amplitude is 1/2.
c) The maximum kinetic energy is increased by a factor of 9.
Explanation:
a) From Mechanical Physics, we remember that the mechanical energy of mass-spring system ([tex]E[/tex]), measured in joules, is the sum of the translational kinetic energy ([tex]K[/tex]), measured in joules, and elastic potential energy ([tex]U[/tex]), measured in joules. That is:
[tex]E = K + U[/tex] (1)
By definitions of translational kinetic energy and elastic potential energy, we have the following expressions:
[tex]K = \frac{1}{2}\cdot m \cdot v^{2}[/tex] (2)
[tex]U = \frac{1}{2}\cdot k\cdot x^{2}[/tex] (3)
Where:
[tex]m[/tex] - Mass, measured in kilograms.
[tex]v[/tex] - Velocity of the mass, measured in meters per second.
[tex]k[/tex] - Spring constant, measured in newtons per meter.
[tex]x[/tex] - Elongation of the spring, measured in meters.
If we know that [tex]U = \frac{1}{9}\cdot E[/tex], [tex]k = k[/tex] and [tex]E = \frac{1}{2}\cdot k \cdot A^{2}[/tex], then:
[tex]\frac{1}{18}\cdot k\cdot A^{2} = \frac{1}{2}\cdot k\cdot x^{2}[/tex]
[tex]\frac{1}{9}\cdot A^{2} = x^{2}[/tex]
[tex]x= \frac{1}{3}\cdot A[/tex]
The potential energy of the system is 1/9 of the total mechanical energy, when [tex]x= \frac{1}{3}\cdot A[/tex].
b) If we know that [tex]k = k[/tex], [tex]x = \frac{1}{2}\cdot A[/tex] and [tex]E = \frac{1}{2}\cdot k \cdot A^{2}[/tex], then the equation of energy conservation associated with the system is:
[tex]\frac{1}{2}\cdot k\cdot A^{2} = \frac{1}{4}\cdot k\cdot A^{2}+K[/tex]
[tex]K = \frac{1}{4}\cdot k\cdot A^{2}[/tex]
The fraction of the total mechanical energy that is kinetic if the displacement is 1/2 the amplitude is 1/2.
c) From the Energy Conservation equation associated with the system, we know that increasing the amplitude by a factor of 3 represents an increase in the elastic potential energy by a factor of 9. Then, the maximum kinetic energy is increased by a factor of 9.
What frequency is received by a person watching an oncoming ambulance moving at 115 km/h and emitting a steady 753 Hz sound from its siren
Answer:
77.6 Hz
Explanation:
What frequency is received by a person watching an oncoming ambulance moving at 115 km/h and emitting a steady 753 Hz sound from its siren.
The given parameters are:
Observer speed = 115 km/h
Source frequency = 753 Hz
Speed of sound = 342 m/s
First convert km/h to m/s
Observer speed = (115 × 1000) / 3600
Observer speed = 31.94 m/s
The frequency received by the person will be:
F = fv / ( V - v )
Where
F = frequency received by the person
f = siren frequency
V = speed of sound
v = speed of the ambulance
Substitute all the parameters into the formula
F = (753 × 31.94) / ( 342 - 31.94 )
F = 24050.82 / 310.06
F = 77.568 Hz
Therefore, the frequency received by a person is approximately 77.6Hz
What is Energy in physics?
Answer:
Energy, in physics, the capacity for doing work. It may exist in potential, kinetic, thermal, electrical, chemical, nuclear, or other various forms. There are, moreover, heat and work—i.e., energy in the process of transfer from one body to another.
Explanation:
Hope this helps!
what is the force of gravitational attraction between a 92 kg student and a 550 g slice of pizza that are 25 cm apart
Answer:
[tex]F = 5.4*10^{-8}\ N[/tex]
Explanation:
Given
Represent the mass of the student with M and the mass of the slice of pizza with m
[tex]M = 92kg[/tex]
[tex]m = 550g[/tex]
[tex]d = 25cm[/tex]
Required
Determine the force of attraction
This is calculated as:
[tex]F = \frac{GMm}{d^2}[/tex]
Where G = gravitational constant
[tex]G = 6.67408 * 10^{-11}\ m^3 kg^{-1} s^{-2}[/tex]
Convert both mass to kilogram and distance to metre
[tex]m = 550g[/tex]
[tex]m = 550kg/1000[/tex]
[tex]m = 0.55kg[/tex]
[tex]d = 25cm[/tex]
[tex]d = 25m/100[/tex]
[tex]d = 0.25m[/tex]
Substitute these values in [tex]F = \frac{GMm}{d^2}[/tex]
[tex]F = \frac{6.67408 * 10^{-11} * 92 * 0.55}{0.25^2}[/tex]
[tex]F = \frac{6.67408 * 92 * 0.55* 10^{-11} }{0.25^2}[/tex]
[tex]F = \frac{337.708448* 10^{-11} }{0.0625}[/tex]
[tex]F = 5403.335168* 10^{-11}[/tex]
[tex]F = 5.403335168* 10^3*10^{-11}[/tex]
[tex]F = 5.403335168*10^{3-11}[/tex]
[tex]F = 5.403335168*10^{-8}[/tex]
[tex]F = 5.4*10^{-8}\ N[/tex]
can vectors be strung together?
Answer:
The head-to-tail method is a graphical way to add vectors, The tail of the vector is the starting point of the vector, and the head (or tip) of a vector is the final, pointed end of the arrow.
Explanation:
why does sound energy even exist
In a double-slit experiment, the second-order bright fringe is observed at an angle of 0.61°. If the slit separation is 0.11 mm, then what is the wavelength of the light?
Answer:
[tex]5.86\times 10^{-7}\ \text{m}[/tex]
Explanation:
d = Slit separation = 0.11 mm
[tex]\theta[/tex] = Angle = [tex]0.61^{\circ}[/tex]
m = Order = 2
[tex]\lambda[/tex] = Wavelength
We have the relation
[tex]d\sin\theta=m\lambda\\\Rightarrow \lambda=\dfrac{d\sin\theta}{m}\\\Rightarrow \lambda=\dfrac{0.11\times 10^{-3}\times \sin0.61^{\circ}}{2}\\\Rightarrow \lambda=5.86\times 10^{-7}\ \text{m}[/tex]
The wavelength of the light is [tex]5.86\times 10^{-7}\ \text{m}[/tex].
An airplane is flying at a speed of 200 m/s in level flight at an altitude of 800 m. A package is to be dropped from the airplane to land on a target on the ground. At what horizontal distance away from the target should the package be released so that it lands on the target
Answer:
The
Explanation:
The horizontal distance covered is known as the range expressed as;
R = U√2H/g
U is the speed = 200m/s
H is the max height = 800m
g is the gravity = 9.8m/s²
R = 200√2(800)/9.8
R = 200√1600/9.8
R = 200√163.27
R = 200(12.78)
R = 2555.54
Hence the package should be released at a distance of 2555.54m
When lightning occurs, it produces a sound wave and a light wave at the same exact time. If u are watching a faraway storm, which wave gets to you first?
An electromagnet needs a magnetic metal core. To produce a magnetic field,
what else is required?
A second metal core?
A solenoid with current or no current running through it? Or a permanent magnet?
Answer:solenoid with current running through it
Explanation:just took the test
The time constant for RC circuit with the values of R1 and C1 is 5ms. What will be the time constant for a new RC circuit with the values: R2=10R1 and C2 = 0.5C1.
a. 2.5ms
b. 15.5ms
c. 50ms
d. 25ms
e. 15ms
Answer:
d. 25 ms
Explanation:
In a RC circuit we call time constant to the product of the resistance times the capacitance, which represents the time when the charge reaches to the 63% of the final value, as follows:[tex]\tau_{1} = R_{1} *C_{1} = 5 ms (1)[/tex]
If we have a new circuit with new values for R and C, the time constant will be defined in the same way, as follows:[tex]\tau_{2} =10* R_{1} *0.5*C_{1} = 5*(R_{1}* C_{1}) = 5* \tau_{1} = 5* 5 ms = 25 ms (2)[/tex]
Hypothesis: If the starting height of a sloped racetrack is increased, then the speed at which a toy car travels along the track will ________ because the toy car ____
Answer:
If the starting height of a sloped racetrack is increased, then the speed at which a toy car travels along the track will increase because the toy car will have a greater acceleration.
Explanation:
I hope this helped
Hypothesis: If the starting height of a sloped racetrack is increased, then the speed at which a toy car travels along the track will increase because the toy car gains more potential energy at the higher starting point.
When a toy car moves along a sloped racetrack, it converts its potential energy (due to its height above the ground) into kinetic energy (energy of motion). The higher the starting height of the racetrack, the more potential energy the toy car possesses initially.
As the toy car moves down the sloped track, it will accelerate due to the force of gravity. The potential energy is converted into kinetic energy, and the car's speed increases. According to the law of conservation of energy, the total mechanical energy (sum of potential and kinetic energy) remains constant as long as no external forces, such as friction, act on the car.
Therefore, if the starting height of the racetrack is increased, the toy car will have more potential energy to start with. As it moves down the track, it will convert this increased potential energy into kinetic energy, resulting in a higher speed compared to when it starts from a lower height.
To know more about speed here
https://brainly.com/question/17661499
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what transition metal has 5 more protons than the halogen found in period 3?
Answer: Titanium (Ti)
Explanation:
First, each element has a unique atomic number Z, that is equal to the number of protons in the nucleus.
The halogen in period 3 is chlorine (Ch)
Chlorine's atomic number is Z = 17, this means that it has 17 protons.
Now we want to find a transition metal that has 5 more protons, then this transition metal has Z = 17 + 5 = 22
Now we can look at the periodic table and find the element with Z = 22, and if this is in the d-block, then this will be a transition metal.
The element with Z = 22 is titanium (Ti)
please help! What is the relationship between velocity and acceleration?
Answer:Acceleration implies any change in the velocity of the object with respect to time. Velocity is nothing but the rate of change of displacement. On the other hand, acceleration is the rate of change of velocity with respect to time.
Explanation:
an object of mass 4kg moving with initial velocity if 20m/s accelerates for 10s and attaind a final velocity of 60m/s calculate the acceleration
Answer:
given us,
mass= 4×9.8gm m(9.8) formula
= 39.2
final velocity (v)= 60m/s
initial velocity (u)= 20m/s
time(t)= 10s
acleration(a)=?
now,
accleration(a)= v-u/t=60- 20/10
=40/10
=4m/s
:. the acceleration is 4 m/s
Explanation:
first we have to calculate mass and we can use acceleration formula
A penny is dropped from rest from a building 100m tall. what kind of motion is this
A. centripetal
B. Free fall
C. Linear
D. projectile
Answer:
this is a projectile
Answer:
D. projectile
Explanation:
Since it's dropped from a rest that means that it's velocity at the beginning is 0.
Use the above picture to fill in the blanks for the following statement.
One of the element carbon combines with one of the element oxygen to form one of the compound carbon dioxide.
Answer:
C + 2O ------ CO2
Explanation:
"One" element of Carbon combines with "Two" elements of Oxygen, to form "One" compound of Carbon dioxide.
I didn't really get what you meant but this is my guess of what you meant
I’ll give you a star if you answer this question. Which of the following is the best example of work being done
on an object?
in the woman's mouth if
she is drinking through a straw extending 0.085 m above the surface of the drink? Note:
Assume the drink has a density of 1015 kg/m^3. ????
Answer:
hi mate,
interesting question, first of all the pressure is determined by using the following formula:
Pg = p * G * h
where p is the density of the liquid, G is the gravity and h is the height difference, in you case you have:
p = 1015 kg/m3
G = 9.8m/s2
h = 0.085 m
insert these values into the equation above:
Pg = 1015 kg/m3 * 9.8m/s2 * 0.085 m = 849.81 kg·m-1·s-2 or 849.81 pascal
hope it helps, :-)
please mark me as brainliest
A hydraulic car jack needs to be designed so it can lift a 2903.57 lb car assuming that a person can exert a force of 24.41 lbs. If the piston the person is pushing on had a radius of 3.26 cm, what should the diameter of the piston be that is used to raise the car?
Answer:
Diameter of the piston would be 0.71 m (71.1 cm)
Explanation:
From the principle of pressure;
[tex]\frac{F_{1} }{A_{1} }[/tex] = [tex]\frac{F_{2} }{A_{2} }[/tex]
Let [tex]F_{1}[/tex] = 2903.57 lb, [tex]F_{2}[/tex] = 24.41 lbs, [tex]r_{2}[/tex] = 3.26 cm = 0.0326 m.
[tex]A_{2}[/tex] = [tex]\pi r^{2}[/tex]
= [tex]\frac{22}{7}[/tex] x [tex](0.0326)^{2}[/tex]
= 0.00334 [tex]m^{2}[/tex]
So that:
[tex]\frac{2903.57}{A_{1} }[/tex] = [tex]\frac{24.41}{0.00334}[/tex]
[tex]A_{1}[/tex] = [tex]\frac{2903.57*0.00334}{24.41}[/tex]
= 0.3973
[tex]A_{1}[/tex] = 0.4 [tex]m^{2}[/tex]
The radius of the piston can be determined by:
[tex]A_{1}[/tex] = [tex]\pi r^{2}[/tex]
0.3973 = [tex]\frac{22}{7}[/tex] x [tex]r^{2}[/tex]
[tex]r^{2}[/tex] = [tex]\frac{0.3973*7}{22}[/tex]
= 0.1264
r = [tex]\sqrt{0.1264}[/tex]
= 0.3555
r = 0.36 m
Diameter of the piston = 2 x r
= 2 x 0.3555
= 0.711
Diameter of the piston would be 0.71 m (71.1 cm).
Which type of mass movement is likely to result in considerable property damage, but rarely causes loss of life? a. debris avalanche b. rock fall c. mudflow d. creep
Answer:
The correct answer is D. Creep.
Explanation:
Ground creep is a slow downward movement of a hill or mountain slope without the formation of demolition forms. The decisive factor for this is the continuous flow of movement of the soil.
The main driver of collapse is the movement of the surface layer particles during expansion in a direction perpendicular to the slope, followed by vertical collapse on contraction. The visible effect of the collapsing is the inclination of fences and poles, as well as trees that grow out of the ground towards the slope and have trunks curved vertically, in more extreme cases it may be cracks on the walls of buildings.
If you are pushing 200 kg of textbooks with acceleration of 2m/s2, how much net force are you exerting on the books? (Fnet=ma)
( There is more than one answer)
200N
100N
400Kg
400N
400 kg.m/s2
Explanation:
m=200kg
a=2m/s2
F=ma
F=200kg×2m/s2
=400kg.m/s2 or 400N
A light truck with manual transmission has a circular brake drum with a diameter of d = 310 millimeters. Each brake pad, which presses against the drum, is s = 306 millimeters long. What central angle is subtended by one of the brake pads? Write your answer in both radians and degrees.
Answer:
113 degrees
1.974 radians
Explanation:
The angle can be calculated using below expression
Angle = arc/r
Where arc= diameter of d = 310 millimeters
r= s = 306 millimeters long.
Since both have the same unit, no need for conversion
Angle = arc/r = 306/(0.5×310 )
= 306/155
= 1.974 radians
Then to find the angle In degrees we have
R x 180/pi = D
Where R= angle in radians= 1.974 radians
1.974 x 180/π
Where π= 22/7
= 113 degrees( approximately)
Therefore, central angle is subtended by one of the brake pads is 1.974 radians
A car starts from rest and accelerates uniformly over a time of 7 seconds for a distance of 190m. Find the the acceleration of the car.
Answer:
a = 7.75 [m/²]
Explanation:
To solve this problem we must use the following equation of kinematics.
[tex]x=x_{0} +v_{o} *t + (\frac{1}{2})*a*t^{2}[/tex]
where:
x = final distance = 190 [m]
Xo = initial distance = 0
Vo = initial velocity = 0 (car starts from the rest)
a = acceleration [m/s²]
t = time = 7 [s]
190 = 0 + (0*7) + 0.5*a*(7²)
190 = 0.5*49*a
a = 7.75 [m/²]
A series RCL circuit contains a 65.2-Ω resistor, a 2.26-μF capacitor, and a 2.08-mH inductor. When the frequency is 2400 Hz, what is the power factor of the circuit?
Answer:
The power factor of the circuit is 0.99
Explanation:
Given;
resistance of the resistor, R = 65.2 ohms
capacitance of the capacitor, C = 2.26 μF = 2.26 x 10⁻⁶ F
inductance, L = 2.08 mH = 2.08 x 10⁻³ H
frequency of the AC, f = 2400 Hz
The angular frequency is given by;
ω = 2πf
ω = 2π(2400) = 15081.6 rad/s
The inductive reactance is given by;
XL = ωL
XL = (15081.6 x 2.08 x 10⁻³)
XL = 31.37 ohms
The capacitive reactance is given by;
[tex]X_c = \frac{1}{\omega C} \\\\X_c = \frac{1}{(15081.6)(2.26*10^{-6} )}\\\\X_c = 29.34 \ ohms[/tex]
The phase difference is given by;
[tex]tan\phi = \frac{X_l - X_c}{R}\\\\ tan\phi =\frac{31.37-29.34}{65.2} \\\\tan\phi = 0.0311 \\\\\phi = tan^{-1} (0.0311)\\\\\phi = 1.78^0[/tex]
The power factor is given by;
CosФ = Cos(1.78) = 0.99
Therefore, the power factor of the circuit is 0.99
A 760-kg horse whose power output is 1 hp is pulling a sled over the snow at 3.9 m/s. Find the force the horse exerts on the sled. Round your intermediate step to one decimal place and the final answer to two decimal places.
Answer:
191 N
Explanation:
Power can be regarded as the amount of energy that is been transfered at a unit time and can be calculated using the Express below
Po = F*V
P= power
F= force
V= velocity
From the question, we were given power output as 1 hp and velocity= 3.9 m/s.
But
1hp= 746 Watts = 746 Joules/s.
Then substitute the values
Po = F*V = 746 J/s
F ×3.9 = 746
F= 746/3.9
F = 191 N.
Therefore, the force the horse exerts on the sled iss 191 N
1. An object in motion tends to stay in
motion because it has ___?____. (inertia or
terminal velocity)
Answer: intertia
Explanation:
The displacement of a transvers wave travelling on a string is represented by D1 = 4.2sin(0.84.x - 47t + 21) where D1 and x are in cm and t in s.Find an equation that represents a wave which, when traveling in the opposite direction, will produce a standing wave when added to this one
Answer:
The equation for such type of wave is [tex]D_2 = sin(0.84.x + 47t + 21)[/tex]
Explanation:
From the question we are told that
The displacement is [tex]D_1 = 4.2sin(0.84.x - 47t + 21)[/tex]
Here the wave number is k= 0.84
The angular frequency is [tex]w = 47[/tex]
The phase shift is [tex]\phi = 21[/tex]
Generally the equation that represents a wave which, when traveling in the opposite direction, will produce a standing wave when added to this one is mathematically represented as
[tex]D_2 = sin(0.84.x + 47t + 21)[/tex]
How do we use energy transformation in our daily lives?
Answer:hat are some examples of energy transformation?
The Sun transforms nuclear energy into heat and light energy.
Our bodies convert chemical energy in our food into mechanical energy for us to move.
An electric fan transforms electrical energy into kinetic energy.
Explanation:
You have a source of energy containing 21 gj of energy at 600k how much this energy can be converted to work when rejecting heat to the atmosphere at 27°C?
Answer:
Available energy = 35 x 10⁶ J
Explanation:
Given:
Amount of energy (Q) = 21 gj = 21 x 10⁹ J
Temperature T1 = 600 k
Temperature T0 = 27 + 273 = 300k
Find:
Available energy
Computation:
Available energy = Q[1/T0 - 1/T1]
Available energy = 21 x 10⁹ J[1/300 - 1/600]
Available energy = 35 x 10⁶ J
A television of mass 15 kg sits on a table. The coefficient of static friction
between the table and the television is 0.35. What is the minimum applied
force that will cause the television to slide?
A) 38 N
B) 147 N
C) 51 N
D) 79 N
Answer:
more than 51.45 N
__________________________________________________________
We are given:
Mass of the television = 15 kg
Coefficient of Static friction = 0.35
Minimum force required to move the television:
Normal Force:
We know that the normal force is equal and opposite to the Weight of the television
Weight of the television = Mg
[where m is the mass and g is the acceleration due to gravity]
Weight = 15 * 9.8
Weight = 147 N
Force of Friction:
We are given the coefficient of Friction = 0.35
We know that coefficient of Friction = Force of friction / Normal Force
replacing the variables
0.35 = Force of Friction / 147
Force of Friction = 147 * 0.35 [multiplying both sides by 147]
Force of Friction = 51.45 N
Since a force of 51.45 N is will be applied opposite to the direction of application of Force, the television will only move when we apply more force than 51.45 N
Answer:
it is C
Explanation: