Answer:
w = [tex]\sqrt{\frac{2gy}{r^2 + \frac{1}{2} R^2 } }[/tex]
Explanation:
For this exercise let's start by applying Newton's second law to the mass with the string
W - T = m a
In this case, as the system is going down, we will assume the vertical directional down as positive.
T = W - m a
Now we apply Newton's second law for rotational motion to the pulley of radius r. We will assume the positive counterclockwise rotations
∑ τ = I α
T r = I α
the moment of inertia of the disk is
I = ½ M R²
angular and linear acceleration are related
a = α r
we substitute
T r = (½ m R²) (a / r)
T = ½ m ([tex]\frac{R}{r}[/tex] )² a
we write our two equations
T = W - m a
T = ½ m ([tex]\frac{R}{r}[/tex] )² a
we solve the system of equations
W - m a = ½ m (\frac{R}{r} )² a
m g = m a [ 1 + ½ (\frac{R}{r} )² ]
a = [tex]\frac{g}{ 1 + \frac{1}{2} (\frac{R}{r})^2 }[/tex]
this acceleration is constant throughout the trajectory, so with the angular and lineal kinematics relations
w² = w₀² + 2 α θ
v² = v₀² + 2 a y
as the system is released its initial angular velocity is zero
w² = 0 + 2 α θ
v² = 0 + 2 a y
we look for the angular acceleration
a =α r
α = a / r
α = [tex]\frac{g}{r (1 + \frac{1}{2} (\frac{R}{r})^2 }[/tex]
we look for the angle, remember that they must be measured in radians
θ = s / r
in this case we approximate the arc to the distance
s = y
θ = y / r
we substitute
w = [tex]\sqrt{2 \frac{g}{ r( \frac{1}{2} (\frac{R}{r})^2 } \frac{y}{r} }[/tex]
w = [tex]\sqrt{\frac{2gy}{r^2 + \frac{1}{2} R^2 } }[/tex]
for the simple case where r = R
w = [tex]\sqrt{ \frac{2gy}{ \frac{3}{2} R^2 } }[/tex]
w = [tex]\sqrt{ \frac{4}{3} \frac{gy}{R^2} }[/tex]
A box of weight 20N rests on a horizontal floor. A maximum horizontal force of 6N is required to move the box along the floor .If the weight of 10N is added to the box , find the minimum horizontal force required to move the box.
calculate the speed of atrain
that travels 540 meters in 30
seconds?
Answer:
The train is traveling 18 meters per second.
Explanation:
540/30 = 18
To check your answer do 18 * 30 and it equals 540
How is the L-section filter useful at both low and high frequencies?
Answer: High pass filters, and in particular LC high pass filters are used in many RF applications where they block the lower frequencies and allow through higher frequency signals. Typically LC filters are used for the higher radio frequencies where active filters are not so manageable, and inductors more appropriate.
Answer:
high pass filters and in particular LC high pass filter are used in many RF application where they block the lower frequencies and allow through higher frequency signals. Typically LC filters are used for the higher radio frequencies where active filters are not so manageable and indicators more appropriate
What is quantum physics?
Answer:
A fundamental theory that provides a description of the physical properties of nature at the scale of atoms and subatomic particles.
Explanation:
A 5- kg object experiences forces as shown in the diagram. Which statement best describes the motion of the object
Answer: D. The object would have an acceleration of 6 m/s/s to the right.
Explanation:
I got it right on USA test prep
o reduce the drag coefficient and thus to improve the fuel efficiency, the frontal area of a car is to be reduced. Determine the amount of fuel and money saved per year as a result of reducing the frontal area from 18 to 14 ft2. Assume the car is driven 12,000 mi a year at an average speed of 55 mi/h. Take the density and price of gasoline to be 50 lbm/ft3 and $3.10/gal, respectively; the density of air to be 0.075 lbm/ft3, the heating value of gasoline to be 20,000 Btu/lbm; and the overall efficiency of the engine to be 30 percent. Take the drag coefficient as CD
Complete question
To reduce the drag coefficient and thus to improve the fuel efficiency, the frontal area of a car is to be reduced. Determine the amount of fuel and money saved per year as a result of reducing the frontal area from 18 to 14 ft2. Assume the car is driven 12,000 mi a year at an average speed of 55 mi/h. Take the density and price of gasoline to be 50 lbm/ft3 and $3.10/gal, respectively; the density of air to be 0.075 lbm/ft3, the heating value of gasoline to be 20,000 Btu/lbm; and the overall efficiency of the engine to be 30 percent. Take the drag coefficient as CD=0.3 for a passenger car.
Answer:
22.22%
$57
Explanation:
From the question we are told that
Initial area of frontal area [tex]a_1=18ft^2[/tex]
Final area of frontal area [tex]a_2=14ft^2[/tex]
Distance covered a year [tex]D=12000mile[/tex]
Average speed a year [tex]V_{avg}=55mile/h[/tex]
Density [tex]\rho=50 lbm/ft3[/tex]
Price [tex]P= $3.10/gal[/tex]
Density of air [tex]\rho_{air} 0.075 lbm/ft3[/tex]
Heating value of gasoline [tex]Q=20,000 Btu/lbm[/tex]
Efficiency [tex]\eta=30\%[/tex]
Drag coefficient [tex]CD=0.3[/tex]
[tex]\triangle A=18-14ft^2=4ft^2[/tex]
Generally the equation for drag force [tex]C_D[/tex] is mathematically given as
[tex]F_D=\frac{C_DAPV^2}{2}[/tex]
[tex]F_D=\frac{0.3*18*0.075*(80.685^2)*A}{2}[/tex]
[tex]F_D=73.24Alb[/tex]
where [tex]v=55mil/h*1.467=80.685ft/s[/tex]
Generally the equation for work done W is mathematically given as[tex]W=F_D*L[/tex]
where [tex]L=12000mile*5280[/tex]
[tex]L=63360000[/tex]
[tex]W=73.24A*63360000[/tex]
[tex]W=4.6*10^9A[/tex]
Generally the equation for overall efficiency [tex]\eta[/tex] is mathematically given as
where
[tex]W_{req}=required\ gasoline\ power\ efficiency[/tex]
[tex]\eta=\frac{W}{W_{req}}[/tex]
[tex]W_{req}=\frac{W}{\eta}[/tex]
[tex]W_{req}=\frac{4.6*10^9}{0.3}[/tex]
[tex]W_{req}=1.55*10^{10}A[/tex]
Generally the equation for reduction fee with change in frontal area [tex]\triangle M[/tex] is mathematically given as
[tex]\triangle M =\triangle Vgasoline*cost[/tex]
Where
[tex]\triangle Vgasoline= volume\ reduction\ of\ gasoline[/tex]
[tex]\triangle Vgasoline=\frac{E_{req}}{H*P}[/tex]
[tex]\triangle Vgasoline=\frac{1.55*10^{10}A}{20000*778.169*32.2*50}[/tex]
if
[tex]20000btu/ibm=20000*778.169*32.2(1bm.ft^2/s)[/tex]
[tex]\triangle Vgasoline=\frac{1.55*10^{10}A}{20000*778.169*32.2*50}[/tex]
[tex]\triangle Vgasoline=0.61859A[/tex]
Therefore
[tex]\triangle M =0.61859A*3.10[/tex]
if [tex]1ft^2=7.48gal[/tex]
[tex]\triangle M =0.61859(4)*3.10*7.48[/tex]
[tex]\triangle M = \$ 57.671[/tex]
Generally the equation for reduction of fuel [tex]F_r[/tex]is mathematically given as
[tex]F_r=\frac{\triangle A}{\triangle i}*100[/tex]
where
[tex]\triangle i=18ft^2[/tex]
[tex]F_r=\frac{4}{18}*100[/tex]
Fuel reduction price by reducing front area is 22.22%
Money saved per year is $57
is ice a fluid at room temperature?
Answer:
Ice is the solid state of water, a normally liquid substance that freezes to the solid state at temperatures of 0 °C (32 °F) or lower and expands to the gaseous state at temperatures of 100 °C (212 °F) or higher.
Explanation:
The vector matrix [6 -2] is rotated at different angles. Match the angles of rotation with the vector matrices they produce.
Answer:
Hello your question is incomplete hence I will give you a general answer as regards rotation of vector matrix assuming angle of rotation = [tex]\frac{\pi }{4}[/tex]
answer :
angle of rotation = [tex]\frac{\pi }{4}[/tex]
vector matrix produced = attached below
Explanation:
lets assume the vector matrix [ 6, -2 ] is rotated clockwise by an angle of [tex]\frac{\pi }{4}[/tex]
The resultant matrix = attached below
Result of the rotation = attached below
attached below is the detailed solution
Answer: I got it right on Edmentum
Explanation: Answers attached below
what is energy and types of energy
You have probably noticed that carrying a person in a pool of water is much easier than carrying a person through air. To understand why, find the buoyant force exerted by air and by water on the person. Assume the average volume of a person is 0.092 m3, and that the person is submerged in air and water respectively. (Give the magnitude.)
air: ________
water :_______
Answer:
The answer is "0.91238 and 744.8"
Explanation:
In this scenario it is easier to take a person to the water-pool than to transport the people in the air, as the person's strength is increased by water upwards:
[tex]f_b \to m \to mg =person \\\\F_B \ in\ air = v\ & air\ g \\\\[/tex]
[tex]=0.076 \times 1.225 \times 9.8 \\\\ =0.91238 \ N\\\\[/tex]
[tex]F_B \ in \ water = v \& water \ g \\\\[/tex]
[tex]=0.076 \times 1000 \times 9.8\\\\= 744.8 \ N\\[/tex]
A pendulum is constructed from a heavy metal rod and a metal disk, both of uniform mass density. The center of the disk is bolted to one end of the rod, and the pendulum hangs from the other end of the rod. The rod has a mass of =1.0 kg and a length of =49.8 cm. The disk has a mass of =4.0 kg and a radius of =24.9 cm. The acceleration due to gravity is =9.8 m/s2.
The pendulum is held with the rod horizontal and then released. What is the magnitude of its angular acceleration at the moment of release?
The magnitude of the angular acceleration of the pendulum at the moment of release is; α = 18.45 rad/s²
We are given;
Mass of rod; m = 1 kg
Length of rod; L = 49.8 cm = 0.498 m
Mass of Disk; M = 4 kg
Radius of disk; r = 24.9 cm = 0.249 m
Let us first calculate the torque acting from the formula;
τ = mg(L/2) + MgL
Thus;
τ = (1 × 9.8 × (0.498/2)) + (4 × 9.8 × 0.498)
τ = 21.96 N.m
Using parallel axis theorem, we can find the moment of inertia about the given axis as;
I = (mL²/3) + ½MR² + ML²
Plugging in the relevant values gives;
I = (1 * 0.498²/3) + ½(4 * 0.249²) + (4 * 0.498²)
I = 1.19 kg.m²
The angular acceleration is given by the formula;
α = I/τ
α = 21.96/1.19
α = 18.45 rad/s²
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Q7. A 2kg ball is released from a height of 20m.
What is it velocity when its height has decreased to 5
m?
Answer:
Given,
Mass, m = 2kg
Height or distance, s = 20m
Initial velocity, u = 0m/s
Acceleration due to gravity, g = 10m/s (It is 9.8m/s but can be assumed 10m/s for simplifying calculations)
(Because the object is is just dropped)
Final velocity, v = ?
Solution
v^2 = u^2 + 2as (u^2 means u raised to power 2)
=> v^2 = 0^2 + 2*10*20
=> v^2 = 400
=> v = 20
Thus the velocity just before the body strikes the ground will be 20m/s.
5. During a heat transfer investigation, students filled two cups with water. One cup contains 100mL of cold water while the other contains 100 mL of hot water.
A metal heat wire is placed inside the water of both cups and thermometers are attached to each cup. Which of the following BEST explains how the heat is transferred? Cold Water Hot Water.
A. This investigation would not result in any heat being transferred.
B. Convection, because the metal wire was heated through convection currents.
C. Radiation, because the metal wire was heated by electromagnetic waves.
D. Conduction, because the metal wire was in direct contact with water in both containers.
Answer:
D.Conduction, because the metal wire was in direct contact with water in both containers
Conduction, because the metal wire was in direct contact with water in both containers. Option D is correct.
Given that,
Students filled two cups with water. One cup contains 100mL of cold water while the other has 100 mL of hot water. A metal heat wire is placed inside the water of both cups and thermometers are attached to each cup.
It is to be identified, the system contains which type of heat transfer between the cups
Heat transfer is the process, in a thermodynamic system, when an object at a higher temperature is placed with an object at has a lower temperature, after some time the system attains equilibrium because heat flows from higher temperature to lower temperature.
In the given question,
Cups, that are connected through a metal wire, one is hot and the other is cold, Principal of conduction state that when there is a system of connected bodies the heat flows throughout the connected system till the thermal equilibrium attain. Implies heat flow from hot cup to cold cup through the wire through conduction heat transfer.
Thus, Conduction, because the metal wire was in direct contact with water in both containers. Option D is correct.
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Which explanation best describes a wave?
A.
a disturbance that travels through a medium with a transfer of energy and matter
B.
a disturbance that travels through a medium without a transfer of energy and matter
C.
a disturbance that travels through a medium with a transfer of energy and without a transfer of matter
D.
a disturbance that travels through a medium with a transfer of matter and without a transfer of energy
E.
a disturbance that travels only in the absence of a material medium
Answer:
D
Explanation:
A disturbance that travels through a medium with a transfer of matter and without a transfer of energy best describes a wave. Option D best describes a wave.
What is wave?A wave is a phenomenon that flows across a material medium without leaving any lasting mark. Mechanical or electromagnetic waves can be used to classify it. Transverse and longitudinal are the two main forms.
Wave motion that is parallel to the wave direction is described as longitudinal wave.
A wave is a disturbance that moves across a medium with a transfer of matter , but not an energy transfer.
A disturbance that travels through a medium with a transfer of matter and without a transfer of energy best describes a wave.
Hence, option D best describes a wave
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Can anyone help please
Answer:
Option C, the current is constant through the wire.
Explanation:
Ok, so we know that as larger cross-section we have, smaller resistance, so makes sense to think that the current will be larger in the first piece of wire.
But now let's think in a simpler case.
Suppose that in the image we see pipes, and through these pipes, there is water flowing.
You would say that the water flow in WX is larger than the current in XY?
No, it can´t be, the volume of water that leaves WX in a lapse of time Δt, must be the exact same volume of water that enters XY in that lapse of time, then the water flow is constant.
The only thing that can happen is that the velocity at which the water moves in WX is smaller than the velocity at which the water moves in the other parts.
The same thing happens here, the current will be constant, and the thing that changes is the velocity at which the electrons flow in each part of the wire.
So if you actually had a wire like this, you would see that the thinner parts heat a lot more than the others, and this happens because the electrons in those parts have a lot more kinetic energy.
The correct graph is C.
Archerfish are tropical fish that hunt by shooting drops of water from their mouths at insects above the water’s surface to knock them into the water, where the fish can eat them. A 65-g fish at rest just at the surface of the water can expel a 0.30-g drop of water in a short burst of 5.0 ms. High-speed measurements show that the water has a speed of 2.5 m/s just after the archerfish expels it. What is the average force the fish exerts on the drop of water?
(a) 0.00015 N;
(b) 0.00075 N;
(c) 0.075 N;
(d) 0.15 N.
Answer:
(d) 0.15 N
Explanation:
mass of the fish, m₁ = 65 g = 0.065 kg
initial velocity of the fish, u₁ = 0
mass of water expelled by the fish, m₂ = 0.30 g = 0.0003 kg
time during which the water was expelled, t = 5.0 ms = 5.0 x 10⁻³ s
velocity of the water, v = 2.5 m/s
The magnitude of force of the exerted water is equal to the magnitude of force the fish exerted on the water.
The magnitude of force of the exerted water is calculated as follows;
[tex]F = ma = m\frac{v}{t} \\\\F = \frac{mv}{t} \\\\F = \frac{m_2 \ \times \ v}{t} \\\\F = \frac{0.0003 \ \times \ 2.5}{5 \times 10^{-3}} \\\\F = 0.15 \ N[/tex]
The correct option is D.
Therefore, the average force the fish exerts on the drop of water is 0.15 N.
7. A 3.0 kg object travels vertically at a constant
velocity of 1.5 m/s. What is the increase in
gravitational potential energy after 5.0 s?
Answer:
220.7
Explanation:
distance traveled is 1.5*5=7.5m
PE gain is MGH=3*9.81*7.5=220.7
Which statement is true for two pieces of iron at the same temperature ? A. The total kinetic energy of their particles is equal
The complete options are;
A. The average kinetic energy of their particles is the same.
B. The total kinetic energy of their particles is equal.
C. Heat flows from the larger object to the smaller object.
D. Heat flows from the object with higher potential energy to the object with lower potential energy.
Answer:
Explanation:
From the relationship between average kinetic energy and temperature, we have the formula;
E_k = (3/2)kT
Where;
k is a constant known as boltzmann constant.
T is known as temperature
We can see that at the same temperature (T), kinetic energy will remain the same because from the formula, E_k depends km only the temperature.
Thus, average kinetic energy of their particles saying that.
Suppose you take a whole apple pie (because pie is better than cake!!) How do the shape, taste, and the weight of the whole pie compare with the shape, taste, and weight of all the slices together?
Answer:
I ATE APPLE PIE YESTERDAY
Explanation:
528 nm light passes through a single slit. the second (m=2) diffraction minimum occurs at an angle of 3.48 degrees. what is the width of the slit
Answer:
1.74
Explanation:
right on acellus
Answer:
1.74
Explanation:
acellus
I WILL REPORT YOU IF YOU ANSWER WITH LINK!!! WILL GIVE BRAINLIEST
You have two identical bowling balls that are 1.00 m apart as measured from their centers. There is an attractive force of gravity between them due to their mass. When a net charge of +0.40 nC is placed on each bowling ball, the force exerted by the electrostatic forces exactly balances the force of gravity on the bowling balls resulting in a net charge of zero. The formula for the electrostatic force is similar to the formula for the gravitational force. There is a constant that is multiplied by the magnitude of each of the two charges and divided by the square of the distance between them. What two conclusions can you draw from this information?
CHOOSE 2 ANSWERS
Answer:
I think is is
Explanation:
B and C why because i have a gut feeling
PLEASE HELP
A problem says a plane is accelerating
3.42 m/s2 northeast. Which one of these
tables includes that information correctly?
Answer:
The answer is C, I just guessed and got it right lol
Explanation:
5.
What is gravity?
a) A force
D b) Energy
c) A push
d) All of them
science
A). force
hope it helps and your day will be full of happiness
We can see stars like the Sun because they
Answer:
are nearby and bright i hope this helps
10 You are given the following list of vo-
lumes: 0.45 m3; 375 cm3; 75 cL; 0.6 dm3.
a. Express all the volumes of the list in
liters.
b. Arrange these volumes in a descending
order.
Volumes can be transfered to liters only when their measurement units are dm³. a) Which means that: 0.45m³=450dm³ you move the decimal place three places to the right because m³ is larger measurement unit than dm³. 375 cm³ = 0.375 dm³; 75cl = 0.75l because of the prefix centi. 0.6dm³ = 0.6 dm³
So it will be 450l; 0.375l; 0.75l; 0.6l
b) 450l>0.75l>0.6l>0.375l
0.45m³>75cl>0.6dm³>375cm³
I hope i didn't make a mistake, but it would be good if somebody else answered too, so you can compare the answers and see if i made a mistake
The given volumes in liter will be 450 L, 0.375 L, 0.75 L, 0.6 L and the arrangement in descending order will be 450 L > 0.75 L > 0.6 L > 0.37 L .
What is Volume?Every three-dimensional item takes up space in some way. The volume of this area is what is used to describe it. The area covered within an entity's three-dimensional bounds is referred to as its volume. The object's size is another name for it.
As per the given information in the question,
a.
The given volume in a meter cube is 0.45.
Unit conversion:
1 m³ = 1000 L
So, 0.45 m³ = 0.45 × 1000
= 450 L
The given volume in a centimeter cube is 375.
Unit conversion:
1 cm³ = 0.001 L
375 cm³ = 0.001 × 375
= 0.375 L.
The given volume in a centiliter cube is 75.
Unit conversion:
1 cl³ = 0.01 L
75 cl³ = 75 × 100
= 0.75 L
The given volume in the decimeter cube is 0.6.
1 dm³ = 1 L
0.6 dm³ = 0.6 L
b.
So, the volumes in descending order will be,
450 L > 0.75 L > 0.6 L > 0.37 L or,
0.45 m³ > 75 cl³ > 0.6 dm³ > 375 cm³
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What 2 environments once existed where the Grand Canyon is located today?
The entire park area is considered to be a semi-arid desert, but distinct habitats are located at different elevations along the 8,000-foot elevation gradient. Near the Colorado River, riparian vegetation and sandy beaches prevail.
If a gas turned into a solid without going through the liquid state and how do you reverse it?
Answer:
put it in a volcano
Explanation:
After your school's team wins the regional championship, students go to the dorm roof and start setting off fireworks rockets. The rockets explode high in the air and the sound travels out uniformly in all directions. If the sound intensity is 1.67 10-6 W/m2 at a distance of 233 m from the explosion, at what distance from the explosion is the sound intensity half this value
Answer:
the distance is 315.3696 m
Explanation:
The computation of the distance is given below:
Given that
Sound intensity = 1.67 × 10^-6 W/m^2
And, the distance = 233 m
Now as we know that
Power = Intensity × surface area
1.67 × 10^-6 × 4π(233)^2 = 1.67 × 10^-6 ÷ 2× 4π × d^2
d^2 = 2 × (223)^2
= √2 × 223
= 315.3696 m
Hence, the distance is 315.3696 m
A basketball is at rest on the floor. It is heated with a Bunsen burner to make it warmer. A student argues
that the thermal energy in the basketball could be converted to kinetic energy and the basketball will
spontaneously move upwards. This claim violates which law of nature?
Answer:
Newton's first law of motion - The law of inertia
Explanation:
The student's claim violates Newton's first law of motion which states that a body will continue in its state of rest or uniform motion except a force is applied to change that state of rest or uniform motion.
In the case of the student, no external force is applied to the basketball, so as to change its inertia, so it continues to stay in the same position. But, the student assumes that the kinetic energy of the ball will change as its thermal energy can be converted to kinetic energy.
This is incorrect because, the thermal energy only raises the temperature of the basketball and thus the energy of the molecules of the ball, it cannot cause the kinetic energy of the basketball to change since it applies NO FORCE to be basketball so as to change its inertia.
PLEASE HELP ME IN THE QUESTION !!
a. 75 kg, The mass of an object is the amount of matter that constitutes that object and is independent of the acceleration of gravity and is constant under any circumstances.
_________________________________
b. Weight = mass × gravity acceleration
♡ On the Earth : Weight = 75 × 10
Weight = 750 N
♡ On the Venus : Weight = 75 × 8.87
Weight = 665.25 N
