Answer:
The number of molecules displaced in a vibration makes the amplitude of a sound.
To get up on the roof, a person (mass 69.0 kg) places a 6.40 m aluminum ladder (mass 11.0 kg) against the house on a concrete pad with the base of the ladder 2.00 m from the house. The ladder rests against a plastic rain gutter, which we can assume to be frictionless. The center of mass of the ladder is 2 m from the bottom. The person is standing 3 m from the bottom. What are the magnitudes (in N) of the forces on the ladder at the top and bottom
Answer:
N = 243.596 N ≈ 243.6 N
Explanation:
mass of person = 69 kg ( M )
mass of aluminium ladder = 11 kg ( m )
length of ladder = 6.4 m ( l )
base of ladder = 2 m from the house (d )
center of mass of ladder = 2 m from the bottom of ladder
person on ladder standing = 3 m from bottom of ladder
Calculate the magnitudes of the forces at the top and bottom of the ladder
The net torque on the ladder = o ( since it is at equilibrium )
assuming: the weight of the person( mg) acting at a distance x along the ladder. the weight of the ladder ( mg) acting halfway along the ladder and the reaction N acting on top of the ladder
X = l/2
x = 6.4 / 2 = 3.2
find angle formed by the ladder
cos ∅ = d/l
∅ = [tex]cos^{-1][/tex] 2/6.4 = [tex]cos^{-1}[/tex]0.3125 ≈ 71.79⁰
remember the net torque around is = zero
to calculate the magnitude of forces on the ladder we apply the following formula
[tex]N = \frac{mg(dcosteta)+ Mgxcosteta}{lsinteta}[/tex]
m = 11 kg, M = 69 kg, l = 6.4 , x = 3, teta( ∅ )= 71.79⁰, g = 9.8
back to equation N = [tex]\frac{11*9.8(2*cos71.79)+ 69*9.8*3* cos71.79}{6.4sin71.79}[/tex]
N = (67.375 + 633.938) / 2.879
N = 243.596 N ≈ 243.6 N
In this problem you will consider the balance of thermal energy radiated and absorbed by a person.Assume that the person is wearing only a skimpy bathing suit of negligible area. As a rough approximation, the area of a human body may be considered to be that of the sides of a cylinder of length L=2.0m and circumference C=0.8m.For the Stefan-Boltzmann constant use σ=5.67×10−8W/m2/K4.Part aIf the surface temperature of the skin is taken to be Tbody=30∘C, how much thermal power Prb does the body described in the introduction radiate?Take the emissivity to be e=0.6.Express the power radiated into the room by the body numerically, rounded to the nearest 10 W.part bFind Pnet, the net power radiated by the person when in a room with temperature Troom=20∘C
Answer:
The thermal power emitted by the body is [tex]P_t = 286.8 \ Wm^{-2}[/tex]
The net power radiated is [tex]P_{net} = 460 \ W[/tex]
Explanation:
From the question we are told that
The length of the assumed hum[tex]T_{room} = 20 ^oC[/tex]an body is L = 2.0 m
The circumference of the assumed human body is [tex]C = 0.8 \ m[/tex]
The Stefan-Boltzmann constant is [tex]\sigma = 5.67 * 10^{-8 } \ W\cdot m^{-2} \cdot K^{-4}.[/tex]
The temperature of skin [tex]T_{body} = 30^oC[/tex]
The temperature of the room is
The emissivity is e=0.6
The thermal power radiated by the body is mathematically represented as
[tex]P_t = e * \sigma * T_{body}^4[/tex]
substituting value
[tex]P_t = 0.6 * 5.67*10^{-8} * (303)^4[/tex]
[tex]P_t = 286.8 \ Wm^{-2}[/tex]
The net power radiated by the body is mathematically evaluated as
[tex]P_{net} = P_t * A[/tex]
Where A is the surface area of the body which is mathematically evaluated as
[tex]A = C* L[/tex]
substituting values
[tex]A = 0.8 * 2[/tex]
[tex]A = 1.6 m^2[/tex]
=> [tex]P_{net} = 286.8 * 1.6[/tex]
=> [tex]P_{net} = 460 \ W[/tex]
where would you expect to find vesicles of neurotransmitters
A. Synaptic gap
B. postsynaptic dendrites
C. Channels in the postsynaptic
D. Presynaptic terminal button
Answer:
D. Presynaptic terminal button
explanation:
Terminal Buttons are small knobs at the end of an axon that release chemicals called neurotransmitters. The terminal buttons form the Presynaptic Neuron
hope this helped!
small car has a head-on collision with a large truck. Which of the following statements concerning the magnitude of the average force due to the collision is correct? A small car has a head-on collision with a large truck. Which of the following statements concerning the magnitude of the average force due to the collision is correct? It is impossible to tell since the velocities are not given. The truck experiences the greater average force. It is impossible to tell since the masses are not given. The small car and the truck experience the same average force. The small car experiences the greater average force.
Answer:
The correct option is D: "The small car and the truck experience the same average force."
Explanation:
The magnitude of the average force experienced by both bodies in motion is the same as explained by Newton's third law of motion. The force exerted by each body is equal and opposite in direction. The resulting acceleration experienced by each vehicle, however, will not be the same. It is greater for the small car.
A small car and an SUV are at a stoplight. The car has a mass equal to half that of the SUV, and the SUV's engine can produce a maximum force equal to twice that of the car. When the light turns green, both drivers floor it at the same time. Which vehicle pulls ahead of the other vehicle after a few seconds?
Complete Question
A small car and an SUV are at a stoplight. The car has amass equal to half that of the SUV, and the SUV's engine can produce a maximum force equal to twice that of the car. When the light turns green, both drivers floor it at the same time. Which vehicle pulls ahead of the other vehicle after a few seconds?
a) It is a tie.
b) The SUV
c) The car
Answer:
The correct option is a
Explanation:
From the question we are told that
The mass of the car is [tex]m_c[/tex]
The force of the car is F
The mass of the SUV is [tex]m_s = 2 m_c[/tex]
The force of the SUV is [tex]F_s = 2 F[/tex]
Generally force of the car is mathematically represented as
[tex]F= m_ca_c[/tex]
[tex]a_c[/tex] is acceleration of the car
Generally force of the car is mathematically represented as
[tex]F_s = m_s * a_s[/tex]
[tex]a_s[/tex] is acceleration of the SUV
=> [tex]2 F = 2 m_c a_s[/tex]
[tex]F = m_c a_s[/tex]
=> [tex]m_c a_s = m_ca_c[/tex]
So [tex]a_s = a_c[/tex]
This means that the acceleration of both the car and the SUV are the same
Some cats can be trained to jump from one location to another and perform other tricks. Kit the cat is going to jump through a hoop. He begins on a wicker cabinet at a height of 1.765 m above the floor and jumps through the center of a vertical hoop, reaching a peak height 3.130 m above the floor. (Assume the center of the hoop is at the peak height of the jump. Assume that +x axis is in the direction of the hoop from the cabinet and +y axis is up. Assume g = 9.81 m/s2.)
(a) With what initial velocity did Kit leave the cabinet if the hoop is at a horizontal distance of 1.560 m from the cabinet?
v_0 = m/s
(b) If Kit lands on a bed at a horizontal distance of 3.582 m from the cabinet, how high above the ground is the bed?
m
Answer:
a. the initial velocity of the cat is 5.95 m/s at 60.2° from the horizontal
b. 0.847 m
Explanation:
a. Using v² = u² + 2as, we find the initial vertical velocity of the cat. Now at the peak height, v = final velocity = 0, u = initial velocity and a = -g = 9.8 m/s², s vertical distance travelled by the cat from its position on the cabinet = Δy = 3.130 m - 1.765 m = 1.365 m.
Substituting these variables into the equation, we have
0² = u² + 2(-9.8m/s²) × 1.365 m
-u² = -26.754 m²/s²
u = √26.754 m²/s²
u = 5.17 m/s
To find its initial horizontal velocity, u₁ we first find the time t it takes to reach the peak height from
v = u + at. where the variables mean the same as above.
substituting the values, we have
0 = 5.17 m/s +(-9.8m/s²)t
-5.17 m/s = -9.8m/s²t
t = -5.17 m/s ÷ (-9.8m/s²)
= 0.53 s
Now, the horizontal distance d = u₁t = 1.560 m
u₁ = d/t = 1.560 m/0.53 s = 2.96 m/s
So, the initial velocity of the cat is V = √(u² + u₁²)
= √((5.17 m/s)² + (2.96 m/s)²)
= √(26.729(m/s)² + 8.762(m/s)²)
= √(35.491 (m/s)²)
= 5.95 m/s
its direction θ = tan⁻¹(5.17 m/s ÷ 2.96 m/s) = 60.2°
So, the initial velocity of the cat is 5.95 m/s at 60.2° from the horizontal
(b)
First, we find the time t' it takes the cat to land on the bed from d' = u₁t'
where d' = horizontal distance of cabinet from bed = 3.582 m
u₁ = horizontal velocity = 2.96 m/s
t' = d'/u₁
= 3.582 m/2.96 m/s
= 1.21 s
The vertical between the bed and cabinet which is the vertical distance moved by the cat is gotten from Δy = ut' +1/2at'²
substituting u = initial vertical velocity = 5.17 m/s, t' = 1.21 s and a = -g = -9.8 m/s² into Δy, we have
Δy = ut' +1/2at'² = 5.17 m/s × 1.21 s +1/2(- 9.8 m/s²) × (1.21 s)² = 6.256 - 7.174 = -0.918 m
Δy = y₂ - y₁
Since our initial position is the position of the cabinet above the ground = y₁ = 1.765 m
y₂ = position of bed above ground.
Δy = y₂ - y₁ = -0.918 m
y₂ - 1.765 m = -0.918 m
y₂ = 1.765 m - 0.918 m
= 0.847 m
A parallel-plate capacitor in air has a plate separation of 1.30 cm and a plate area of 25.0 cm2. The plates are charged to a potential difference of 255 V and dis-connected from the source. The capacitor is then immersed in distilled water. Determine a) the charge on the plates before and after immersion.b) the capacitance and potential difference after immersion.c) the change in energy of the capacitor.
Answer:
Explanation:
capacitance of air capacitor
C = ε₀ A / d
ε₀ is permittivity of medium , A is plate area , d is distance between plate .
C = 8.85 x 10⁻¹² x 25 x 10⁻⁴ / 1.3 x 10⁻²
= 170.19 x 10⁻¹⁴ F .
charge on the capacitor when it is charged to potential of 255 V
= CV , C is capacitance and V is potential
= 170.19 x 10⁻¹⁴ x 255
= 4.34 x 10⁻¹⁰ C .
After it is disconnected from the source , and it is immersed in water , charge on it remains the same .
So its charge when immersed in water will be constant at 4.34 x 10⁻¹⁰ C.
b )
When it is immersed in water its capacity increases k times where k is dielectric constant of water which is 80 .
capacitance of capacitor in water = 80 x 170.19 x 10⁻¹⁴ F
= 13615.2 x 10⁻¹⁴ F .
= 1.36 x 10⁻¹⁰ F
potential difference = charge / capacitance
= 4.34 x 10⁻¹⁰ / 1.36 x 10⁻¹⁰
= 3.2 V
c )
Energy of capacitor = 1/2 C V²
Initial energy = 1/2 x 170.19 x 255² x 10⁻¹⁴
= 55.33 x 10⁻⁹ J
Final energy = 1/2 x 1.36 x 10⁻¹⁰ x 3.2²
= .7 x 10⁻⁹ J .
decrease of energy = 54.63 x 10⁻⁹ J .
The inhabitants of a small island export a cloth made from a plant that grows only on their island. A clothier from New York, believing that he can save money by "cutting out the middleman," decides to travel to the island and buy the cloth himself. Ignorant of the local custom where strangers are offered outrageous prices initially, the clothier accepts (much to everyone's surprise) the initial price of 400 tepizes/m^2. The price of this cloth in New York is 120 dollars/yard^2. If the clothing maker bought 500 m^2 of this fabric, how much money did he lose? Use 1tepiz= 0.625dollar and 0.9144m = 1yard.
Answer:
Explanation:
purchase price = 400 tepizes / m²
1 tepiz = .625 dollar
purchase price in terms of dollar = 400 x .625 dollar / m²
= 250 dollar / m²
.9144 m = 1 yard
1 m = 1.0936 yard
1m² = 1.196 yard²
price in terms of dollar / yards²
= 250 / 1.196 dollar / yard²
= 209 dollar / yard²
Price of cloth in New York = 120 dollar / yard²
loss = 209 - 120 = 89 dollar / yard²
500 m² = 500 x 1.196 yard²
= 598 yard²
net loss in purchasing 500 m² cloth
= 598 x 89
= 53222 dollar .
An accident in a laboratory results in a room being contaminated by a radioisotope with a half life of 4.5 hours. If the radiation is measured to be 64 times the maximum permissible level, how much time must elapse before the room is safe to enter? The mass of Helium atom is 4.002602 u (where u = 1.66 x 10-27 kg) but the mass of 1 proton is 1.00730 u and 1 neutron is 1.00869 u. Calculate the binding energy per nucleon in MeV.
Answer:
a) t = 27.00 h
b) B = 6.84 MeV/nucleon
Explanation:
a) The time can be calculated using the following equation:
[tex] R = R_{0}e^{-\lambda*t} [/tex]
Where:
R: is the radiation measured at time t
R₀: is the initial radiation
λ: is the decay constant
t: is the time
The decay constant can be calculated as follows:
[tex] t_{1/2} = \frac{ln(2)}{\lambda} [/tex]
Where:
t(1/2): is the half life = 4.5 h
[tex] \lambda = \frac{ln(2)}{t_{1/2}} = \frac{ln(2)}{4.5 h} = 0.154 h^{-1} [/tex]
We have that the radiation measured is 64 times the maximum permissible level, thus R₀ = 64R:
[tex] \frac{R}{64R} = e^{-\lambda*t} [/tex]
[tex] t = -\frac{ln(1/64)}{\lambda} = -\frac{ln(1/64)}{0.154 h^{-1}} = 27.00 h [/tex]
b) The binding energy (B) can be calculated using the following equation:
[tex]B = \frac{(Z*m_{p} + N*m_{n} - M_{A})}{A}*931.49 MeV/u[/tex]
Where:
Z: is the number of protons = 2 (for [tex]^{4}_{2}He[/tex])
[tex]m_{p}[/tex]: is the proton mass = 1.00730 u
N: is the number of neutrons = 2 (for [tex]^{4}_{2}He[/tex])
[tex]m_{n}[/tex]: is the neutron mass = 1.00869 u
[tex]M_{A}[/tex]: is the mass of the He atom = 4.002602 u
A = N + Z = 2 + 2 = 4
The binding energy of [tex]^{4}_{2}He[/tex] is:
[tex]B = \frac{(2*1.00730 + 2*1.00869 - 4.002602)}{4}*931.49 MeV/u = 7.35\cdot 10^{-3} u*931.49 MeV/u = 6.84 MeV/nucleon[/tex]
Hence, the binding energy per nucleon is 6.84 MeV.
I hope it helps you!
A driver wearing a seat beat decelerates at roughly the same rate as the car it self. Since many modern cars have a "crumble zone" built into the front of the car, let us assume that the car decelerates of a distance of 0.9 m. What is the net force acting on a 65 kg driver who is driving at 18 m/sec and comes to rest in this distance
Answer:
11,700Newton
Explanation:
According to Newton's second law, Force = mass × acceleration
Given mass = 65kg.
Acceleration if the car can be gotten using one of the equation of motion as shown.
v² = u²+2as
v is the final velocity = 18m/s
u is the initial velocity = 0m/s
a is the acceleration
s is the distance travelled = 0.9m
On substitution;
18² = 0²+2a(0.9)
18² = 1.8a
a = 324/1.8
a = 180m/²
Net force acting on the body = 65×180
Net force acting on the body = 11,700Newton
A heavy copper ball of mass 2 kg is dropped from a fiftieth-floor apartment window. Another one with mass 1 kg is dropped immediately after 1 second. Air resistance is negligible. The difference between the speeds of the two balls:__________.
a. increases over time at first, but then stays constant.
b. decreases over time.
c. remains constant over time.
d. increases over time.
Answer:
C
Explanation:
Because everything on Earth falls at the same speed, the masses of the balls do not matter. Since the acceleration due to gravity is constant, their speeds will both be increasing at the same rate, and therefore the difference in speeds would remain constant until they hit the ground. Hope this helps!
Photoelectric effect:
A. What is the maximum kinetic energy of electrons ejected from barium (W0=2.48eV) when illuminated by white light, lambda=410-750nm?
B. The work functions for sodium, cesium, copper, and iron are 2.3, 2.1, 4.7, and 4.5eV, respectively. Which of these metals will not emit electrons when visible light shines on it?
Answer:
A. K = 0.546 eV
B. cooper and iron will not emit electrons
Explanation:
A. This is a problem about photoelectric effect. Then you have the following equation:
[tex]K=h\nu-\Phi=h\frac{c}{\lambda} -\Phi[/tex] (1)
K: kinetic energy of the ejected electron
Ф: Work function of the metal = 2.48eV
h: Planck constant = 4.136*10^{-15} eV.s
λ: wavelength of light = 410nm - 750nm
c: speed of light = 3*10^8 m/s
As you can see in the equation (1), higher the wavelength, lower the kinetic energy. Then, the maximum kinetic energy is obtained with the lower wavelength (410nm). Thus, you replace the values of all variables :
[tex]K=(4.136*10^{-15}eV)\frac{3*10^8m/s}{410*10^{-9}m}-2.48eV\\\\K=0.546eV[/tex]
B. First you calculate the energy of the photon with wavelengths of 410nm and 750nm
[tex]E_1=(4.136*10^{-15}eV)\frac{3*10^{8}m/s}{410*10^{-9}m}=3.02eV\\\\E_2=(4.13610^{-15}eV)\frac{3*10^{8}m/s}{750*10^{-9}m}=1.6544eV[/tex]
You compare the energies E1 and E2 with the work functions of the metals and you can conclude:
sodium = 2.3eV < E1
cesium = 2.1 eV < E1
cooper = 4.7eV > E1 (this metal will not emit electrons)
iron = 4.5eV > E1 (this metal will not emit electrons)
70 pointss yall !!! helpp
Answer:
A= The type of plant
B= How tall the plant is
Explanation:
A carousel has a diameter of 6.0-m and completes one rotation every 1.7s. Find the centripetal acceleration of the traveler in m / s2.
Answer:
The centripetal acceleration of the traveler is [tex]40.98\ m/s^2[/tex]
Explanation:
It is given that, A carousel has a diameter of 6.0-m and completes one rotation every 1.7 s.
We need to find the centripetal acceleration of the traveler. It is given by the formula as follows :
[tex]a=\dfrac{v^2}{r}[/tex]
r is radius of carousel
[tex]v=\dfrac{2\pi r}{T}[/tex]
So,
[tex]a=\dfrac{4\pi ^2r}{T^2}[/tex]
Plugging all the values we get :
[tex]a=\dfrac{4\pi ^2\times 3}{(1.7)^2}\\\\a=40.98\ m/s^2[/tex]
So, the centripetal acceleration of the traveler is [tex]40.98\ m/s^2[/tex].
I really need help with this question someone plz help !
Answer:D
Explanation:
Given
Same force is applied to each ball such that all have different masses
and Force is given by the product of mass and acceleration
[tex]F=m\times a[/tex]
[tex]a=\frac{F}{m}[/tex]
So acceleration of ball A
[tex]a_A=\frac{F}{0.5}=2F[/tex]
acceleration of ball B
[tex]a_B=\frac{F}{0.75}=\frac{4F}{3}=1.33F[/tex]
acceleration of ball C
[tex]a_C=\frac{F}{1}=F[/tex]
acceleration of ball D
[tex]a_D=\frac{F}{7.3}=\frac{F}{7.3}[/tex]
It is clear that acceleration of ball D is least.
Which person will most likely hear the loudest sound?
A
B
C
D
Answer:
The youngest person
Explanation:
Hearing worsens with age
Please mark brainliest
Answer:
A
Explanation:
The person closest to the origin of the sound will most likely hear the loudest sound. ^^
In each pair, select the body with more internal energy.
Answer:
rt
Explanation:
You are watching an object that is moving in SHM. When the object is displaced 0.560 m to the right of its equilibrium position, it has a velocity of 2.45 m/s to the right and an acceleration of 8.60 m/s2 to the left. Part A How much farther from this point will the object move before it stops momentarily and then starts to move back to the left
Answer:
2.95m
Explanation:
The farthest distance the object can move is the radius of the circle of which the Simple harmonic motion is assumed to be a part
But V = w× r; where V is velocity,
w is angular velocity and r is radius.
Also,
a= w2r; where a is linear acceleration
but a = v× r ; by comparing both equations
Hence r = a/v =8.6/2.45 =3.51m
But the horizontal distance of the motion is given by:
X = rcosx ; where x is the angle
X is the distance covered.
We know that the maximum value of cos x is 1 which is 0°
When the object moves in a fashion directly parallel to an horizontal distance, maximum distance would be reached and hence:
X = r=3.51m
Meaning the object needs to travel 3.51-0.56=2.95m further.
Note: the acceleration of the motion is constant whether it is swinging towards the left or right.
When the object is displaced 0.560 m to the right of its equilibrium position, it has a velocity of 2.45 m/s to the right and an acceleration of 8.60 m/s2 to the left and the amplitude of motion A = 0.732 m.
What is Amplitude of motion?
The distance between the central and extreme points for a moving particle is known as the amplitude of motion.
The given data to find the amplitude of motion,
Object displaced = 0.560 m
Velocity = 2.45 m/s
Acceleration = 8.60 m/s²
Starting with sine:
x(t) = Asin(ωt)
so that t = 0, x = 0
x(t) = 0.56 m = Asin(ωt)
v(t) = x(t)'= 2.45 m/s = Aωcos(ωt)
a(t) = v(t)'= -8.60 m/s² = -Aω²sin(ωt)
x(t) / a(t) = Asin(ωt) / -Aω²sin(ωt)
0.56m / -8.60 m/s² = -1 / ω²
ω² = 15.3571 rad^2/s^2
ω = 3.91881 rad/s
x(t) / v(t) = Asin(ωt) / Aωcos(ωt)
0.560m / 2.45m/s = tan(3.91t) / 3.91rad/s
0.8937= tan(3.91t)
t = 0.176 s
x(0.176) = Asin(3.59×0.176)
0.65 m= Asin(0.631)
A = 0.732 m is the amplitude of motion.
To know more about Amplitude of motion,
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What is the minimum frequency with which a 200-turn, flat coil of cross sectional area 300 cm2 can be rotated in a uniform 30-mT magnetic field if the maximum value of the induced emf is to equal 8.0 V
Answer:
The minimum frequency of the coil is 7.1 Hz
Explanation:
Given;
number of turns, N = 200 turns
cross sectional area, A = 300 cm² = 300 x 10⁻⁴ m²
magnitude of magnetic field strength, B = 30 x 10⁻³ T
maximum value of the induced emf, E = 8 V
Maximum induced emf is given as;
E = NBAω
where
ω is angular velocity (ω = 2πf)
E = NBA2πf
where;
f is the minimum frequency, measured in hertz (Hz)
f = E / (NBA2π)
f = 8 / (200 x 30 x 10⁻³ x 300 x 10⁻⁴ x 2 x 3.142)
f = 7.073 Hz
f = 7.1 Hz
Therefore, the minimum frequency of the coil is 7.1 Hz
The minimum frequency of the coil in the case when it should be rotated in a uniform 30-mT magnetic field is 7.1 Hz.
Calculation of the minimum frequency:Since
number of turns, N = 200 turns
cross-sectional area, A = 300 cm² = 300 x 10⁻⁴ m²
the magnitude of magnetic field strength, B = 30 x 10⁻³ T
the maximum value of the induced emf, E = 8 V
Now
Maximum induced emf should be
E = NBAω
here,
ω is angular velocity (ω = 2πf)
Now
E = NBA2πf
here,
f is the minimum frequency
So,
f = E / (NBA2π)
f = 8 / (200 x 30 x 10⁻³ x 300 x 10⁻⁴ x 2 x 3.142)
f = 7.073 Hz
f = 7.1 Hz
Therefore, the minimum frequency of the coil is 7.1 Hz.
Learn more about frequency here: https://brainly.com/question/24470698
An object with a mass of 1500 g (grams) accelerates 10.0 m/s2 when an
unknown force is applied to it. What is the amount of the force
Answer:
15N
Explanation:
F=ma
m=1500g = 1.5kg
a=10m/s2
1.5×10=15 N
Answer:15000gms^-2
Explanation:
F=m×a
m=1500g, a=10ms^-2
F=(1500×10)gms^-2
F=15000gms^-2
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At what distance from a 70.0 Watt speaker is the intensity 0.0195 W/m^2
(Treat the speaker as point of the source)
(Unit=meters)
PLEASE HELP ME!
Answer:
Distance = 16.9 m
Explanation:
We are given;
Power; P = 70 W
Intensity; I = 0.0195 W/m²
Now, for a spherical sound wave, the intensity in the radial direction is expressed as a function of distance r from the center of the sphere and is given by the expression;
I = Power/Unit area = P/(4πr²)
where;
P is the sound power
r is the distance.
Thus;
Making r the subject, we have;
r² = P/4πI
r = √(P/4πI)
r = √(70/(4π*0.0195))
r = √285.6627
r = 16.9 m
Answer:
16.9 m
Explanation:
A 1000-kg car is moving down the highway at 14m/s. What is the momentum?
Explanation:
Momentum = mass × velocity
p = mv
p = (1000 kg) (14 m/s)
p = 14000 kg m/s
The momentum of the car as it moves down the highway at the given speed is 14000-kg.m/s
Given the data in the question
Mass of the car; [tex]g = 1000kg[/tex]Velocity of the car; [tex]v = 14m/s[/tex]Momentum; [tex]p = ?[/tex]Momentum is the product of the mass of a particle and its velocity.
Momentum = Mass × Velocity
[tex]P = m \ * \ v[/tex]
We substitute our given values into the equation
[tex]P = 1000kg \ * \ 14m/s\\\\P = 14000kg.m/s[/tex]
Therefore, the momentum of the car as it moves down the highway at the given speed is 14000-kg.m/s
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A type of friction that occurs when air pushes against a moving object causing it to negatively accelerate
a) surface area
b) air resistance
c) descent velocity
d) gravity
Answer:
Air resistance
Answer B is correct
Explanation:
The friction that occurs when air pushes against a moving object causing it to negatively accelerate is called as air resistance.
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A skateboarder, starting from rest, rolls down a 12.8-m ramp. When she arrives at the bottom of the ramp her speed is 8.89 m/s. (a) Determine the magnitude of her acceleration, assumed to be constant. (b) If the ramp is inclined at 32.6 ° with respect to the ground, what is the component of her acceleration that is parallel to the ground?
Answer:
a) a = 3.09 m/s²
b) aₓ = 2.60 m/s²
Explanation:
a) The magnitude of her acceleration can be calculated using the following equation:
[tex] V_{f}^{2} = V_{0}^{2} + 2ad [/tex]
Where:
[tex]V_{f}[/tex]: is the final speed = 8.89 m/s
[tex]V_{0}[/tex]: is the initial speed = 0 (since she starts from rest)
a: is the acceleration
d: is the distance = 12.8 m
[tex] a = \frac{V_{f}^{2}}{2d} = \frac{(8.89 m/s)^{2}}{2*12.8 m} = 3.09 m/s^{2} [/tex]
Therefore, the magnitude of her acceleration is 3.09 m/s².
b) The component of her acceleration that is parallel to the ground is given by:
[tex] a_{x} = a*cos(\theta) [/tex]
Where:
θ: is the angle respect to the ground = 32.6 °
[tex] a_{x} = 3.09 m/s^{2}*cos(32.6) = 2.60 m/s^{2} [/tex]
Hence, the component of her acceleration that is parallel to the ground is 2.60 m/s².
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A skateboarder, starting from rest, rolls down a 12.8-m ramp the magnitude of the skateboarder's acceleration is approximately 3.07 [tex]m/s^2[/tex], the component of her acceleration that is parallel to the ground is approximately 1.66 [tex]m/s^2[/tex].
(a) The following kinematic equation can be used to calculate the skateboarder's acceleration:
[tex]v^2 = u^2 + 2as[/tex]
[tex](8.89)^2 = (0)^2 + 2a(12.8)[/tex]
78.72 = 25.6a
a = 78.72 / 25.6
a = 3.07 [tex]m/s^2[/tex]
(b) Trigonometry can be used to calculate the part of her acceleration that is parallel to the ground. We are aware that the ramp's angle with the ground is 32.6°.
[tex]a_{parallel }= a * sin(\theta)[/tex]
Plugging in the values:
[tex]a_{parallel[/tex] = 3.07 [tex]m/s^2[/tex]* sin(32.6°)
[tex]a_{parallel[/tex]≈ 1.66 [tex]m/s^2[/tex]
Therefore, the component of her acceleration that is parallel to the ground is approximately 1.66 [tex]m/s^2[/tex].
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URGENT : Which of the following is the most stable isotope? Explain.
Answer:
Plutonium–238
Explanation:
The stability of isotopes is largely dependent on their half-life.
Half life of an isotope is the time taken for the initial mass of the isotope to be halfed or we can say that the half-life of an isotope is the time taken for the mass of the isotope to become half the initial mass.
From the above definition, we discovered that if the time taken for the mass of the isotope to become half its initial mass is long, then the isotope must be very stable. On the other hand, if the time taken to become half its initial mass is short, then the isotope is unstable because.
We can thus say that, the longer the half-life the more stable the isotope and the shorter the half-life, the less stable the isotope will be.
Considering the table given in the question above and with the ideas we have obtained from the explanation above, we can see that Plutonium–238 has the longest half-life. Therefore Plutonium–238 will be more stable.
Compare the energy consumption of two commonly used items in the household. Calculate the energy used by a 1.40 kW toaster oven, Wtoaster , which is used for 5.40 minutes , and then calculate the amount of energy that an 11.0 W compact fluorescent light (CFL) bulb, Wlight , uses when left on for 10.50 hours .
Energy = (power) x (time)
-- For the toaster:
Power = 1.4 kW = 1,400 watts
Time = 5.4 minutes = 324 seconds
Energy = (1,400 W) x (324 s) = 453,600 Joules
-- For the CFL bulb:
Power = 11 watts
Time = 10.5 hours = 37,800 seconds
Energy = (11 W) x (37,800 s) = 415,800 Joules
-- The toaster uses energy at 127 times the rate of the CFL bulb.
-- The CFL bulb uses energy at 0.0079 times the rate of the toaster.
-- The toaster is used for 0.0086 times as long as the CFL bulb.
-- The CFL bulb is used for 116.7 times as long as the toaster.
-- The toaster uses 9.1% more energy than the CFL bulb.
-- The CFL bulb uses 8.3% less energy than the toaster.
Light bulb 1 operates with a filament temperature of 3000 K, whereas light bulb 2 has a filament temperature of 2000 K. Both filaments have the same emissivity, and both bulbs radiate the same power. Find the ratio A1/A2 of the filament areas of the bulbs.
Answer:
A₁/A₂ = 0.44
Explanation:
The emissive power of the bulb is given by the formula:
P = σεAT⁴
where,
P = Emissive Power
σ = Stefan-Boltzman constant
ε = Emissivity
A = Surface Area
T = Absolute Temperature of Surface
FOR BULB 1:
Since, emissivity and emissive power are constant.
Therefore,
P = σεA₁T₁⁴ ----------- equation 1
where,
A₁ = Surface Area of Bulb 1
T₁ = Temperature of Bulb 1 = 3000 k
FOR BULB 2:
Since, emissivity and emissive power are constant.
Therefore,
P = σεA₂T₂⁴ ----------- equation 2
where,
A₂ = Surface Area of Bulb 2
T₂ = Temperature of Bulb 1 = 2000 k
Dividing equation 1 by equation 2, we get:
P/P = σεA₁T₁⁴/σεA₂T₂⁴
1 = A₁(3000)²/A₂(2000)²
A₁/A₂ = (2000)²/(3000)²
A₁/A₂ = 0.44
During a baseball game, a baseball is struck at ground level by a batter. The ball leaves the baseball bat with an initial speed v0 = 38 m/s at an angle θ = 35° above horizontal. Let the origin of the Cartesian coordinate system be the ball's position the instant it leaves the bat. Air resistance may be ignored throughout this problem.
Part (a) Express the magnitude of the ball's initial horizontal velocity Or in terms of vo and 20%
Part (b) Express the magnitude of the ball's initial vertical velocity vOy in terms of vo and 0. 20%
Part (c) Find the ball's maximum vertical height Amat in meters above the ground.
Part (d) Create an expression in terms of vo-e, and g for the time-ur İt takes te ball to travel to its maximum vertical height.
Part (e) Calculate the horizontal distance in meters the ball has traveled when it returns to ground level.
Answer:
a) v₀ₓ = v₀ cos θ , b) v_{oy} = v₀ sin θ , c) y = v_{oy}² / 2g, y = 24.25 m
e) R = 138.46 m
Explanation:
This is a projectile launch exercise
a) let's use trigonometry to find the components of the initial velocity
cos θ = v₀ₓ / v₀
v₀ₓ = v₀ cos θ
v₀ₓ = 38 cos 35
v₀ₓ = 31.13 m / s
b) sin θ = [tex]v_{oy}[/tex] / v₀
v_{oy} = v₀ sin θ
v_{oy} = 38 sint 35
v_{oy} = 21 80 m / s
c, d) to find the maximum height, the vertical speed is zero
v_{y}² = v_{oy}² - 2 g y
0 = [tex]v_{oy}[/tex]² - 2 gy
y = v_{oy}² / 2g
let's calculate
y = 21.80 2 / (2 9.8)
y = 24.25 m
e) They ask to find the horizontal distance
for this we can use the expression of reaches
R = v₀² sin 2θ / g
let's calculate
R = 38² sin (2 35) / 9.8
R = 138.46 m
A car of mass 410 kg travels around a flat, circular race track of radius 83.4 m. The coefficient of static friction between the wheels and the track is 0.286. The acceleration of gravity is 9.8 m/s 2 . What is the maximum speed v that the car can go without flying off the track
Answer:
The maximum speed v that the car can go without flying off the track = 15.29 m/s
Explanation:
let us first lay out the information clearly:
mass of car (m) = 410 kg
radius of race track (r) = 83.4 m
coefficient of friction (μ) = 0.286
acceleration due to gravity (g) = 9.8 m/s²
maximum speed = v m/s
For a body in a constant circular motion, the centripetal for (F) acting on the body is given by:
F = mass × ω
where:
F = maximum centripetal force = mass × μ × g
ω = angular acceleration = [tex]\frac{(velocity)^2}{radius}[/tex]
∴ F = mass × ω
m × μ × g = m × [tex]\frac{v^{2} }{r}[/tex]
410 × 0.286 × 9.8 = 410 × [tex]\frac{v^{2} }{83.4}[/tex]
since 410 is on both sides, they will cancel out:
0.286 × 9.8 = [tex]\frac{v^{2} }{83.4}[/tex]
2.8028 = [tex]\frac{v^{2} }{83.4}[/tex]
now, we cross-multiply the equation
2.8028 × 83.4 = [tex]v^{2}[/tex]
[tex]v^{2}[/tex] = 233.754
∴ v = √(233.754)
v = 15.29 m/s
Therefore, the maximum speed v that the car can go without flying off the track = 15.29 m/s
Assume that the coefficient of static friction between the board and the box is not known at this point. What is the magnitude of the acceleration of the box in terms of the friction force f?
Answer:
Explanation:
From Newton's second Law of Motion,
F = ma
Ff + F = ma
Where F is the applied force, Ff is the frictional force, a is the acceleration and m is the mass of the object or box.
Magnitude of the acceleration:
a = Ff+F/m
This must act in the direction of F or the box would slide or accelerate off the negative side of the board (taking the direction of F to be positive
