Answer:
I think 9.5
Explanation:
............
The intensity at a certain distance from a bright light source is 7.20 W/m2 .
A. Find the radiation pressures (in pascals) on a totally absorbing surface and a totally reflecting surface.
B. Find the radiation pressures (in atmospheres) on a totally absorbing surface and a totally reflecting surface.
Answer:
A) P_rad.abs = 2.4 × 10^(-8) Pa and P_rad.ref = 4.8 × 10^(-8) Pa
B) P_rad.abs = 2.369 × 10^(-13) atm and P_rad.ref = 4.738 × 10^(-13) atm
Explanation:
A) The formula for radiation pressure for absorbed light is given as;
P_rad = I/c
Where I is the intensity = 7.20 W/m² and c is the speed of light = 3 × 10^(8) m/s
Thus;
P_rad = 7.2/(3 × 10^(8))
P_rad.abs = 2.4 × 10^(-8) Pa
Now formula for radiation pressure for reflected light is given as;
P_rad = 2I/c
Thus;
P_rad = (2 × 7.2)/(3 × 10^(8))
P_rad.ref = 4.8 × 10^(-8) Pa
B) Now, 1.013 × 10^(5) Pa = 1 atm
Thus, for the absorbed surface, we have;
P_rad.abs = (2.4 × 10^(-8))/(1.013 × 10^(5))
P_rad.abs = 2.369 × 10^(-13) atm
For the reflecting surface, we have;
P_rad_ref = (4.8 × 10^(-8))/(1.013 × 10^(5))
P_rad.ref = 4.738 × 10^(-13) atm
Two 75 W (120 V) lightbulbs are wired in series, then the combination is connected to a 120 V supply. Part A How much power is dissipated by each bulb
Answer:
300 W
Explanation:
power of each bulb P = 75 W
voltage in the circuit = 120 V
we know that electrical power P = IV ....1
and V = IR
we can also say that I = V/R
substituting for I in equation 1, we have
P = [tex]V^{2}/R[/tex] ....2
The total total power in the circuit = 75 x 2 = 150 W
from equation 2, we have
150 = [tex]120^{2} /R[/tex]
R = [tex]120^{2}/150[/tex] = 96 Ω this is the resistance of the whole circuit.
This resistance is due to the two light bulbs, for each light bulb since they are arranged in series
R = 96/2 = 48 Ω
From P = [tex]V^{2}/R[/tex]
for each light bulb, power is
P = [tex]120^{2} /48[/tex] = 300 W
it is easier to drag a stone than to kick it?why.
Answer:
you are going to expend energy to give a lot of velocity (and momentum) to your foot in order to transfer it the stone air drag this time the kicking speed is for superior to walking speed.
Thank You
Nuclear plants use radioactive fuel to produce steam which turns a turbine to generate electricity. This is an example of a(n) _____. A) heat pump B) heat mover C) internal combustion engine D) external combustion engine
Answer:
C) internal combustion engineExplanation:
An electric heater draws 13 amperes of current when connected to 120 volts. If the price of electricity is $0.10/kWh, what would be the approximate cost of running the heater for 8 hours?
(A) $0.19
(B) $0.29
(C) $0.75
(D) $1.25
(E) $1.55
Answer:
C $0.75 my friend I wish it is right answer
Light of wavelength 500 nm falls on two slits spaced 0.2 mm apart. If the spacing between the first and third dark fringes is to be 4.0 mm, what is the distance from the slits to a screen?
Answer:
L = 0.8 m
Explanation:
Since, the distance between first and third dark fringes is 4 mm. Therefore, the fringe spacing between consecutive dark fringes will be:
Δx = 4 mm/2 = 2 mm = 2 x 10⁻³ m
but,
Δx = λL/d
λ = wavelength of the light = 500 nm = 5 x 10⁻⁷ m
d = slit spacing = 0.2 mm = 0.2 x 10⁻³ m
L = Distance between slits and screen = ?
Therefore, using the values, we get:
2 x 10⁻³ m = (5 x 10⁻⁷ m)(L)/(0.2 x 10⁻³)
L = (2 x 10⁻³ m)(0.2 x 10⁻³ m)/(5 x 10⁻⁷ m)
L = 0.8 m
What happens to the magnetic field when you reverse the direction of current by sliding the battery voltage bar past 0 volts
Answer:
The polarity of the magnetic field changes
Explanation:
This because The magnetic field generated is always perpendicular to the direction of the current and parallel to the solonoid. Hence if we reverse the current the direction of magnetism also reverses. In other words the magnetic poles gets reversed (North pole becomes south pole and the south pole becomes the north pole)
You have two capacitors and want to connect them across a voltage source (battery) to store the maximum amount of energy. Should they be connected in series or in parallel?
Answer:
In parallel
Explanation:
Ctotal = C1 + C2 + ... + Cn
Three resistors, each having a resistance, R, are connected in parallel to a 1.50 V battery. If the resistors dissipate a total power of 3.00 W, what is the value of R
Answer:
The value of resistance of each resistor, R is 2.25 Ω
Explanation:
Given;
voltage across the three resistor, V = 1.5 V
power dissipated by the resistors, P = 3.00 W
the resistance of each resistor, = R
The effective resistance of the three resistors is given by;
R(effective) = R/3
Apply ohms law to determine the current delivered by the source;
V = IR
I = V/R
I = 3V/R
Also, power is calculated as;
P = IV
P = (3V/R) x V
P = 3V²/R
R = 3V² / P
R = (3 x 1.5²) / 3
R = 2.25 Ω
Therefore, the value of resistance of each resistor, R is 2.25 Ω
A cube has a mass of 100 grams and its density is determined to be 1 g/cm3. The volume of the cube must be _____. 0.1 cm3 1 cm3 10 cm3 100 cm3
Answer: The volume of the block will be [tex]100cm^3[/tex]
Explanation:
Density is defined as the mass contained per unit volume.
[tex]Density=\frac{mass}{volume}[/tex]
Given : Mass of cube = 100 grams
Density of cube = [tex]1g/cm^3[/tex]
Putting in the values we get:
[tex]Volume=\frac{mass}{density}[/tex]
[tex]Volume=\frac{100g}{1g/cm^3}=100cm^3[/tex]
Thus volume of the block will be [tex]100cm^3[/tex]
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.
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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:
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A light beam inside a container of some liquid hits the surface of the liquid/air interface. Depending on the angle, the light beam may or may not be able to get out into the air medium. At what angle will the beam of light be totally reflected back into the liquid in the container
Answer:
Following are the solution to the given question:
Explanation:
Applying the Snell Law:
when is the liquid's refractive index, is the air's refractive index.
the liquid's refractive index, the air's index of refraction.
It is the limiting case when , Inside the interphase of two mediums, light is scattered. Thus,
[tex]n_l \sin \theta_l = n_a \sin 90^\circ = n_a[/tex]
[tex]\theta_l = \arcsin \dfrac{n_a}{n_l} =\arcsin \dfrac{1}{1.38} = 46.4^\circ[/tex]
From the incident angles [tex]\theta_l[/tex] is greater than 46.4°, that is the light reflected back into the liquid.
Give an example of a fad diet that is not healthy and one that is healthy. Explain how you know the difference.
Answer:
Good Diet: ! gallon of water a day, Fruits, Vegetables, White meats(Chicken), Don't eat past 3 PM.
Bad Diet: Pizza, Red meat, Baked goods, Eating at late hours.
Explanation: I know the difference because, When you drink water first thing in the morning it gets your metabolism running. Than means you can digest foods better, you want to feed your body good foods but you should not eat until you feel stuffed. You should eat until you are no longer starving. Than you should drink a cup of water in between meals. I know you should not eat past 3 pm because your body needs time to digest foods because you should never go to sleep with a full stomach. I know the difference between good food and bad food because when you eat healthy food and a balanced diet, your body will have more energy and you wont feel tired afterwards. Eating bad foods and food with artificial sugars will clump up in your kidneys, and your body will have small bursts of energy but you will feel lazy afterwards...Your body is supposed to stay energized from a healthy meal in order to give you the energy your body needs to exercise. If you feel droopy all the time and you don't want to do anything, than you are unhealthy.
Answer:
A vegetarian diet is an example of a good fad diet if you do it correctly. It can help you get lots of veggies and good nutrients from them while still following the non-meat diet you want. This can be effective and good for weight loss becasue you are still eating and getting all the good nutrients and calories from less fatty foods.
Vegan diet (some can be successful but many people fail and do not do good that is why I choose this) The problem with this fad diet is that it can cause nutritional deficiencies and lead to a host of additional health problems, including negatively impacting hormonal health and metabolism. Many people also struggle to find healthy vegan food and end up eating bad and fatty foods instead.
Explanation:
Got a 100
What is a benefit of joining the YMCA instead of a private health club?
The YMCA has nicer equipment and buildings.The YMCA has nicer equipment and buildings. , ,
The YMCA is likely to be in an upscale neighborhood.The YMCA is likely to be in an upscale neighborhood. , ,
The YMCA is much more affordable.The YMCA is much more affordable. , ,
The YMCA has restaurants and spa services.
Answer:
Explanation:
This depends on where you are.
The YMCA where I grew up was affordable. Very. Or my mother would not have let me go.
What is the maximum speed (in units of m/s) with which a car can round a
flat horizontal curve of radius (r=60 m), if the coefficient of static friction between tires and
road is (0.4)?
A) 5
B) 15.5
€) 240
D) 25.1
Answer:
B) 15.5 m/s
Explanation:
r = 60m
μs = 0.4
using the formula max V = √r*g*μs (flat roadway)
v = sqrt(60 * 10 * 0.4)
v = 15.5 m/s
what happened when aniline is treated with benzene diazonium chloride
Answer:
p-aminoazobenzene is formed
Explanation:
The reaction of benzene diazonium chloride and aniline takes place in a basic medium and leads to the formation of an azo compound which is also a dye. The terminal diazonium nitrogen of the benzene diazonium ion is coupled to the aniline at the para-position. The product of the reaction, p-aminoazobenzene is a yellow dye.
Benzene diazonium chloride is prepared by diazotization of aniline in the presence of hydrochloric acid. The full reaction of aniline and benzene diazonium chloride is shown in the image attached to this answer.
An organ pipe of length 3.0 m has one end closed. The longest and next-longest possible wavelengths for standing waves inside the pipe are
Answer:
The longest wavelength for closed at one end and open at the other is
y / 4 where y is the wavelength - that is node - antinode
The next possible wavelength is 3 y / 4 - node - antinode - node -antinode
y / 4 = 3 m y = 12 meters the longest wavelength
3 y / 4 = 3 m y = 4 meters 1 / 3 times as long
A circular coil of wire 8.40 cm in diameter has 17.0 turns and carries a current of 3.20 A . The coil is in a region where the magnetic field is 0.610 T.Required:a. What orientation of the coil gives the maximum torque on the coil ?b. What is this maximum torque in part (A) ?c. For what orientation of the coil is the magnitude of the torque 71.0 % of the maximum found in part (B)?
Answer:
a) for the torque to be maximum, sin should be maximum
i.e (sinФ)maximum = 1
b) therefore the Maximum torque is
Tmax = 0.1838 × 1 = 0.1838 N.m
c) Given the torque is 71.0% of its maximum value; Ф = 45.24⁰ ≈ 45⁰
Explanation:
Given that; Diameter is 8.40 cm,
Radius (R) = D/2 = 8.40/2 = 4.20 cm = 0.042 m
Number of turns (N) = 17
Current in the loop (I) = 3.20 A
Magnetic field (B) = 0.610 T
Let the angle between the loop's area vector A and the magnetic field B be
Now. the area of the loop is;
A = πR²
A = 3.14 ( 0.042 )²
A = 0.005539 m²
Torque on the loop (t) = NIABsinФ
t = 17 × 3.20 ×0.005539 × 0.610 × sinФ
t = 0.1838sinФ N.m
for the torque to be maximum, sin should be maximum
i.e (sinФ)maximum = 1
therefore the Maximum torque is
Tmax = 0.1838 × 1 = 0.1838 N.m
Given the torque is 71.0% of its maximum value
t = 0.71 × tmax
t = 0.71 × 0.1838
t = 0.1305
Now
0.1305 N.m = 0.1838 sinФ N.m
sinФ = 0.1305 / 0.1838
sinФ = 0.71001
Ф = sin⁻¹ 0.71001
Ф = 45.24⁰ ≈ 45⁰
Distinguish between physical and chemical changes. Include examples in your explanations.
Answer:
Chemical changes are recognized when a substance changes its properties permanently and it cannot be the same substance as before.
Instead the physical changes implies that if you can return to the same substance through a reverse process.
Explanation:
A chemical change is, by example, a combustion, if a sheet of paper burns, its result is ashes, the ashes cannot go back to being a sheet of paper because its properties changed, heat energy was generated that changed matter permanently.
A physical change, by example, is that of freezing water, the water becomes ice, but this can easily become water again if the temperature is increased, its properties do not change and the chemistry of the substance does not change.
A chemical change takes place when a chemical reaction takes place, while when a matter changes forms but not the chemical identity then a physical change takes place.
• A product or a new compound formation takes place from a chemical change as the rearrangement of atoms takes place to produce novel chemical bonds.
• In a chemical change always a chemical reaction takes place.
• Some of the chemical changes examples are souring milk, burning wood, digesting food, mixing acid and base, cooking food, etc.
• In a physical change no new chemical species form.
• The changing of the state of a pure substance between liquid, gas, or solid is a physical change as there is no change in the identity of the matter.
• Some of the physical changes are melting of ice, tempering of steel, breaking a bottle, crumpling a sheet of aluminum foil, boiling water, and shredding paper.
Thus, a new substance is formed during a chemical change, while a physical change does not give rise to a new substance.
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Find the momentum of a particl with a mass of one gram moving with half the speed of light.
Answer:
129900
Explanation:
Given that
Mass of the particle, m = 1 g = 1*10^-3 kg
Speed of the particle, u = ½c
Speed of light, c = 3*10^8
To solve this, we will use the formula
p = ymu, where
y = √[1 - (u²/c²)]
Let's solve for y, first. We have
y = √[1 - (1.5*10^8²/3*10^8²)]
y = √(1 - ½²)
y = √(1 - ¼)
y = √0.75
y = 0.8660, using our newly gotten y, we use it to solve the final equation
p = ymu
p = 0.866 * 1*10^-3 * 1.5*10^8
p = 129900 kgm/s
thus, we have found that the momentum of the particle is 129900 kgm/s
An electric train operates on 800 V. What is its power consumption when the current flowing through the train's motor is 2,130 A?
Answer:
1704 kWExplanation:
To solve for the power consumed by the trains motor we have to employ the formula for power which is
Power= current * voltage
Given that
voltage V= 800 V
current I= 2130 A
Substituting in the formula for power we have
Power= 2130*800= 1704000 watt
Power = 1704 kW
This is the amount of energy consumed, transferred or converted per unit of time
Hence the power consumed by the trains motor is 1704 kW
With the same block-spring system from above, imagine doubling the displacement of the block to start the motion. By what factor would the following change?
A. Kinetic energy when passing through the equilibrium position.
B. Speed when passing through the equilibrium position.
Answer:
A) K / K₀ = 4 b) v / v₀ = 4
Explanation:
A) For this exercise we can use the conservation of mechanical energy
in the problem it indicates that the displacement was doubled (x = 2xo)
starting point. At the position of maximum displacement
Em₀ = Ke = ½ k (2x₀)²
final point. In the equilibrium position
[tex]Em_{f}[/tex] = K = ½ m v²
Em₀ = Em_{f}
½ k 4 x₀² = K
(½ K x₀²) = K₀
K = 4 K₀
K / K₀ = 4
B) the speed value
½ k 4 x₀² = ½ m v²
v = 4 (k / m) x₀
if we call
v₀ = k / m x₀
v = 4 v₀
v / v₀ = 4
In a double-slit experiment the distance between slits is 5.0 mm and the slits are 1.4 m from the screen. Two interference patterns can be seen on the screen: one due to light of wavelength 450 nm, and the other due to light of wavelength 590 nm. What is the separation in meters on the screen between the m = 5 bright fringes of the two interference patterns?
Answer:
Δy = 1 10⁻⁴ m
Explanation:
In double-slit experiments the constructive interference pattern is described by the equation
d sin θ = m λ
In this case we have two wavelengths, so two separate patterns are observed, let's use trigonometry to find the angle
tan θ = y / L
as the angles are small,
tan θ = sin θ / cos θ = sin θ
substituting
sin θ = y / L
d y / L = m λ
y = m λ / d L
let's apply this formula for each wavelength
λ = 450 nm = 450 10⁻⁹ m
m = 5
d = 5.0 mm = 5.0 10⁻³ m
y₁ = 5 450 10⁻⁹ / (5 10⁻³ 1.4)
y₁ = 3.21 10⁻⁴ m
we repeat the calculation for lam = 590 nm = 590 10⁻⁹ m
y₂ = 5 590 10⁻⁹ / (5 10⁻³ 1.4)
y₂= 4.21 10⁻⁴ m
the separation of these two lines is
Δy = y₂ - y₁
Δy = (4.21 - 3.21) 10⁻⁴ m
Δy = 1 10⁻⁴ m
Two blocks A and B have a weight of 11 lb and 5 lb , respectively. They are resting on the incline for which the coefficients of static friction are μA = 0.16 and μB = 0.23. Determine the incline angle θ for which both blocks begin to slide. Also find the required stretch or compression in the connecting spring for this to occur. The spring has a stiffness of k = 2.1 lb/ft .
Answer:
[tex]\theta=10.20^{\circ}[/tex]
[tex]\Delta l=0.10 ft[/tex]
Explanation:
First of all, we analyze the system of blocks before starting to move.
[tex]\Sum F_{x}=P_{A}sin(\theta)+P_{B}sin(\theta)-F_{fA}-F_{fB}=0[/tex]
[tex]\Sum F_{x}=11sin(\theta)+5sin(\theta)-0.16N_{A}-0.23N_{B}=0[/tex]
[tex]11sin(\theta)+5sin(\theta)-0.16P_{A}cos(\theta)-0.23P_{B}cos(\theta)=0[/tex]
[tex]11sin(\theta)+5sin(\theta)-0.16*11cos(\theta)-0.23*5cos(\theta)=0[/tex]
[tex]11sin(\theta)+5sin(\theta)-0.16*11cos(\theta)-0.23*5cos(\theta)=0[/tex]
[tex]16sin(\theta)-2.91cos(\theta)=0[/tex]
[tex]tan(\theta)=0.18[/tex]
[tex]\theta=arctan(0.18)[/tex]
[tex]\theta=10.20^{\circ}[/tex]
Hence, the incline angle θ for which both blocks begin to slide is 10.20°.
Now, if we do a free body diagram of block A we have that after the block moves, the spring force must be taken into account.
[tex]P_{A}sin(\theta)-F_{fA}-F_{spring}=0[/tex]
Where:
[tex]F_{spring} = k\Delta l=2.1\Delta l[/tex]
[tex]P_{A}sin(\theta)-0.16*11cos(\theta)-2.1\Delta l=0[/tex]
[tex]\Delta l=\frac{11sin(\theta)-0.16*11cos(\theta)}{2.1}[/tex]
[tex]\Delta l=0.10 ft[/tex]
Therefore, the required stretch or compression in the connecting spring is 0.10 ft.
I hope it helps you!
(a) The inclined angle for which both blocks begin to slide is 10.3⁰.
(b) The compression of the spring is 0.22 ft.
The given parameters;
mass of block A, = 11 lbmass of block B, = 5 lbcoefficient of static friction for A, = 0.16coefficient of static friction for B, = 0.23 spring constant, k = 2.1 lb/ftThe normal force on block A and B:
[tex]F_n_A = m_Agcos \ \theta\\\\F_n_B = m_Bgcos \ \theta[/tex]
The frictional force on block A and B:
[tex]F_f_A = \mu_s_AF_n_A \\\\F_f_B = \mu_s_BF_n_A[/tex]
The net force on the blocks when they starts sliding;
[tex](m_Ag sin \theta+ m_Bgsin\theta) - (F_f_A + F_f_B) = 0\\\\m_Ag sin \theta+ m_Bgsin\theta = F_f_A + F_f_B\\\\m_Ag sin \theta+ m_Bgsin\theta = \mu_Am_Agcos\theta \ + \ \mu_Bm_Bgcos\theta\\\\gsin\theta(m_A + m_B) = gcos\theta (\mu_Am_A + \mu_Bm_B)\\\\\frac{sin\theta}{cos \theta} = \frac{\mu_Am_A\ + \ \mu_Bm_B}{m_A\ + \ m_B} \\\\tan\theta = \frac{(0.16\times 11) \ + \ (0.23 \times 5)}{11 + 5} \\\\tan\theta = 0.1819\\\\\theta = tan^{-1}(0.1819)\\\\\theta = 10.3 \ ^0[/tex]
The change in the energy of the blocks is the work done in compressing the spring;
[tex]\Delta E = W\\\\F_A (sin \theta )d- \mu F_n d= \frac{1}{2} kd^2\\\\F_A sin\theta \ - \ \mu F_A cos\theta = \frac{1}{2} kd\\\\d = \frac{2F_A(sin\theta - \mu cos \theta) }{k} \\\\d = \frac{2\times 11(sin \ 10.3\ - \ 0.16\times cos \ 10.3) }{2.1} \\\\d = 0.22 \ ft[/tex]
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Sunlight reflected from a smooth ice surface is completely polarized. Determine the angle of incidence. (nice = 1.31.)
Answer:
Explanation:
We shall apply Brewster's law to solve the problem . Let i be the angle of reflection required. According to this law ,
tan i = μ where i is angle of incidence , μ is refractive index of the medium .
Here i = ? , μ = 1.31
tani = 1.31
i = 53° approx .
At the angle of 53° incidence , the reflected ray will be completely polarised .
A satellite in geostationary orbit is used to transmit data via electromagnetic radiation. The satellite is at a height of 35,000 km above the surface of the earth, and we assume it has an isotropic power output of 1.0 kW (although, in practice, satellite antennas transmit signals that are less powerful but more directional).
Required:
a. Reception devices pick up the variation in the electric field vector of the electromagnetic wave sent out by the satellite. Given the satellite specifications listed in the problem introduction, what is the amplitude E0 of the electric field vector of the satellite broadcast as measured at the surface of the earth? Use ϵ0=8.85×10^−12C/(V⋅m) for the permittivity of space and c=3.00×10^8m/s for the speed of light.
b. Imagine that the satellite described in the problem introduction is used to transmit television signals. You have a satellite TV reciever consisting of a circular dish of radius R which focuses the electromagnetic energy incident from the satellite onto a receiver which has a surface area of 5 cm^2. How large does the radius R of the dish have to be to achieve an electric field vector amplitude of 0.1 mV/m at the receiver?
Answer:
1. 6.99x 10^-6V/m
2. 18m
Explanation:
See attached file
A bullet is fired from a rifle pointed 45 degrees above horizontal. The bullet leaves the muzzle traveling 1400 m/s. How many seconds does it take the bullet to reach the high point of its trajectory?
The bullet's vertical velocity at time [tex]t[/tex] is
[tex]v=1400\dfrac{\rm m}{\rm s}-gt[/tex]
where [tex]g=9.80\frac{\rm m}{\mathrm s^2}[/tex] is the acceleration due to gravity.
At its highest point, the bullet's vertical velocity is 0, which happens
[tex]0=1400\dfrac{\rm m}{\rm s}-gt\implies t=\dfrac{1400\frac{\rm m}{\rm s}}g\approx\boxed{142.857\,\mathrm s}[/tex]
(or about 140 s, if you're keeping track of significant figures) after being fired.
A circuit contains a single 220 pF capacitor hooked across a battery. It is desired to store three times as much energy in a combination of two capacitors by adding a single capacitor to this one.
How would you hook it up?
The capacitor is connected in series to the original capacitor
or
The capacitor is connected in parallel to the original capacitor
I believe its parallel
but now What would its value be?
Answer
The capacitor should be connected in parallel as parallel connection gives the arithmetic sum of capacitance which will give a corresponding sum of energy while capacitors in series gives the sum of the reciprocal if the individual capacitance
A fireperson is 50 m from a burning building and directs a stream of water from a fire hose at an angle of 300 above the horizontal. If the initial speed of the stream is 40 m/s the height that the stream of water will strike the building is
Answer:
We can think the water stream as a solid object that is fired.
The distance between the fireperson and the building is 50m. (i consider that the position of the fireperson is our position = 0)
The angle is 30 above the horizontal. (yo wrote 300, but this has no sense because 300° implies that he is pointing to the ground).
The initial speed of the stream is 40m/s.
First, using the fact that:
x = R*cos(θ)
y = R*sin(θ)
in this case R = 40m/s and θ = 30°
We can use the above relation to find the components of the velocity:
Vx = 40m/s*cos(30°) = 34.64m/s
Vy = 20m/s.
First step:
We want to find the time needed to the stream to hit the buildin.
The horizontal speed is 34.64m/s and the distance to the wall is 50m
So we want that:
34.64m/s*t = 50m
t = 50m/(34.64m/s) = 1.44 seconds.
Now we need to calculate the height of the stream at t = 1.44s
Second step:
The only force acting on the water is the gravitational one, so the acceleration of the stream is:
a(t) = -g.
g = -9.8m/s^2
For the speed, we integrate over time and we get:
v(t) = -g*t + v0
where v0 is the initial speed: v0 = 20m/s.
The velocity equation is:
v(t) = -g*t + 20m/s.
For the position, we integrate again over time:
p(t) = -(1/2)*g*t^2 + 20m/s*t + p0
p0 is the initial height of the stream, this data is not known.
Now, the height at the time t = 1.44s is
p(1.44s) = -5.9m/s^2*(1.44s)^2 + 20m/s*1.44s + po
= 16.57m + p0
So the height at wich the stream hits the building is 16.57 meters above the initial height of the fire hose.