Answer:
386.13 N
Explanation:
The kinetic energy of the baseball is converted into workdone in moving the glove backward( work energy theorem).
Therefore, KE of the ball
[tex]\frac{1}{2} mv^2 =\frac{1}{2}(0.145)35^2\\ = 88.81 \text{J}[/tex]
Now, workdone in moving the glove
W= Fd
where F = Force applied, d = displacement of the glove= 0.23 cm.
88.81 = F×0.23
F= 88.81/0.23 = 386.13 N
You measure the power delivered by a battery to be 4.26 W when it is connected in series with two equal resistors. How much power will the same battery deliver if the resistors are now connected in parallel across it
Answer:
The power delivered by the battery is 17.04 W
Explanation:
Power through a circuit is given as
P = IV ....1
where P is the power
I is the current through the circuit
V is the voltage through the circuit
The voltage in a circuit is given as
V = IR ....2
Let us take the value of each resistor as equal to R
when connected in series, the total resistance will be
[tex]R_{t}[/tex] = R + R = 2R
If we assume constant voltage through the circuit, then from equation 2, the current in this case is
I = V/2R
If the resistors are connected in parallel, then the total resistance will be
[tex]\frac{1}{R_{t} }[/tex] = [tex]\frac{1}{R}[/tex] +
[tex]R_{t}[/tex] = R/2
The current in this case will be increased since the resistance is reduced
I = 2V/R
comparing the two situations, we can see that the current increased when connected in parallel to a ratio of
[tex]\frac{2V}{R}[/tex] ÷ [tex]\frac{V}{2R}[/tex] =
This means that the current increased 4 times
From equation 1, we can see that electrical power is proportional to the current at a constant voltage, therefore, the power will also increase by four times to
P = 4 x 4.26 = 17.04 W
16. If one body is positively charged and another body is negatively charged, free electrons tend to
O A. move from the negatively charged body to the positively charged body
O B. remain in the positively charged body
OC. move from the positively charged body to the negatively charged body
O D. remain in the negatively charged body
Answer:
Hey there!
The correct answer would be option A. If one body is positively charged and another body is negatively charged, free electrons tend to move from the negatively charged body to the positively charged body
Let me know if this helps :)
g As observed on earth, a certain type of bacteria is known to double in number every 24 hours. Two cultures of these bacteria are prepared, each consisting initially of one bacterium. One culture is left on earth and the other placed on a rocket that travels at a speed of 0.893c relative to the earth. At a time when the earthbound culture has grown to 256 bacteria, how many bacteria are in the culture on the rocket, according to an earth-based observer
Answer:
86.4 hrs
Explanation:
The amount of bacteria is initially 1
It doubles every 24 hrs.
After first 24 hrs, the amount = 2
After next 24 hrs = 4
After next 24 hrs = 8
After next 24 hrs = 16
After next 24 hrs = 32
After next 24 hrs = 64
After next 24 hrs = 128
After next 24 hrs = 256
Total time taken to reach 256 = 24 x 8 = 192 hrs
For the bacteria culture on the rocket that travels at a speed of 0.893c relative to the earth, this time is contracted by the relationship
t = t'(1 - ¥^2)^0.5
Where t is the contracted time =?
t' is the time on earth
¥ = v/c
Where v is the speed of the rocket
c is the speed of light
since v = 0.893c
¥ = 0.893
Substituting, we have
t = 192 x (1 - 0.893^2)^0.5
t = 192 x 0.2025^0.5
t = 192 x 0.45 = 86.4 hrs
Question 5 of 25
Which of the following means that a mirror is convex?
A. +d;
B. -d;
O C. +f
O D. -f
The sign that represents a convex mirror is +f (option C). Details about convex mirror can be found below.
What is a convex mirror?A convex mirror is that which is curved or bowed outward like the outside of a bowl or sphere or circle.
The focal length is the distance at which a lens or mirror is in focus. The focal length (f) is usually positive (+) for a convex mirror.
Therefore, the sign that represents a convex mirror is +f.
Learn more about convex mirror at: https://brainly.com/question/3627454
#SPJ1
"When red light in vacuum is incident at the Brewster angle on a certain glass slab, the angle of refraction is"
Complete Question
When red light in vacuum is incident at the Brewster angle on a certain glass slab, the angle of refraction is [tex]36.0 ^o[/tex] . What are
(a) the index of refraction of the glass and
(b) the Brewster angle?
Answer:
a
[tex]n_r = 1.376[/tex]
b
[tex]i = 54^o[/tex]
Explanation:
From the question we are told that
The angle of refraction is [tex]r = 36.0 ^o[/tex]
Generally according Brewster law
[tex]i + r = 90[/tex]
Here [tex]i[/tex] is the angle of incidence which is also the Brewster angle
So
[tex]i + 36.0 = 90[/tex]
[tex]i = 54^o[/tex]
Now the refractive index is mathematically represented as
[tex]n_r = tan (i)[/tex]
substituting values
[tex]n_r = tan (54)[/tex]
[tex]n_r = 1.376[/tex]
A vertical spring stretches 3.8 cm when a 13-g object is hung from it. The object is replaced with a block of mass 20 g that oscillates in simple harmonic motion. Calculate the period of motion.
Answer:
The period of motion is 0.5 second.
Explanation:
Given;
extension of the spring, x = 3.8 cm = 0.038 m
mass of the object, m = 13 g = 0.013 kg
Determine the force constant of the spring, k;
F = kx
k = F / x
k = mg / x
k = (0.013 x 9.8) / 0.038
k = 3.353 N/m
When the object is replaced with a block of mass 20 g, the period of motion is calculated as;
[tex]T = 2\pi\sqrt{\frac{m}{k} } \\\\T = 2\pi\sqrt{\frac{0.02}{3.353} } \\\\T = 0.5 \ second[/tex]
Therefore, the period of motion is 0.5 second.
Electromagnetic radiation is more common than you think. Radio and TV stations emit radio waves when they broadcast their programs; microwaves cook your food in a microwave oven; dentists use X rays to check your teeth. Even though they have different names and different applications, these types of radiation are really all the same thing: electromagnetic (EM) waves, that is, energy that travels in the form of oscillating electric and magnetic fields. Which of the following statements correctly describe the various applications listed above?
a) All these technologies use radio waves, including low-frequency microwaves.
b) All these technologies use radio waves, including high-frequency microwaves.
c) All these technologies use a combination of infrared waves and high-frequency microwaves.
d) Microwave ovens emit in the same frequency band as some wireless Internet devices.
e) The radiation emitted by wireless Internet devices has the shortest wavelength of all the technologies listed above.
f) All these technologies emit waves with a wavelength in the range 0.10 to 10.0 m.
g) All the technologies emit waves with a wavelength in the range 0.01 to 10.0 km.
Answer:
d) Microwave ovens emit in the same frequency band as some wireless Internet devices.
Explanation:
Microwave are radio waves of short wavelength, from about 10 centimetres to one millimetre, in the Super High Frequency and the Extremely High Frequency bands. Microwaves can penetrate into materials and deposit their energy below the surface which is why is is used in microwave heating found in microwave oven. Transmission of data sometimes involves the use of microwaves to send and receive information over a long distance. Microwaves are the mainly used in radar, used for satellite communication, and wireless networking technologies such as Wi-Fi.
A ferry boat sails east across a lake at 10 km/h. A woman is walking east on
the boat at 1.5 km/h. What is her speed relative to the boat?
A. 8.5 km/h west
B. 8.5 km/h east
C. 1.5 km/h east
O D. 1.5 km/h west
Answer:
B
8.5 km/h east
Explanation:
Relative velocity= Va -Vb
=10-1.5
=8.5 km/h east
The concept relative speed is used when two or more bodies moving with some speed are considered. The relative speed of woman to the boat is 8.5 km/h east. The correct option is B.
What is relative speed?The relative speed of two bodies is defined as the sum of their speeds if they are moving in the opposite direction and it is the difference of their speeds if they are moving in the same direction.
The speed of the moving body with respect to the stationary body is known as the relative speed. The term relative means in comparison to. The relative speed is a scalar quantity.
Here both the boat and women are travelling in the same direction. So the relative speed is given as:
Relative speed = 10 - 1.5 = 8.5 km / h
Therefore the relative speed is 8.5 km/h east.
Thus the correct option is B.
To know more about relative speed, visit;
https://brainly.com/question/11476119
#SPJ7
Design a voltage divider to provide the following approximate voltages with respect to ground using a 30 V source: 8.18 V, 14.7 V, and 24.6 V. The current drain on the source must be limited to no more than 1 mA. The number of resistors, their values, and their wattage ratings must be specified. A schematic showing the circuit arrangement and resistor placement must be provided
Answer:
R₁ = 14.7 10³ Ω , R₂ = 8.18 10³ Ω , R₃ = 1.72 10³ Ω , R₄ = 5.4 10³ Ω 1/8 W resistor
Explanation:
For this exercise we must use a series circuit since the sum of the voltage on each resin is equal to the source voltage (V = 30 V)
Therefore we build a circuit with 4 resistors in series, in such a way that
V = i R
let the voltage
1st resistance
V = i R
R₁ = V / i
R₁ = 14.7 / 1 10⁻³
R₁ = 14.7 10³ Ω
power is
P = V i
P = 14.7 1 10⁻³
P = 14.7 10⁻³ W = 0.0147 W
a resistance of ⅛ W is indicated
2nd resistance
R₂ = 8.18 / 1 10⁻³
R₂ = 8.18 10³ Ω
Power
P = 8.18 1 10⁻³
P = 0.00818W
a 1/8 W resistor
3rd resistance
this resistance is calculated in such a way that
V₁ + V₂ + V₃ = 24.6
V₃ = 24.6 - V₁ -V₂
V₃ = 24.6 - 14.7 - 8.18
V₃ = 1.72 V
R₃ = 1.72 / 1 10⁻³
R₃ = 1.72 10³ Ω
power
P = Vi
P = 1.72 10⁻³
P = 0.00172 W
a resistance of ⅛ W
To obtain the voltage of 24.6 we use this three resistors together
4th resistance
The value of this resistance is calculated so that the sum of all the voltages reaches the source voltage
30 = V₁ + V₂ + V₃ + V₄
V₄ = 30 - V₁ -V₂ -V₃
V₄ = 30 -14.7 - 8.18 - 1.72
V₄ = 5.4 V
R₄ = 5.4 / 1 10⁻³
R₄ = 5.4 10³ Ω
Power
P = V i
P = 5.4 10⁻³
P = 0.0054 W
⅛ W resistance
The values of these resistance are commercially
Let's check the consumption of the circuit
R_total = R₁ + R₂ + R₃ + R₄
R_total = (14.7 + 8.18 + 1.72 + 5.4) 10³
R_total = 30 10³
the current circulating in the circuit is
i = V / R_total
i = 30/30 10³
i = 1 10⁻³ A
therefore it is within the order requirement.
for connections see attached diagram
A toroidal solenoid with 400 turns of wire and a mean radius of 6.0 cm carries a current of 0.25 A. The relative permeability of the core is 80.
(a) What is the magnetic field in the core?
(b) What part of the magnetic field is due to atomic currents?
Answer:
A) 0.0267 T
B) 0.0263 T
Explanation:
Given that
The number of turns, N = 400
Radius of the wire, r = 6 cm = 0.06 m
Current in the wire, I = 0.25 A
Relative permeability, K(m) = 80
See the attached picture for the calculation
A city of Punjab has a 15 percent chance of wet weather on any given day. What is the probability that it will take a week for it three wet weather on 3 separate days?
Answer: 0.0617
Explanation:
Given: The probability of wet weather on any given day in a city of Punjab : p=15%=0.15
Let X be a binomial variable that represents the number of days having wet weather.
Binomial probability formula : [tex]P(X=x)=^nC_xp^x(1-p)^x[/tex], where n= total outcomes, p = probability of success in each outcomes.
Here, n= 7 ( 1 week = 7 days)
The probability that it will take a week for it three wet weather on 3 separate days:
[tex]P(X=3)^=\ ^7C_3(0.15)^3(1-0.15)^{7-3}\\\\=\dfrac{7!}{3!(7-3)!}(0.15)^3(0.85)^4\\\\=\dfrac{7\times6\times5}{3\times2}\times 0.003375\times0.52200625\approx0.0617[/tex]
Hence, the required probability =0.0617
A bar magnet is dropped from above and falls through the loop of wire. The north pole of the bar magnet points downward towards the page as it falls. Which statement is correct?a. The current in the loop always flows in a clockwise direction. b·The current in the loop always flows in a counterclockwise direction. c. The current in the loop flows first in a clockwise, then in a counterclockwise direction. d. The current in the loop flows first in a counterclockwise, then in a clockwise direction. e. No current flows in the loop because both ends of the magnet move through the loop.
Answer:
b. The current in the loop always flows in a counterclockwise direction.
Explanation:
When a magnet falls through a loop of wire, it induces an induced current on the loop of wire. This induced current is due to the motion of the magnet through the loop, which cause a change in the flux linkage of the magnet. According to Lenz law, the induced current acts in such a way as to repel the force or action that produces it. For this magnet, the only opposition possible is to stop its fall by inducing a like pole on the wire loop to repel its motion down. An induced current that flows counterclockwise in the wire loop has a polarity that is equivalent to a north pole on a magnet, and this will try to repel the motion of the magnet through the coil. Also, when the magnet goes pass the wire loop, this induced north pole will try to attract the south end of the magnet, all in a bid to stop its motion downwards.
The current in the loop always flows in a counterclockwise direction. Hence, option (b) is correct.
The given problem is based on the concept and fundamentals of magnetic bars. When a magnet falls through a loop of wire, it induces an induced current on the loop of wire. There is some magnitude of current induced in the wire.
This induced current is due to the motion of the magnet through the loop, which cause a change in the flux linkage of the magnet. According to Lenz law, the induced current acts in such a way as to repel the force or action that produces it. For this magnet, the only opposition possible is to stop its fall by inducing a like pole on the wire loop to repel its motion down. An induced current that flows counterclockwise in the wire loop has a polarity that is equivalent to a north pole on a magnet, and this will try to repel the motion of the magnet through the coil. Also, when the magnet goes pass the wire loop, this induced north pole will try to attract the south end of the magnet, all in a bid to stop its motion downwards.Thus, we can say that the current in the loop always flows in a counterclockwise direction. Hence, option (b) is correct.
Learn more about the magnetic field here:
https://brainly.com/question/14848188
An ac source of period T and maximum voltage V is connected to a single unknown ideal element that is either a resistor, and inductor, or a capacitor. At time t = 0 the voltage is zero and increasing toward a maximum. At time t = T/4 the current in the unknown element is equal to zero, and at time t = T/2 the current is I = -I max, where Imax is the current amplitude. What is the unknown element?
a. a resistor
b. an inductor or a capacitor
c. an inductor
d. a capacitor
The mass (M) of a piece of metal is directly proportional to its volume (V), where the proportionality constant is the density (D) of the metal. (1) Write an equation that represents this direct proportion, in which D is the proportionality constant. The density of lead metal is 11.3 g/cm3. (2) What is the mass of a piece of lead metal that has a volume of 17.3 cm3
Answer:
1) M = 11.3V2) 195.49 gramsExplanation:
1) If the mass (M) of a piece of metal is directly proportional to its volume (V), where the proportionality constant is the density (D) of the metal, this is expressed mathematically as shown;
M ∝ V
M = kV
For every proportionality sign, there will always be a proportionality constant 'k'
Since the proportionality constant is the density (D) of the metal, the equation will become;
M = DV
Given the density to be 11.3 g/cm3, the equation will become;
M = 11.3V
Hence, the equation that represents this direct proportion, in which D is the proportionality constant with metal density of 11.3g/cm³ is M = 11.3V
2) If the volume of the metal is 17.3cm³, on substituting this values into the equation in (1) to get the mass of the metal, we will have;
M = 11.3V
M = 11.3 * 17.3
M = 195.49 grams
Hence, the mass of a piece of lead metal that has a volume of 17.3 cm³ is 195.49 grams.
Consider a bus traveling to the west (negative x direction) that begins to slow down as it approaches a traffic light. Which statement concerning its acceleration in the x direction is correct
Complete question is;
Consider a bus traveling to the west (-x direction) begins to slow down as it approaches a traffic light. Which statement concerning its acceleration in the x direction is correct
a) The bus is decelerating and its acceleration is positive.
b) The bus is decelerating, and its acceleration is negative.
c) The acceleration is zero.
d) A statement cannot be made using the information given.
Answer:
Option A - bus is decelerating and acceleration is positive.
Explanation:
We are told that the bus is travelling in (negative x direction) and begins to slow down. Since the bus is slowing down, it means that the bus is undergoing a negative acceleration which is called deceleration.
Thus, the bus is decelerating.
Since it is moving in the negative x-axis, it means acceleration is now; -(-a) which gives +a.
Thus, bus is decelerating and acceleration is positive.
NASA is giving serious consideration to the concept of solar sailing. A solar sailcraft uses a large, low- mass sail and the energy and momentum of sunlight for propulsion.
Should the sail be absorbing or reflective? Why?
a. The sail should be reflective because in this case the momentum transferred to the sail per unit area per unit time is smaller than for absorbing sail, therefore the radiation pressure is larger for the reflective sail
b. The sail should be absorbing because in this case the momentum transferred to the sail per unit area per unit time is larger than for reflective sail, therefore the radiation pressure is larger for the absorbing sail
c. The sail should be absorbing because in this case the momentum transferred to the sail per unit area per unit time is smaller than for reflective sail, therefore the radiation pressure is larger for the absorbing sail.
d. The sail should be reflective because in this case the momentum transferred to the sail per unit area per unit time is larger than for absorbing sail, therefore the radiation pressure is larger for the reflective sail
Answer:
d. The sail should be reflective because in this case the momentum transferred to the sail per unit area per unit time is larger than for absorbing sail, therefore the radiation pressure is larger for the reflective sail.
Explanation:
Let us take the momentum of a photon unit as u
we know that the rate of change of momentum is proportional to the force exerted.
For a absorbing surface, the photon is absorbed, therefore the final momentum is zero. From this we can say that
F = (u - 0)/t = u/t
for a unit time, the force is proportional to the momentum of the wave due to its energy density. Therefore,
F = u
For a reflecting surface, the momentum of the wave strikes the sail and changes direction. Since we know that the speed of light does not change, then the force is proportional to
F = (u - (-u))/t = 2u/t
just as the we did above, it becomes
F = 2u.
From this we can see that the force for a reflective sail is twice of that for an absorbing sail, and we know that the pressure is proportional to the force for a given area. From these, we conclude that the sail should be reflective because in this case the momentum transferred to the sail per unit area per unit time is larger than for absorbing sail, therefore the radiation pressure is larger for the reflective sail.
Suppose, we have a parallel plate capacitor and we know the following about it: Area of each plate = $0.0012m^2$ Distance between the two plates = $0.002m$ Charge on each plate after fully charging the capacitor = $2\times10^{-6}C$ Potential difference between the plates after fully charging the capacitor = $4\times 10^{-3}V$ My solution: We know that the electric field intensity at a point between two equally and oppositely charged plates is $\LARGE\frac{\sigma}{\epsilon_0}$. So, for the above case, $$\large E = \frac{\sigma}{\epsilon_0}$$ $$\large\implies E = \frac{\frac{2\times10^{-6}}{0.0012}}{8.85\times10^{-12}}{NC^{-1}}$$ $$\large\implies E =188323917.1NC^{-1}$$ My book's solution: $$E = \frac{V}{d}$$ $$\implies E=\frac{4\times 10^{-3}V}{0.002m}NC^{-1}$$ $$\implies E = 2NC^{-1}$$ If the books solution is correct, could you please explain why my answer is wrong and the book's is correct? Thanks in advance!
Answer:
udegsgsfsjtajtsiaitskhsigsfjsjgsyoeyodogdoydyosiskgoydoydiydiyddohdohdohyodhodohdoydoydoydosoydogdkgdohdhdohdgodyodoydoydyodoydyodoydohxohdohxohxohxohxogxkx skzjgz a few days
a trombone can be modeled like an open closed air tube. the trombone plays a fifth harmonic of 159 hz. the speed of sound is 343 m/s. what is the wavelength of this sound
Answer:
The wavelength is 2.16 m.
Explanation:
Given the speed of the sound = 343 m/s
Trombone generate the frequency = 159 Hz
Now we have to find the wavelength of the sound. Here, we can find the wavelength by dividing the speed of the sound with frequency.
The wavelength of the sound = Speed of sound/frequency
Wavelength of the sound = 343 / 159 = 2.16 m
A metal sample of mass M requires a power input P to just remain molten. When the heater is turned off, the metal solidifies in a time T. The heat of fusion of this metal is
Answer:
L = Pt/M
Explanation:
Power, P= Q/t = mL/t
we know that, (Q=m×l)
Now ⇒l= Pt/M
Thus l= Pt/M
Show that the entire Paschen series is in the infrared part of the spectrum. To do this, you only need to calculate the shortest wavelength in the series.
Answer and Explanation:
The computation of the shortest wavelength in the series is shown below:-
[tex]\frac{1}{\lambda} = R(\frac{1}{n_f^2} - \frac{1}{n_i^2} )[/tex]
Where
[tex]\lambda[/tex] represents wavelength
R represents Rydberg's constant
[tex]n_f[/tex] represents Final energy states
and [tex]n_i[/tex] represents initial energy states
Now Substitute is
[tex]1.097\times 10^7\ m^{-1}\ for\ R, \infty for\ n_i,\ 3 for\ n_i,\\\\\ \frac{1}{\lambda} = R(\frac{1}{n_f^2} - \frac{1}{n_i^2} )[/tex]
now we will put the values into the above formula
[tex]= 1.097\times 10^7 m^{-1}(\frac{1}{3^2} - \frac{1}{\infty^2} )\\\\ = 1.097\times10^7\ m^{-1} (\frac{1}{9} )[/tex]
[tex]= 1218888.889 m^{-1}[/tex]
Now we will rewrite the answer in the term of [tex]\lambda[/tex]
[tex]\lambda = \frac{1}{1218888.889} m\\\\ = 0.82\times 10^{-6} m[/tex]
So, the whole Paschen series is in the part of the spectrum.
What is the radiation pressure 1.5 m away from a 700 W lightbulb? Assume that the surface on which the pressure is exerted faces the bulb and is perfectly absorbing and that the bulb radiates uniformly in all directions.
Answer:
3.30 x 10^-7 Pascal
Explanation:
distance r = 1.5 m
power P = 700 W
the radiation pressure is given as
Pr = P/A*c
where
area of the surface A = 4πr^2
calculate for A
speed of light is c = 3×10^8 m/s
plugging above values in equation above gives
Pr = 3.30 x 10^-7 Pascal
A rod of length L is hinged at one end. The moment of inertia as the rod rotates around that hinge is ML2/3. Suppose a 2.50 m rod with a mass of 3.00 kg is hinged at one end and is held in a horizontal position. The rod is released as the free end is allowed to fall. What is the angular acceleration as it is released?
Answer:
6 rad/s²
Explanation:
Sum the torques about the hinge.
∑τ = Iα
mg(L/2) = mL²/3 α
g/2 = L/3 α
α = 3g/(2L)
α = 3 (10 m/s²) / (2 × 2.50 m)
α = 6 rad/s²
Define the following, and give the letter which we will abbreviate them by:
Center of curvature:
Vertex:
Focal Point:
Radius of curvature:
Focal length:
Answer:
As in explanation.
Explanation:
A) Centre of Curvature: This is defined as the point in the center of the sphere from which the mirror was sliced. It is represented by the letter "C"
B) Vertex: It is defined as the point on the mirror's surface where the principal axis meets the mirror. It is represented by the letter A.
C) Focal Point: This is defined as the Midway point between the vertex and the center of curvature. It is represented by the letter "F"
D) Radius of Curvature: This is defined as the distance from the vertex to the center of curvature. It is represented by the letter "R"
E) Focal Length: This is defined as the distance from the mirror to the focal point. It's represented by the letter "f"
What type of tectonic plate boundary exists along the edge of the North American plate near the coast of Northern California, Oregon, and Washington?
A reverse fault, like the Cascadia subduction zone off the coast of Oregon and Northern California (north of Mendocino California), has relatively deep earthquakes—like the 1964 Alaska earthquake and the 2004 Sumatra earthquake that caused the Boxing Day Tsunami.
True
False
Megathrust earthquakes can be strongest in magnitude—stronger than a San Andreas earthquake like 1906
Answer:
-transform plate boundary
- false
You need to make a spring scale to measure the mass of objects hung from it. You want each 1.0 cm length along the scale to correspond to a mass difference of 0.10 kg. What should be the value of the spring constant?
Answer:
The spring constant should be:
[tex]k= 98\, \frac{N}{m}[/tex]
Explanation:
Use Hooke's law for this problem, knowing that the magnitude of the force (F) on the spring equals the stretching it experiences [tex]\Delta x[/tex] times the spring constant "k":
[tex]F=k\,\Delta x[/tex]
in our case, since the mass hanging is given in kg, we need to multiply it by "g" to get the force exerted:
Then if we add to the spring in its relaxed state, a mass of 0.10 kg, and we want for that a displacement of 1 cm (0.01 m), then the value of the spring constant should be:
[tex]k=\frac{F}{\Delta x} \\k=\frac{9.8\,(0.1)}{0.01} \, \frac{N}{m} \\k= 98\, \frac{N}{m}[/tex]
PLEASE HELP Which of the following describes the efficiency of real machines? 1.Efficiency is 100% 2.IMA is always larger than the AMA 3.IMA is always smaller than the AMA 4.IMA is equal to the AMA
Answer:
IMA is always larger than the AMA
Explanation:
IMA is Ideal Mechanical Advantage and it equals the length of effort that is divided by the length of resistance which is given by the formula
IMA= Fr/Fe
Where Fr is the resistance force
Fe is the effort force.
IM= de/dr
Where de is the distance of the applied effort
dr is the distance traveled by the load.
In any real machine, the effort is needed to overcome friction and because of this, the ideal mechanical advantage(IMA) is always larger than the actual mechanical advantage (AMA)
A spherical balloon has a radius of 6.95m and is filled with helium. The density of helium is 0.179 kg/m3, and the density of air is 1.29 kg/m3. The skin and structure of the balloon has a mass of 960kg . Neglect the buoyant force on the cargo volume itself. Determine the largest mass of cargo the balloon can lift.
Answer:
602.27 kg
Explanation:
The computation of the largest mass of cargo the balloon can lift is shown below:-
Volume of helium inside the ballon= (4 ÷ 3) × π × r^3
= (4 ÷ 3) × 3.14 × 6.953
= 1406.19 m3
Mass the balloon can carry = volume × (density of air-density of helium)
= 1406.19 × (1.29-0.179)
= 1562.27 kg
Mass of cargo it can carry = Mass it can carry - Mass of structure
= 1562.27 - 960
= 602.27 kg
2. The glass core of an optical fiber has an index of refraction 1.60. The index of refraction of the cladding is 1.48. What is the maximum angle a light ray can make with the wall of the core if it is to remain inside the fiber?
Answer:
We know that the maximum angle that a light ray can wake with the wall of the core is equipment to the minimum angle with the normal of the core that will give rise in total internal reflection. so using Snell's law the angle is subtracted from 90° to get the maximum angle a light ray can make with the wall of the core if it is to remain inside the fiber.
So using
n1sinစ1. = n2sinစ2
1.6sin(x1) = 1.48sin(90),
But sin(90)=1
1.6sin(စ1) = 1.48,
sin(စ1) = 1.48/1.6
စ = 68°
Explanation:
Answer:
i = 67.66⁰Explanation:
Using the Snell's law formula to solve this question which states that the ratio of the sine of angle of incidence to the sine of angle of refraction is a constant for a given pair of media. This constant is known as the refractive index for the given pair of media. Mathematically,
n = sin(i)/sin(r) where;
i is the angle of incidence
r is the angle of refraction.
n is the refractive index.
Given the refractive index of the optical fibre n₁ = 1.60 and that of cladding n₂ = 1.48
n₂/n₁ = sin(i)/sin(r)
The light ray can make with the wall of the core when its angle of refraction is 90⁰. The angle of incidence at this maximum point is known as the critical angle.
On substitution:
1.48/1.60 = sin(i)/sin90
1.48/1.60 = sin(i)/1
sin(i) = 1.48/1.60
sin(i) = 0.925
i = sin⁻¹0.925
i = 67.66⁰
Hence the maximum angle a light ray can make with the wall of the core if it is to remain inside the fiber is 67.66⁰.
A cyclist moves effortlessly at a constant speed of 12 m / s, but enters a muddy area where the coefficient of kinetic friction is 0.60. Will the rider leave the muddy area without having to pedal if the mud extends 11m? If so, how fast will it emerge?
Answer:
3.5 m/s
Explanation:
There are 3 forces on the cyclist:
Weight force mg pulling down,
Normal force N pushing up,
and friction force Nμ pushing left.
Sum of forces in the y direction:
∑F = ma
N − mg = 0
N = mg
∑F = ma
-Nμ = ma
-mgμ = ma
a = -gμ
a = -(10 m/s²)(0.60)
a = -6 m/s²
Velocity reached at end of 11 m:
v² = v₀² + 2aΔx
v² = (12 m/s)² + 2 (-6 m/s²) (11 m)
v = √12 m/s
v ≈ 3.5 m/s
6. If you wanted to develop a telescope, what kind of lenses would you use for the objective lens (the lens that collects the light) and the eyepiece? Explain your reasoning. Draw a picture with ray tracing of your setup.
Answer:
objetive: a converging lens for large diameter lenses
eyepiece you must select a lens with a small focal length and the diameter is not important
The selected lenses should decrease chromatic aberration.
Explanation:
A telescope is an instrument that collects light from very distant objects, therefore very weak.
Therefore you should select a converging lens for large diameter lenses, to collect magnanimous light and with a large focal length.
For the eyepiece you must select a lens with a small focal length and the diameter is not important
the telescope magnification is
m = f_objective / F_ocular
The selected lenses should decrease chromatic aberration.
In general, these lenses are heavy, so refractory telescopes were imposed, so it uses a concave mirror instead of an objective lens.
Answer: this the real answer try it objetive: a converging lens for large diameter lenseseyepiece you must select a lens with a small focal length and the diameter is not importantThe selected lenses should decrease chromatic aberration.Explanation:A telescope is an instrument that collects light from very distant objects, therefore very weak.Therefore you should select a converging lens for large diameter lenses, to collect magnanimous light and with a large focal length.For the eyepiece you must select a lens with a small focal length and the diameter is not importantthe telescope magnification is m = f_objective / F_ocularThe selected lenses should decrease chromatic aberration.In general, these lenses are heavy, so refractory telescopes were imposed, so it uses a concave mirror instead of an objective lens.
Explanation:
