Answer:
Explanation:
Moment of inertia of sphere I = 2 /5 x m R²
m is mass and R is radius of the sphere .
I = 2/5 x 1800 x 0.5²
= 180 kg m².
For rotational motion starting from rest
θ = 1/2 α t²
Here θ = π /2 = 1.57 radians
t = 12 s
1.57 radians = 1/2 x α x 12²
Angular acceleration α = .022 rad /s²
Torque applied = I α
= 180 kg m² x .022 rad /s²
= 3.96 N.m
b ) Torque = F x r
F = Torque / r
= 3.96 / .5 = 7.92 N .
c )
Average weight of a cellophone is 1.3 N .
So the force applied is a little more than weight of a cellophone.
A car of mass 2100 kg collides with a motorcycle of mass 290 kg. After the collision, the car and motorcycle stick and slide together. The car's velocity just before the collision was<30,-10>m/s , and that of the motorcycle was <10,10>m/s. Determine the velocity of the stuck-together car and motorcycle just after the collision.
Answer:
V = 29.49 m/s
Explanation:
Given that,
The mass of a car,[tex]m_c=2100\ kg[/tex]
The mass of a motorcycle, [tex]m_m=290\ kg[/tex]
The initial velocity of the car,[tex]v_c=30i-10j[/tex]
[tex]|v_c|=\sqrt{30^2+(-10)^2} =31.62\ m/s[/tex]
The initial velocity of the motorcycle,[tex]v_m=10i+10j[/tex]
[tex]|v_m|=\sqrt{10^2+10^2} =14.14\ m/s[/tex]
As they stick together. Let V is the speed. So, using the conservation of momentum,
[tex]m_cv_c+m_mv_m=(m_c+m_m)V\\\\V=\dfrac{m_cv_c+m_mv_m}{(m_c+m_m)}\\\\V=\dfrac{2100\times 31.62+290\times 14.14}{(2100+290)}\\\\V=29.49\ m/s[/tex]
So, the velocity of the stuck together car and the motorcycle after the collision is 29.49 m/s.
gAn optical engineer needs to ensure that the bright fringes from a double-slit are 15.7 mm apart on a detector that is from the slits. If the slits are illuminated with coherent light of wavelength 633 nm, how far apart should the slits be
Answer:
d = 68.5 x 10⁻⁶ m = 68.5 μm
Explanation:
The complete question is as follows:
An optical engineer needs to ensure that the bright fringes from a double-slit are 15.7 mm apart on a detector that is 1.70m from the slits. If the slits are illuminated with coherent light of wavelength 633 nm, how far apart should the slits be?
The answer can be given by using the formula derived from Young's Double Slit Experiment:
[tex]y = \frac{\lambda L}{d}\\\\d =\frac{\lambda L}{y}\\\\[/tex]
where,
d = slit separation = ?
λ = wavelength = 633 nm = 6.33 x 10⁻⁷ m
L = distance from screen (detector) = 1.7 m
y = distance between bright fringes = 15.7 mm = 0.0157 m
Therefore,
[tex]d = \frac{(6.33\ x\ 10^{-7}\ m)(1.7\ m)}{0.0157\ m}\\\\[/tex]
d = 68.5 x 10⁻⁶ m = 68.5 μm
Hannah wants to create a record keeping system to track the inventory needed to efficiently run her lawn and landscape business, such as spare parts, gas cans, string trimmers, etc. Her crew manager will also be using the system. Hannah is considering whether to use Excel or Access. Which one of the following is NOT a benefit of using Access?
a. More data storage
b. Multiuser capability
c. Easier setup
d. Additional reporting features
Answer:
c). Easier setup
Explanation:
As per the question, 'easier setup' cannot be characterized as the advantage of using Access because it comprises of plenty of steps that must be followed in the sequential order to establishing a database or carrying transactions based on time. However, there are plenty of advantages of using Microsoft access like 'enhanced and increased storage of data,' 'hassle free database systems,' 'easy importing of data,' 'highly economical,' 'capability to allow multiple users,' 'extra features for reporting,' and much more. Hence, option c is the correct answer.
what's impulse of
force
Answer:
The impulse experienced by the object equals the change in momentum of the object. In equation form, F.t = m. Δv. In a collision, objects experience an impulse; the impulse causes and is equal to the change in momentum.
In what kind of reaction is water (H20) broken down into hydrogen gas (H2) and oxygen gas (O2)?
A. Combination
B. Decomposition
C. Displacement
D. Combustion
Answer:
Answer is B (Decomposition)
Sorry I really see ur questions but I don't know the answer but next time I will try to answer sorry:(
3. Define 1 standard kilogram?
Answer:
standard kilogram is the SI unit of mass
Answer:
The total mass of platinum-irridum cylinder whose diameter is equal to its height and stored at 0°C in the bureau of weight and measure in France is called 1 standard kilogram
The best and most common way to measure the intensity of a cardiovascular exercise is to determine
O The person's heart rate
O The fatigue level of the person
O Amount of perspiration the person produces
The person's breathing rate
Answer:
the person's heart rate
A CD is spinning on a CD player. In 12 radians, the cd has reached an angular speed of 17 r a d s by accelerating with a constant acceleration of 3 r a d s 2 . What was the initial angular speed of the CD
Answer:
The initial angular speed of the CD is equal to 14.73 rad/s.
Explanation:
Given that,
Angular displacement, [tex]\theta=12\ rad[/tex]
Final angular speed, [tex]\omega_f=17\ rad/s[/tex]
The acceleration of the CD,[tex]\alpha =3\ rad/s^2[/tex]
We need to find the initial angular speed of the CD. Using third equation of kinematics to find it such that,
[tex]\omega_f^2=\omega_i^2+2\alpha \theta\\\\\omega_i^2=\omega_f^2-2\alpha \theta[/tex]
Put all the values,
[tex]\omega_i^2=(17)^2-2\times 3\times 12\\\\\omega_i=\sqrt{217}\\\\\omega_i=14.73\ rad/s[/tex]
So, the initial angular speed of the CD is equal to 14.73 rad/s.
What is the electric field strength between two parallel conducting plates separated by 10 cm and having a potential difference between them of 2000 V?
a.
2000 V/m
b.
200 V/m
c.
20 kV/m
d.
200000 V/m
Answer:
• Potential Difference (V) = 2000 V
• Distance b/w the two parallel plates (d) = 10 cm = 10/100 = 1/10 = 0.1 m
• Electric field (E) = ?
[tex]\implies V = E.d[/tex]
[tex]\implies E = \dfrac{V}{d} [/tex]
[tex]\implies E = \dfrac{2000}{0.1} [/tex]
[tex]\implies E = \dfrac{2000}{ {10}^{ - 1} } [/tex]
[tex]\implies E = 2000 \times {10}^{1} [/tex]
[tex]\implies\bf E = 20000 \:V/m[/tex]
[tex]\implies\bf E = 20\:kV/m[/tex]
Hence, option C) the correct answer.
An inductive circuit contains resistance of 20 ohm and an inductance of 20 H. If an ac voltage of 120 V and frequency 60 Hz is applied to this circuit, the current would be
A 0.0159
A 0.017
A 0.02
A 0.16
Answer:
answer : option (b) 0.016 amp
explanation : resistance of resistor , R = 10 Ω
inductance of inductor , X_LX
L
= 20H
voltage of AC circuit , V = 120volts
frequency, ff =60Hz
so, angular frequency, \omega=2\pi fω=2πf = 2 × π × 60 = 120π rad/s
now, current , i=\frac{V}{\sqrt{R^2+\omega^2L^2}}i=
R
2
+ω
2
L
2
V
= 120/√{10² + (120π)² × 20²}
= 120/√{100 + 14400π² × 400}
after solving this we get, i = 0.016 amp
How does an airpump work?
Explain why it takes much more effort to stop a freight train compared with a car?
Answer:
Train wheels and rails are both made of steel, and the steel-steel friction coefficient is around 0.25. As a result, the stopping time and distance will be three to four times that of a car.
A mass of 5 kg stretches a spring 20 cm. The mass is acted on by an external force of 10 sint4 N (newtons) and moves in a medium that imparts a viscous force of 4 N when the speed of the mass is 2 cm/s. If the mass is set in motion from its equilibrium position with an initial velocity of 7 cm/s.
Required:
Formulate the initial value problem describing the motion of the mass. Assume that g = 9.8 m/s^2.
Answer:Answer:
Initial value problem is:
u'' + 10u' + 98u = (2 sin(t/2) N for u(0) = 0
u'(0) = 0.03m/s
Explanation:
The directions of Fd(t*) and U'(t*) are not specified in the question, so we'll take Fd(t*) to be negative and U'(t*) to be positive. This is due to the fact that the damping factor acts in the direction opposite the direction of the motion of the mass.
M = 5kg; L= 10cm or 0.1m;
F(t) = 10 sin(t/2) N ; Fd(t*) = - 2N
U'(t*) = 4cm/s or 0.04m/s
u(0) = 0
u'(0) = 3cm/s or 0.03m/s
Now, we know that W = KL.
Where K is the spring constant.
And L is the length of extension.
So, k = W/L
W= mg = 5 x 9.81 = 49.05N
So,k = 49.05/0.1 = 490.5kg/s^(2)
Now from spring damping, we know that; Fd(t*) = - γu'(t*)
Where,γ = damping coefficient
So, γ = - Fd(t*)/u'(t*)
So, γ = 2/0.04 = 50 Ns/m
Therefore, the initial value problem which describes the motion of the mass is;
5u'' + 50u' + 490u = (10 sin(t/2) N
Divide each term by 5 to give;
u'' + 10u' + 98u = (2 sin(t/2) N for u(0) = 0
u'(0) = 0.03m/s
Explanation:
A soap bubble was slowly enlarged from a radius of 4cm to 6cm. The amount of work necessary for enlargement was 1.5 x 10^-4 joules. Calculate the surface tension of the soap bubble.
Answer:
[tex]T=3*10^-3 N/m[/tex]
Explanation:
From the question we are told that:
Radius :
[tex]R_1=4=>0.04\\\\R_2=6=>0.06[/tex]
Work [tex]W=1.5 * 10^{-4}[/tex]
Generally the equation for Work done is mathematically given by
[tex]W=TdA[/tex]
Where
[tex]dA=A_2-A_1\\\\dA=(2 \pi r_2^2)(2 \pi r_1^2)[/tex]
[tex]dA=8 \pi*(r_2^2-r_1^2)\\\\dA=8*3.142*(0.06^2-0.04^2)[/tex]
[tex]dA=0.050m^2[/tex]
Therefore
[tex]W=TdA[/tex]
[tex]T=\frac{1.5 * 10^{-4}}{0.05m^2}[/tex]
[tex]T=3*10^-3 N/m[/tex]
5 How does air get polluted?
Answer:
Explanation:
- Pollution from cars
- Burning fossil fuels
what is the gravitational potential in a field produced by an object of mass 2000 kg at a distance of 10 km
Answer:
196 megajoules
Explanation:
Since you are talking about the gravitational potential I am assuming 10km is the height of the object in free fall.
PEg = mgh 2000kg×9.8m/s²×10000m = 196 megajoules
The barometer of a mountain hiker reads 980 mbars at the beginning of a hiking trip and 790 mbars at the end. Neglecting the effect of altitude on local gravitational acceleration, determine the vertical distance climbed. A
Complete Question
The barometer of a mountain hiker reads 980 mbars at the beginning of a hiking trip and 790 mbars at the end. Neglecting the effect of altitude on local gravitational acceleration, determine the vertical distance climbed. Assume an average air density of 1.20kg/m^2
Answer:
[tex]h=1614m[/tex]
Explanation:
From the question we are told that:
Initial Pressure [tex]P_1=980mbar=>98000Pa[/tex]
Final Pressure [tex]P_2=790mbar=>79000Pa[/tex]
Density [tex]\rho=1.20kg/m^2[/tex]
Generally the equation for Height climbed is mathematically given by
[tex]h=\frac{P_1-P_2}{\rho*g}[/tex]
[tex]h=\frac{P_1-P_2}{1.20*9.81}[/tex]
[tex]h=1614m[/tex]
Two carts are involved in an inelastic collision. Cart A with mass 0.900 kg hits cart B with mass 0.550 kg (initially at rest). The two carts stick together after the collision and continue to move along together. Cart A has an initial velocity of 0.29 m/s.
a. What is the final velocity of the two-cart system?
b. What is the initial kinetic energy of cart A?
c. What is the initial kinetic energy of cart B?
d. What is the final kinetic energy of the system?
e. Is kinetic energy conserved for inelastic collisions?
f. Is momentum conserved for inelastic collisions?
Answer:
a) v = 0.18 m / s, b) K₀ₐ = 0.0378 J, c) K_{ob}= 0, d) K = 0.02349 J,
Explanation:
a) For this exercise we must define a system formed by the two cars, so that the forces during the collision are internal and the moment is conserved
initial instant. Before the hole
p₀ = ma v₀ₐ
final intnate. After the crash
p_f = (mₐ + m_b) v
the moment is preserved
p₀ = p_f
mₐ v₀ₐ = (mₐ + m_b) v
v = [tex]\frac{m_a}{m_a+m_b} \ v_{oa}[/tex]
let's calculate
v = [tex]\frac{0.900}{0.900+0.550} \ 0.29[/tex]
v = 0.18 m / s
in the same direction of the movement of carriage A
b) the initial kinetic energy car A
K₀ₐ = ½ m v₀ₐ²
K₀ₐ = ½ 0.900 0.29²
K₀ₐ = 0.0378 J
c) kinetic energy of carriage B
k_{ob} = 0
because the car is stopped
d) the kinetic energy of the system
K = ½ (mₐ + m_b) v²
K = ½ (0.900 + 0.550) 0.18²
K = 0.02349 J
E) we see that part of the kinetic energy is lost, therefore the scientific reeling is not conserved in inelastic collisions
F) and momentum is conserved since it is equal to the variation of the moment and this is conserved in all collisions
A vehicle is used to transport material down a straight aisle. The max acceleration of the vehicle is 1 m/s/s and the max speed of the vehicle is 5m/s. The vehicle starts at the beginning of the aisle. How long does it take to move down the aisle and come to a stop at the other end if:
a) the aisle is 100 meters long?
b) the aisle is 9 meters long?
Answer:
(a) 14.14 s
(b) 4.24 s
Explanation:
maximum acceleration, a = 1 m/s^2
maximum speed, v = 5 m/s
initial speed, u = 0 m/s
(a) distance, s = 100 m
Let the time is t.
Use second equation of motion
[tex]s = u t 0.5 at^2\\\\100 = 0 + 0.5 \times 1 \times t^2\\\\t = 14.14 s[/tex]
(b) distance, s = 9 m
Let the time is t'.
Use second equation of motion
[tex]s = u t + 0.5 at^2\\\\9= 0 + 0.5 \times 1 \times t'^2\\\\t' = 4.24 s[/tex]
The upward normal force exerted by the floor is 710 N on an elevator passenger who weighs 720 N . You may want to review (Pages 107 - 110) . For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Weighing yourself in an elevator. Part A What is the reaction force to the upward normal force exerted by the floor
Answer:
If the person is to remain the floor the reaction force will be equal to the normal force exerted by the floor.
F(normal) - F(reaction) = 0
That means the person is not moving with respect to the elevator.
Expanding the applied forces we have:
Fw - Fn = 720 - 710 = 10 N where the positive direction is chosen as down
Fw is the weight of the person and Fn the force exerted on the person by the elevator,
The acceleration of the person the becomes F = m a = m * 10 N and will be downward agreeing with our choice of coordinate axes.
a fixed mass of gas occupies a volume of 1000 CM3 at 0 degree celsius if it is heated at constant pressure of 100 degree celsius calculate the new volume
Answer:
P V = N R T ideal gas equation
V1 = k * T1 if P is constant and also N and R will be constant
V2 = k * T2 where k is some constant
Or V2 = (T2 / T1) * V1 also known as "Charles Law" for expansion at
constant pressure
V2 = (373 / 273) * 1000 cm^3 = 1366 cm^3 where T is absolute temperature
What process provides the sun with its energy
Answer:
nuclear fusion
The sun generates energy from a process called nuclear fusion. During nuclear fusion, the high pressure and temperature in the sun's core cause nuclei to separate from their electrons. Hydrogen nuclei fuse to form one helium atom. During the fusion process, radiant energy is released.Answer:
nuclear fusion
Explanation:
The sun generates energy from a process called nuclear fusion. During nuclear fusion, the high pressure and temperature in the sun's core cause nuclei to separate from their electrons. Hydrogen nuclei fuse to form one helium atom.
your neighbour is throttling his recent bought motorbike to show off. the sound intensity measured at your window 16m away is 0.25W/m^2. what is the sound intensity level in dB at your friend's house, a distance of 28m away from the noisy bike?
Answer:
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Find the ratio of the Coulomb electric force Fe to the gravitational force Fo between two
electrons in vacuum.
Answer:
thus the coulomb force is F – 8.19x10-8N. this is also an attractive force, although it is traditionally shown as positive since gravitational force is always attractive. the ratio of the magnitude of the electrostatic force to gravitational force in this case is,thus,FFG – 2.27x1039 F F G – 2.27x 10 39.
Two people, who have the same mass, throw two different objects at the same velocity. If the first object is heavier than the second, compare the velocities gained by the two people as a result of recoil.
a. The first person will gain more velocity as a result of recoll.
b. The second person will gain more velocity as a result of recoll.
c. Both people will gain the same velocity as a result of recoll.
d. The velocity of both people will be zero as a result of recoil
Answer:
The first person will gain more velocity as a result of recoil.
Explanation:
Let us recall that from Newton's third law of motion, action and reaction are equation and opposite. A consequence of this law is the proposition that ''momentum can neither be created nor destroyed.''
Hence, when two people who have the same mass, throw two different objects at the same velocity but the first object is heavier than the second, the first object possesses greater momentum than the second object hence the first person will gain more velocity as a result of recoil.
Which formula below correctly states Coulomb's Law?
A. F = kqq/r2
B. F = kqq/r
C. F = qq/kr2
D. F = kr2/qq
[tex]A. \: \: \: \: F = kqq/r^ 2 \\B. \: \: \: \: F = kqq/r \\C. \: \: \: \: F = qq/kr^ 2 \\D. \: \: \: \: F = kr^2 /qq \\ [/tex]
ANSWER:-F is directly proportional to the product of the charges
[tex]F∝qq[/tex]
F is inversely proportional to the square of the distance between them
[tex]F∝ \frac{1}{ {r}^{2} } [/tex]
from above 2 equation:-
we get:-
[tex]F∝ \frac{qq}{ {r}^{2} } [/tex]
To remove proportionality sign we use constant for this case we r using constant k
[tex]F = \frac{Kqq}{ {r}^{2} } [/tex]
So your answer is :-
OPTION A.
[tex]F = \frac{Kqq}{ {r}^{2} } [/tex]
A frictionless spring with a 9-kg mass can be held stretched 1.8 meters beyond its natural length by a force of 80 newtons. If the spring begins at its equilibrium position, but a push gives it an initial velocity of 1.5 m/sec, find the position of the mass after tt seconds. meters
Answer:
the required solution is; x(t) = 0.675sin( 2.222t )
Explanation:
Given the data in the question;
Using both Newton's and Hooke's law;
m[tex]x^{ff[/tex] + k[tex]x[/tex] = 0, [tex]x[/tex](0) = 0, [tex]x^f[/tex](0) = 1.5
given that mass m = 9 kg
[tex]x[/tex] = 1.8 m
k is F / x
hence
k = F / x
given that, F = 80 N
we substitute
k = 80 / 1.8
k = 44.44
so
m[tex]x^{ff[/tex] + k[tex]x[/tex] = 0,
we input
9[tex]x^{ff[/tex] + 44.44[tex]x[/tex] = 0,
[tex]x^{ff[/tex] + 4.9377[tex]x[/tex] = 0
so auxiliary equation is,
r² + 4.9377 = 0
r² = -4.9377
r = √-4.9377
r = ±2.222i
hence, the solution will be;
x(t) = A×cos( 2.222t ) + B×sin( 2.222t )
⇒ [tex]x^t[/tex](t) = -2.222Asin( 2.222t ) + 2.222Bcos( 2.222t )
using initial conditions
x(0) = 0
⇒ 0 = A
[tex]x^t[/tex](t) = 1.5
1.5 = 2.222B
so
B = 1.5 / 2.222 = 0.675
Hence, the required solution is; x(t) = 0.675sin( 2.222t )
An astronaut weighs 202 lb. What is his weight in newtons?
question 1+1677-789909
Answer:
your answer is -788231
Explanation:
1+1677=1678
1678-789909=-788231
What is the maximum wavelength, in nm, of light that can eject an electron from a metal with Φ =4.50 x 10–19 J?
[tex]4.4×10^{-7}\:\text{m}[/tex]
Explanation:
The minimum energy needed to kick out an electron from a metal's surface is when the energy of the incident radiation is equal to the metal's work function [tex]\phi[/tex]:
[tex]E = h\nu - \phi = \dfrac{hc}{\lambda} - \phi = 0[/tex]
or
[tex]\dfrac{hc}{\lambda} = \phi[/tex]
Solving for the wavelength [tex]\lambda[/tex],
[tex]\lambda = \dfrac{hc}{\phi}[/tex]
[tex]\:\:\:\:\:=\dfrac{(6.62×10^{-34}\:\text{J-s})(3.0×10^8\:\text{m/s})}{4.5×10^{-19}\:\text{J}}[/tex]
[tex]\:\:\:\:\:= 4.4×10^{-7}\:\text{m}[/tex]
Note that as the radiation's wavelength increases, its energy decreases. So a radiation whose wavelength is longer than this maximum will lose its ability to kick out an electron from this metal.
The maximum wavelength, in nm, of light that can eject an electron from the metal, given the data is 441.73 nm.
To find the wavelength, the given values are,
Energy (E) = 4.50×10¯¹⁹ J
What is wavelength?The distance between two consecutive crests and troughs is called the wavelength of a wave.
Here, for the wavelength,
Energy (E) = 4.50×10¯¹⁹ J
Planck's constant (h) = 6.626×10¯³⁴ Js
Speed of light (v) = 3×10⁸ m/s
The wavelength of the light can be obtained as illustrated below:
E = hv / λ
Cross multiply λ,
E × λ = hv
Divide both sides by E,
λ = hv / E
Substituting all the values,
λ = (6.626×10¯³⁴ × 3×10⁸) / 4.50×10¯¹⁹
λ = 0.000000441733 m
λ = 441.73nm
λ - The maximum wavelength of light.
Thus, the wavelength of the light that can eject an electron from the metal is 441.73 nm
Learn more about wavelength,
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