Answer:
a. The wooden cylinder b. the wooden cylinder reaches the bottom first because its translational kinetic energy is greater.
Explanation:
a. Who reaches the bottom first
The kinetic energy of the objects is given by
K = 1/2mv² + 1/2Iω² where m = mass of object, v = velocity of object, I = moment of inertia and ω = angular velocity = v/r where r = radius of object
For the wooden cylinder, I = mr²/2 where m = mass of wooden cylinder and r = radius of wooden cylinder and v = velocity of wooden cylinder
So, its kinetic energy, K = 1/2mv² + 1/2(mr²/2)(v/r)²
K = 1/2mv² + 1/4mv²
K = 3mv²/4
For the steel hoop, I' = mr'² where m' = mass of steel hoop and r' = radius of steel hoop and v' = velocity of steel hoop
So, its kinetic energy, K' = 1/2m'v'² + 1/2(m'r'²)(v'/r')²
K' = 1/2m'v'² + 1/2m'v'²
K' = m'v'²
Since both kinetic energies are the same, since the drop from the same height,
K = K'
3mv²/4 = m'v'²
v²/v'² = 4m/3m'
v²/v'² = 4/3(m/m')
v/v' = √[4/3(m/m')]
Since the hoop weighs more than the cylinder m/m' < 1 and 4/3(m/m') < 4/3 ⇒ √ [4/3(m/m')] < √4/3 ⇒ v/v' < 1.16 ⇒ v'/v > 1/1.16 ⇒ v'/v > 0.866. Since 0.866 < 1, it implies v' < v.
Since v' = speed of steel hoop < v = speed of wooden cylinder, the wooden cylinder reaches the bottom first.
b. Why
Since the kinetic energy, K = translational + rotational
We find the translational kinetic energy of each object.
For the wooden cylinder,
K = K₀ + 1/2Iω² where K₀ = translational kinetic energy of wooden cylinder
K - 1/2Iω² = K₀
3/4mv² - 1/2(mr²/2)(v/r)² = K₀
3/4mv² - 1/4mv² = K₀
K₀ = 1/2mv²
For the steel hoop,
K' = K₁ + 1/2I'ω'² where K₁ = translational kinetic energy of steel hoop
K' - 1/2I'ω'² = K₁
m'v'² - 1/2(m'r'²)(v'/r')² = K₁
m'v'² - 1/2m'v'² = K₁
K₁ = 1/2m'v'²
So, K₀/K₁ = 1/2mv²÷1/2m'v'² = mv²/m'v'² = (m/m')(v²/v'²) = (m/m')4/3(m/m') = 4/3(m/m')².
Since (m/m') < 1 ⇒ (m/m')² < 1 ⇒ 4/3(m/m')² < 4/3 ⇒ K₀/K₁ < 1.33 ⇒ K₀ > K₁
So, the kinetic energy of the wooden cylinder is greater than that of the steel hoop.
So, the wooden cylinder reaches the bottom first because its translational kinetic energy is greater.
a. The wooden cylinder b. the wooden cylinder reaches the bottom first because its translational kinetic energy is greater.
What is Kinetic energy?
The energy of the body due to its movement in a particular direction under the influence of a force like a free-falling body due to gravitaional force is called Kinetic energy.
The kinetic energy of the objects is given by
[tex]K = \dfrac{1}{2}mv^2 + \dfrac{1}{2}Iw^2[/tex]
where
m = mass of object,
v = velocity of object,
I = moment of inertia and
ω = angular velocity = v/r where r = radius of object
For the wooden cylinder, I = mr²/2 where m = mass of wooden cylinder and r = radius of wooden cylinder and v = velocity of wooden cylinder
So, its kinetic energy,
[tex]K = \dfrac{1}{2}mv^2 + \dfrac{1}{2}(\dfrac{mr^2}{2})\dfrac{v}{r}^2[/tex]
[tex]K = \dfrac{3mv^2}{4}[/tex]
For the steel hoop,
I' = mr'²
where
m' = mass of steel hoop and
r' = radius of steel hoop and
v' = velocity of steel hoop
So, its kinetic energy,
[tex]K' = \dfrac{1}{2}m'v'^2 + \dfrac{1}{2}(m'r'^2)\dfrac{v'}{r'}^2[/tex]
[tex]K' = \dfrac{1}{2}m'v'^2 + \dfrac{1}{2}m'v'^2[/tex]
K' = m'v'²
Since both kinetic energies are the same, since the drop from the same height,
K = K'
[tex]\dfrac{3mv^2}{4 }= m'v'^2[/tex]
[tex]\dfrac{v^2}{v'^2} =\dfrac{ 4m}{3m'}[/tex]
[tex]\dfrac{v^2}{v'^2} = \dfrac{4}{3}(\dfrac{m}{m'})[/tex]
[tex]\dfrac{v}{v'} = \sqrt{[\dfrac{4}{3}(\dfrac{m}{m'})][/tex]
Since the hoop weighs more than the cylinder m/m' < 1 and 4/3(m/m') < 4/3 ⇒ √ [4/3(m/m')] < √4/3 ⇒ v/v' < 1.16 ⇒ v'/v > 1/1.16 ⇒ v'/v > 0.866. Since 0.866 < 1, it implies v' < v.
Since v' = speed of steel hoop < v = speed of wooden cylinder, the wooden cylinder reaches the bottom first.
(b) Since the kinetic energy, K = translational + rotational
We find the translational kinetic energy of each object.
For the wooden cylinder,
[tex]K = K_o + \dfrac{1}{2}Iw^2[/tex]
where
K₀ = translational kinetic energy of wooden cylinder
[tex]K - \dfrac{1}{2}Iw^2 = K_o[/tex]
[tex]\dfrac{3}{4}mv^2 - \dfrac{1}{2}(\dfrac{mr^2}{2})(\dfrac{v}{r})^2 = K_a[/tex]
[tex]\dfrac{3}{4}mv^2 - \dfrac{1}{4}mv^2 = K_o[/tex]
[tex]K_o = \dfrac{1}{2}mv^2[/tex]
For the steel hoop,
[tex]K' = K_1 + \dfrac{1}{2}I'w'^2[/tex]
where
K₁ = translational kinetic energy of steel hoop
[tex]K' - \dfrac{1}{2}I'w'^2 = K_1[/tex]
[tex]m'v'^2 - \dfrac{1}{2}(m'r'^2)(\dfrac{v'}{r'})^2 = K_1[/tex]
[tex]m'v'^2 - \dfrac{1}{2}m'v'^2 = K_1[/tex]
[tex]K_1= \dfrac{1}{2}m'v'^2[/tex]
So, K₀/K₁ = 1/2mv²÷1/2m'v'² = mv²/m'v'² = (m/m')(v²/v'²) = (m/m')4/3(m/m') = 4/3(m/m')².
Since (m/m') < 1 ⇒ (m/m')² < 1 ⇒ 4/3(m/m')² < 4/3 ⇒ K₀/K₁ < 1.33 ⇒ K₀ > K₁
So, the kinetic energy of the wooden cylinder is greater than that of the steel hoop.
So, the wooden cylinder reaches the bottom first because its translational kinetic energy is greater.
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If our atmosphere had a uniform density of 1.25 kg/m3 all the way up to a border with empty space above, that border would be Answer km above sea level. The pressure at sea level is 1 atm = 105 N/m2 and g = 10 m/s2. Enter your answer as an integer.
Answer:
The border is 8km above sea level.
Explanation:
We know that:
Density = 1.25 kg/m^3
Pressure = 10^5 N/m^2
g = 10m/s^2
Now, suppose that we have a virtual rectangle, such that its bases have an area of 1m^2 and the rectangle has a height equal to H.
This virtual figure has a volume V = 1m^2*H, and it is filled with air (which we know that has a density 1.25 kg/m^3)
Then the total mass inside that volume is:
M = (1.25 kg/m^3)*V = (1.25 kg/m^3)*(1m^2*H)
The weight of this mass is:
W = g*M = (10m/s^2)*(1.25 kg/m^3)*(1m^2*H)
And if we divide the weight in a given surface, let's say 1 m^2, we get the pressure per square meter, which we know is equal to 10^5 N/m^2
then:
P = 10^5 N/m^2 = (10m/s^2)*(1.25 kg/m^3)*(1m^2*H)*(1/m^2)
Whit this equation we can find the value of H.
10^5 N/m^2 = (10m/s^2)*(1.25 kg/m^3)*(1m^2*H)*(1/m^2)
10^5 N = (10m/s^2)*(1.25 kg/m^3)*(1m^2*H)
(10^5 N)/(10 m/s^2) = (1.25 kg/m^3)*(1m^2*H)
(10^4 kg) = (1.25 kg/m^3)*(1m^2*H)
(10^4 kg)/( 1.25 kg/m^3) = 1m^2*H
8,000 m^3 = 1m^2*H
(8,000 m^3)/(1m^2) =H
8,000 m = H
And we want this answer in km, knowing that 1,000m = 1km
8,000m = 8km = H
The border is 8km above sea level.
Height of boundaries is 8.2 km
Given that:Normal density = 1.25 kg/m³
1 atm = 101325 N/m²
Find:Height of boundaries
Computation:Pressure = Height × Density × Gravitational acceleration
101325 = Height × 1.25 × 9.8
101325 = Height × 12.25
Height of boundaries = 101325 / 12.25
Height of boundaries = 8271.42 m
Height of boundaries = 8.2 km
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A 2.0-kg cart is rolling along a frictionless, horizontal track towards a 1.8-kg cart that is held initially at rest. The carts are loaded with strong magnets that cause them to attract one another. Thus, the speed of each cart increases. At a certain instant before the carts collide, the first cart's velocity is 5.9 m/s, and the second cart's velocity is -2.7 m/s. (a) What is the total momentum of the system of the two carts at this instant
Answer:
the total momentum of the system before collision is 6.94 kgm/s
Explanation:
Given;
mass of the first cart, m₁ = 2.0 kg
mass of the second cart, m₂ = 1.8 kg
velocity of the first cart before collision, u₁ = 5.9 m/s
velocity of the second cart before collision, u₂ = -2.7 m/s
The total momentum of the system before collision is calculated as follows;
[tex]P_t = P_1 + P_2 \\\\P_t = m_1u_1 + m_2u_2\\\\P_t = (2\times 5.9) + (1.8 \times -2.7)\\\\P_t = 11.8 - 4.86\\\\P_t = 6.94 \ kgm/s[/tex]
Therefore, the total momentum of the system before collision is 6.94 kgm/s
The following statements address the science behind the pulley system illustrated:
A. The pulleys increase the entropy of the system.
B. The force applied to the rope is less than the force needed to lift the object.
C. The pulleys help generate as much energy as possible.
D. The pulleys multiply energy input, resulting in more energy output.
E. The pulleys generate no thermal energy.
Which of these statements is/are true?
i. Statements A and B
ii. Statements D and E
iii. Only statement C
iv. All of the statements
Answer:
i. Statements A and B
Explanation:
Sana nakatulong
A 64.0 cm long cord is vibrating in such a manner that it forms a standing wave with two antinodes. (The cord is fixed at both ends.) Which harmonic does this wave represent
Answer:
the wave represents the second harmonic.
Explanation:
Given;
length of the cord, L = 64 cm
The first harmonic of a cord fixed at both ends is given as;
[tex]f_o = \frac{V}{2L}[/tex]
The wavelength of a standing wave with two antinodes is calculated as follows;
L = N---> A -----> N + N ----> A -----> N
Where;
N is node
A is antinode
L = N---> A -----> N + N ----> A -----> N = λ/2 + λ/2
L = λ
The harmonic is calculated as;
[tex]f = \frac{V}{\lambda} \\\\f = \frac{V}{L} = 2(\frac{V}{2L} ) = 2(f_o) = 2^{nd} \ harmonic[/tex]
Therefore, the wave represents the second harmonic.
L = λ
Select the correct answer Which object is an insulator
A. iron
b. cooper
c. plastic
d. salt water
What is the definition of the half-life of a radioactive isotope?
answer: The time it takes for half the parent nuclei in a sample to become daughter nuclei.
Answer: The half-life is the amount of time it takes for a given isotope to lose half of its radioactivity. If a radioisotope has a half-life of 14 days, half of its atoms will have decayed within 14 days. In 14 more days, half of that remaining half will decay, and so on.
What kind of energy is in a moving skateboard
Answer:
I guess it is kinetic energy
Answer:
kinetic energy because my dog told me
We have seen that the voltage of a concentration cell can be affected by the concentrations of aqueous components and/or temperature. The identity of the redox pair also affects the observed voltage of a concentration cell in a somewhat subtle way. Carefully consider the Nernst equation. Rank the redox pairs below from greatest (1) to smallest (3) voltage in a concentration cell, assuming equal values of T and Q for all cells. Assume multimeter leads are connected to that measured voltages are positive.
a. Copper metal/copper(l) ion
b. Aluminum/aluminum ion
c. Magnesium metal/magnesium ion
Answer:
1) Magnesium metal/magnesium ion
2) Aluminum/aluminum ion
3) Copper metal/copper(l) ion
Explanation:
The activity series is a series that shows the ease of reactivity of substances in an electrochemical cell.
The substances that are higher up in the series are more reactive in electrochemical cells.
Magnesium is the first element in the series that has the most negative redox potential then followed aluminium.
Hence, according to Nernst,
1) Magnesium metal/magnesium ion
2) Aluminum/aluminum ion
3) Copper metal/copper(l) ion
A 0.70-kg disk with a rotational inertia given by MR 2/2 is free to rotate on a fixed horizontal axis suspended from the ceiling. A string is wrapped around the disk and a 2.0-kg mass hangs from the free end. If the string does not slip then as the mass falls and the cylinder rotates the suspension holding the cylinder pulls up on the mass with a force of______
Answer:
The force will be "9.8 N".
Explanation:
The given values are:
mass,
m = 0.7 kg
M = 2
g = 9.8
Now,
⇒ [tex]\tau = T \alpha[/tex]
then,
⇒ [tex]\frac{1}{2}mR^2(\frac{1}{R}\frac{dv}{dt}) =M(g-a_t)R[/tex]
⇒ [tex]\frac{1}{2}m \ a_t=m(g-a_t)[/tex]
⇒ [tex]a_t=\frac{2g}{(\frac{m}{M} +2)}[/tex]
On substituting the values, we get
⇒ [tex]=\frac{2\times 9.8}{\frac{0.7}{2} +2}[/tex]
⇒ [tex]=8.34 \ m/s[/tex]
hence,
⇒ [tex]T=mg+M(g-a_t)[/tex]
On substituting the values, we get
⇒ [tex]=0.7\times 9.8+2(9.8-8.34)[/tex]
⇒ [tex]=6.86+2(1.46)[/tex]
⇒ [tex]=6.86+2.92[/tex]
⇒ [tex]=9.8 \ N[/tex]
A solenoid that is 93.9 cm long has a cross-sectional area of 17.3 cm2. There are 1270 turns of wire carrying a current of 7.80 A. (a) Calculate the energy density of the magnetic field inside the solenoid. (b) Find the total energy in joules stored in the magnetic field there (neglect end effects).
Answer:
[tex]65.6\ \text{J/m}^3[/tex]
[tex]0.11\ \text{J}[/tex]
Explanation:
B = Magnetic field = [tex]\mu_0 \dfrac{N}{l}I[/tex]
[tex]\mu_0[/tex] = Vacuum permeability = [tex]4\pi10^{-7}\ \text{H/m}[/tex]
N = Number of turns = 1270
[tex]l[/tex] = Length of solenoid = 93.9 cm = 0.939 m
[tex]I[/tex] = Current = 7.8 A
A = Area of solenoid = [tex]17.3\ \text{cm}^2[/tex]
Energy density of a solenoid is given by
[tex]u_m=\dfrac{B^2}{2\mu_0}\\\Rightarrow u_m=\dfrac{(\mu_0 \dfrac{N}{l}I)^2}{2\mu_0}\\\Rightarrow u_m=\dfrac{\mu_0N^2I^2}{2l^2}\\\Rightarrow u_m=\dfrac{4\pi\times 10^{-7}\times 1230^2\times 7.8^2}{2\times 0.939^2}\\\Rightarrow u_m=65.6\ \text{J/m}^3[/tex]
The energy density of the magnetic field inside the solenoid is [tex]65.6\ \text{J/m}^3[/tex]
Energy is given by
[tex]U_m=u_mAl\\\Rightarrow U_m=65.6\times 17.3\times 10^{-4}\times 0.939\\\Rightarrow U_m=0.11\ \text{J}[/tex]
The total energy in joules stored in the magnetic field is [tex]0.11\ \text{J}[/tex].
The data table for the decomposition reaction of hydrogen peroxide H2 O2 shows how the reaction rate changes over time which statement describes the conclusion you can sharpen the table
The data table for the decomposition reaction of hydrogen peroxide H₂ O₂ shows down over time as the reactant rate get used up.
What is rate, reaction and rate of reaction?
Rate- The rate of a particular chemical reaction is calculated by dividing the rate of change in a reactant's or product's concentration by the coefficient from the given balanced equation.
Reactions- They are defined as the change of a chemical substance into an innovative substance through the formation and breaking of bonds among distinct atoms.
Rate of reaction- It is defined as the ratio of the increase in product concentration per unit time to the decrease in reactant concentration per unit time. The rate of reaction varies greatly.
It can be seen that with the concentration, the rate of decomposition is also decreased. Generally, it is found that as per hour concentration and rate of decomposition decreases as well.
Therefore, (A) option is the correct answer.
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The moon does not stay at the same distance from the earth.why?
Answer:
The moon does not stay at the same distance of the earth because the ortbit of the moon is slightly elliptical. If earth is not tilted at an angle of 66.5°, there will be no change in the season and the earth will have equal length of days and night.
Explanation:
mark me brainlest
a disk of radius 25 cm spinning at a rate of 30 rpm slows to a stop over 3 seconds. what is the angular acceleration?
b. how many radians did the disk turn while stopping?
c. how many revolutions?
Answer:
too many
Explanation:
What is the order of the events for the water cycle on a typical warm day?
А
rain, snow, sleet
B
precipitation, evaporation, rain
с
evaporation, condensation, precipitation
D
condensation, evaporation, precipitation
Please respond to this for 15 points. Please don’t put in a link.
Answer:
e. Combustion
Explanation:
In Combustion reaction, a substance reacts with oxygen from the air and resultant product is that it releases carbon dioxide and water.
Here,
2C2H6 is the substance that reacted with 7O2 (Oxygen) to release 4CO2 (Carbon Dioxide) and 6H2O (Water).
A fixed 14.1-cm-diameter wire coil is perpendicular to a magnetic field 0.52 T pointing up. In 0.28 s , the field is changed to 0.23 T pointing down. Part A What is the average induced emf in the coil
Answer:
the average induced emf in the coil is 0.016 V.
Explanation:
Given;
diameter of the wire, d = 14.1 cm = 0.141 m
change in magnetic filed strength, dB = 0.52 T - 0.23 T = 0.29 T
change in time, dt = 0.28 s
The area of the wire is calculated as follows;
[tex]A = \frac{\pi d^2}{4} \\\\A = \frac{\pi \times (0.141)^2}{4} \\\\A = 0.0156 \ m ^2[/tex]
The induced emf is calculated as follows;
[tex]emf = \frac{dBA}{dt} \\\\emf = \frac{0.29 \times 0.0156}{0.28} \\\\emf = 0.016 \ V[/tex]
Therefore, the average induced emf in the coil is 0.016 V.
What is the reason that the moon looks dimmer before eclipse? Why does it take some time to be brighter again after eclipse?
Answer:
Why does it take sometimes to be brighter again after eclipse? The moon looks dimmer before lunar eclipse because the moon enters into shadow of penumbra region of earth. As a result, the brightness of moon decreases and looks dimmer.
Explanation:
Answer: The moon looks dimmer before lunar eclipse because the moon enters into shadow of penumbra region of earth. As a result, the brightness of moon decreases and looks dimmer.
Explanation:
As air pressure decreases, what happens
to the density of the atmosphere?
A. increases
B. decreases
C. stays the same
D. not enough information to tell
Answer:
I believe it is B, not 100% sure though
Explanation:
Answer:
A. increases
Explanation:
The relationship between air pressure (atmospheric pressure) and the density of the atmosphere is inversely proportional.
Red light of wavelength 630 nm passes through two slits and then onto a screen that is 1.3 m from the slits. The center of the 3rd order bright band on the screen is separated from the central maximum by 0.90 cm. a) What is the frequency of the light, the slit separation, and the angle of the 3rd order bright band
Answer:
a) f = 4.76 10¹⁴ Hz, b) d = 2.73 10⁻⁴ m, c) θ = 6.923 10⁻³ rad
Explanation:
a) In this problem the frequency of light is asked, let's use the relationship between the speed of the wave, its wavelength and its frequency
c = λ f
f = c /λ
f = [tex]\frac{3 \ 10^8}{630 \ 10^{-9}}[/tex]
f = 4.76 10¹⁴ Hz
b) slit separation (d)
the expression for the constructive interference of the double-slit experiment is
d sin θ = m λ
let's use trigonometry
tan θ = y / L
tan θ = [tex]\frac{sin \theta}{cos \theta}[/tex]
in general the angles are small, so we can approximate
tan θ = sin θ
tan θ = y/L
we substitute
d y / L = m λ
d = m L λ / y
we calculate
d = 3 1.3 630 10⁻⁹ /0.90 10⁻²
d = 2.73 10⁻⁴ m
c) the angle
tan θ = y / L
θ = tan⁻¹ y / L
θ = tan⁻¹ 0.9 10⁻² / 1.3
θ = tan⁻¹ 6,923 10⁻³
let's find the angle in radians
θ = 6.923 10⁻³ rad
A rifle can shoot a 4.00 g bullet at a speed of 998 m/s. Find the kinetic energy of the bullet. What work is done on the bullet if it starts from rest?
Answer:
1992.008J
Explanation:
A +0.0129 C charge feels a 4110 N
force from a -0.00707 C charge. How
far apart are they?
[?] m
Answer:
r = 14.13 m
Explanation:
Given that,
Charge 1, q₁ = +0.0129 C
Charge 2, q₂ = -0.00707 C
The force between charges, F = 4110 N
We need to find the distance between charges. The formula for the force between charges is given by :
[tex]F=k\dfrac{q_1q_2}{r^2}[/tex]
Where
r is the distance between charges
So,
[tex]r=\sqrt{\dfrac{kq_1q_2}{F}} \\\\r=\sqrt{\dfrac{9\times 10^9\times 0.0129 \times 0.00707 }{4110 }} \\\\r=14.13\ m[/tex]
So, the distance between charges is equal to 14.13 m.
Answer:
14.13 m
Explanation:
acellus
Question 7 of 11
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A 1655 kg car drives down the highway. If the car has a momentum of 61250 kg. m/s, what is the velocity of the car?
Answer:
velocity = 37.01 m/s
Explanation:
momentum = mass * velocity
61250 = 1655 * x
x = 61250 / 1655
x = 37.0090634441
Which of the following best describes wind?
A А
Sinking warm air moving a few feet above the ground
B
An air current formed by changes in ocean tides
с
Cool air rushing in to fill an area of low pressure
D
Rising warm air pushing cool air down toward Earth
The correct statement about the wind is:
Cool air rushing in to fill an area of low pressureWhat is the wind?Wind is the movement of air currents in relation to the Earth's surface, which is caused by pressure differences and air movement.
Characteristics of the windIt is a meteorological phenomenon originated in the movements of rotation and translation of the Earth.When the rising air cools and loses the moisture it was carrying, due to condensation and rain, the result is dry and cool air.Therefore, we can conclude that the wind is the current of air that occurs in the atmosphere due to natural causes, from high pressure areas to low pressure areas.
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A vertical straight conductor X of length 0.5m is held along the positive X-axis and situated in a uniform horizontal magnetic field of 0.1T which is pointing towards the positive Y-axis. (i) Calculate the magnitude and direction of force on X, when a current of 4A is passed through it. (ii) Through what angle must X be turned in a vertical plane so that the force on X is halved
Answer:
i. 0.2 N ii. 30°
Explanation:
(i) Calculate the magnitude and direction of force on X, when a current of 4A is passed through it.
The magnetic force F = BILsinФ where B = magnetic field strength = 0.1 T, I = current = 4 A and L= length of conductor = 0.5 m. Since the conductor X of length 0.5m is held along the positive X-axis and situated in a uniform horizontal magnetic field of 0.1T which is pointing towards the positive Y-axis, both B and L are perpendicular to each other. So, Ф = 90°
So, F = BILsinФ
F = 0.1 T × 4 A ×0.5 m × sin90°
F = 0.1 T × 4 A ×0.5 m × 1
F = 0.2 N
(ii) Through what angle must X be turned in a vertical plane so that the force on X is halved
If F' = BILsinФ' where Ф'=the new angle, and BIL = F
F'/F = sinФ'
Since F'/F = 1/2
sinФ' = 1/2
Ф' = sin⁻¹(1/2) = 30°
A carnival ride starts at rest and is accelerated from an initial angle of zero to a final angle of 6.3 rad by a rad counterclockwise angular acceleration of 2.0 s2 What is the angular velocity at 6.3 rad?
The final angular velocity of the carnival ride at a displacement of 6.3 rad is 25.2 rad/s.
Final angular velocity of the carnival ride
The final angular velocity of the carnival ride is determined by applying third kinematic equation as shown below;
ωf = ωi + 2αθ
where;
ωf is the final angular velocity of the carnival ride = ?ωi is the initial angular velocity of the carnival ride = 0α is the angular acceleration = 2.0 rad/s²θ is the angular displacement of the carnival ride = 6.3 radωf = 0 + 2(2.0) x 6.3
ωf = 25.2 rad/s
Thus, the final angular velocity of the carnival ride at a displacement of 6.3 rad is 25.2 rad/s.
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Answer: 5.0 rad/s
Explanation: Because that’s what khan said so try it out.
A hand dryer blows heated air downwards out of the exit duct at a velocity of 4 m/s. The temperature and density of the ambient air at the inlet are 15 C and 1.23 kg/m3, while at the outlet it has temperature 35 C and density 1.15 kg/m3 The blower power is 10.0 W and the heater power is 715 W. Consider the inlet to be at the large mass of ambient air which has negligible velocity.
a) What is the pressure at the outlet? 4 m/s, 35 C
b) You will be applying the energy equation. Why can you ignore any height differences in this situation?
c) If the specific heat of air C-1000 J/(kg K), where Δυ-C Δ T, find the change in internal energy per unit mass from the inlet to outlet.
d) Find the mass flow rate through the dryer.
e) What is the power loss in the system?
f) What is the loss in the system?
g) What is the head loss in the system?
h) What is the total loss coefficient of the system, referred to the outlet velocity?
i) If there were no heater, would the temperature of gas at the outlet be higher, the same, or lower than the inlet? Explain why.
Answer:
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Explanation:
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A dentist uses a concave mirror to examine a tooth that is 1.00
cm in front of the mirror. The image of the tooth forms 10.0 cm
behind the mirror. What is the mirror's radius of curvature?
Answer:
-2.2cm
Explanation:
A dentist uses a concave mirror to examine a tooth that is 1.00 cm in front of the mirror. The image of the tooth forms 10.0 cm behind the mirror. What is the mirror's radius of curvature 0.909 m.
To determine the mirror's radius of curvature, we can use the mirror formula:
1/f = 1/v - 1/u
Where:
f is the focal length of the mirror
v is the image distance (distance of the image from the mirror)
u is the object distance (distance of the object from the mirror)
In this case, the object distance (u) is 1.00 cm and the image distance (v) is -10.0 cm (since the image is formed behind the mirror, the distance is negative).
1/f = 1/(-10.0) - 1/(1.00)
Simplifying the equation:
1/f = -0.1 - 1
1/f = -1.1
Now, we can find the reciprocal of both sides of the equation:
f/1 = -1/1.1
f ≈ -0.909 m
The negative sign indicates that the mirror is concave.
Therefore, the mirror's radius of curvature is approximately 0.909 m.
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Helppp!!! It’s due right now. Review question.
Answer:
A person that consistently runs 3 meters evert second
Explanation:
Because as a human walks 3 meters every 1 second it isn't consider uniform. It has to be in a erect motion
A 4-foot spring measures 8 feet long after a mass weighing 8 pounds is attached to it. The medium through which the mass moves offers a damping force numerically equal to 2 times the instantaneous velocity. Find the equation of motion if the mass is initially released from the equilibrium position with a downward velocity of 7 ft/s. (Use g
Correct question is;
A 4-foot spring measures 8 feet long after a mass weighing 8 pounds is attached to it. The medium through which the mass moves offers a damping force numerically equal to √2 times the instantaneous velocity. Find the equation of motion if the mass is initially released from the equilibrium position with a downward velocity of 7 ft/s. (Use g = 32 ft/s²)
Answer:
x(t) = 7te^(-2t√2)
Explanation:
We are given;
Weight; W = 8 lbs
mass; m = W/g
g = 32 ft/s²
Thus;
m = 8/32
m = ¼ slugs
From Newton's second law we can write the equation as;
m(d²x/dt²) = -kx - β(dx/dt)
Rearranging this, we have;
(d²x/dt²) + (β/m)(dx/dt) + (k/m)x = 0
Where;
β is damping constant = √2
k is spring constant = W/s
Where s = 8ft - 4ft = 4ft
k = 8/4
k = 2
Thus,we now have;
(d²x/dt²) + (√2/(¼))(dx/dt) + (2/(¼))x = 0
>> (d²x/dt²) + (4√2)dx/dt + 8x = 0
The auxiliary equation of this is;
m² + (4√2)m + 8 = 0
Using quadratic formula, we have;
m1 = m2 = -2√2
The general solution will be gotten from;
x_t = c1•e^(mt) + c2•t•e^(mt)
Plugging in the relevant values gives;
x_t = c1•e^(mt) + c2•t•e^(mt)
At initial condition of t = 0, x_t = 0 and thus; c1 = 0
Also at initial condition of t = 0, x'(0) = 7 and thus;
Since c1 = 0, then c2 = 7
Thus,equation of motion is;
x(t) = 7te^(-2t√2)
Pls quickly brainliest to the first to anwser
Answer:
8m/s^2
Explanation:
hope it helps........
Explanation:
you're supposed to know the formula of acceleration which is velocity of a time then you can solve the question