Answer:
a) The kinetic energy of the particle at any time t is [tex]K = 50+120\cdot t^{2}+72\cdot t^{4}[/tex].
b) The acceleration of the particle at time t is [tex]a= 12\cdot t[/tex]. The force acting on the particle at time t is [tex]F = 48\cdot t[/tex].
c) The power being delivered to the particle at time t is [tex]\dot W = 240\cdot t +288\cdot t^{3}[/tex].
d) The work done on the particle in the interval t = 0 to t = 5 is 48000 joules.
Explanation:
a) The kinetic energy of the particle is entirely translational, whose formula is:
[tex]K = \frac{1}{2}\cdot m \cdot v^{2}[/tex] (1)
Where:
[tex]K[/tex] - Translational kinetic energy, measured in joules.
[tex]m[/tex] - Mass of the particle, measured in kilograms.
[tex]v[/tex] - Velocity of the particle, measured in meters per second.
The velocity of the particle is the rate of change of the position of the particle in time, that is:
[tex]v = 5+6\cdot t^{2}[/tex] (2)
Where [tex]t[/tex] is the time, measured in seconds.
By substituting on (1), we have the following expression: ([tex]m = 4\,kg[/tex])
[tex]K = 2\cdot (5+6\cdot t^{2})^{2}[/tex]
[tex]K = 2\cdot (25+60\cdot t^{2} +36\cdot t^{4})[/tex]
[tex]K = 50+120\cdot t^{2}+72\cdot t^{4}[/tex]
The kinetic energy of the particle at any time t is [tex]K = 50+120\cdot t^{2}+72\cdot t^{4}[/tex].
b) The acceleration of the particle is the rate of change of the velocity of the particle in time, that is:
[tex]a= 12\cdot t[/tex] (3)
Where [tex]a[/tex] is the acceleration of the particle, measured in meters per square second.
The acceleration of the particle at time t is [tex]a= 12\cdot t[/tex].
The force is obtained by multiplying (3) by the mass of the particle. That is to say: ([tex]m = 4\,kg[/tex])
[tex]F = m\cdot a[/tex] (4)
[tex]F = 48\cdot t[/tex]
The force acting on the particle at time t is [tex]F = 48\cdot t[/tex].
c) According to the Work-Energy Theorem, the change in kinetic energy of the particle equals the change in the net work done on the particle. In this case, the power is equal to the rate of change in kinetic energy.
[tex]\dot W = \dot K[/tex] (5)
[tex]\dot W = \frac{d}{dt}(50+120\cdot t^{2}+72\cdot t^{4})[/tex]
[tex]\dot W = 240\cdot t +288\cdot t^{3}[/tex]
The power being delivered to the particle at time t is [tex]\dot W = 240\cdot t +288\cdot t^{3}[/tex].
d) The work done on the particle ([tex]W[/tex]), measured in joules, is equal to the change of the kinetic energy of the particle:
[tex]W = K(5)-K(0)[/tex] (6)
[tex]W = [50+120\cdot (5)^{2}+72\cdot (5)^{4}]-[50+120\cdot (0)^{2}+72\cdot (0)^{4}][/tex]
[tex]W = 48000\,J[/tex]
The work done on the particle in the interval t = 0 to t = 5 is 48000 joules.
A locomotive creates a
59,400 N force, which creates
an acceleration of 0.145 m/s.
What is the mass of the
locomotive?
Unit=kg
Answer:
410,000 kg
Explanation:
Use Newton's second law
F = ma
m = F/a
m = 59,400 N/(.145 m/s) = 410,000 kg
20 POINTS
In order to maximize the acceleration of an object, one should
maximize the mass
maximize the force
minimize the velocity
maximize the inertia
Two identical bars are conducting heat from a region of higher temperature to one of lower temperature. In arrangement A, the bars conduct 80 J of heat in a certain amount of time. How much heat is conducted in B during the same time
Answer:
Q' = 320 J
Explanation:
The arrangements are given in attachment. The Fourier's Law of Heat Conduction states that:
Q = KAΔT/L
where,
Q = Heat Transferred
K = Constant (Conduction Coefficient)
A = Surface Area of Heat Transfer
ΔT = Difference of Temperature between two surfaces
L = Length between surfaces
For Arrangement AL
Q = 80 J
Therefore,
80 = KAΔT/L ------------- equation (1)
Now, for arrangement B:
A' = 2 A (As, the rods are now connected in parallel with each other)
L' = L/2
Therefore,
Q' = K(2A)ΔT/(L/2)
Q' = 4 KAΔT/L
using equation (1)
Q' = 4(80 J)
Q' = 320 J
Image formed by a plane mirror is
Answer: A plane mirror always forms a virtual image (behind the mirror). The image and object are the same distance from a flat mirror, the image size is the same as the object size, and the image is upright.
Explanation:
The speed of a space shuttle is 10 / express this in /�
Answer:
268.22m/s
Explanation:
Given;
10mile/min to m/s
We need to convert between the two units;
Using the dimensions;
1 mile = 1609.34m
60s = 1min
Now;
10 x [tex]\frac{mile}{min}[/tex] x [tex]\frac{1min}{60s}[/tex] x [tex]\frac{1609.34m}{1mile}[/tex]
= 268.22m/s
If 500 cal of heat are added to a gas, and the gas expands doing 500 J of work on its surroundings, what is the change in the internal energy of the gas?
Answer:
The change in the internal energy of the gas 1,595 J
Explanation:
The first law of thermodynamics establishes that in an isolated system energy is neither created nor destroyed, but undergoes transformations; If mechanical work is applied to a system, its internal energy varies; If the system is not isolated, part of the energy is transformed into heat that can leave or enter the system; and finally an isolated system is an adiabatic system (heat can neither enter nor exit, so no heat transfer takes place.)
This is summarized in the expression:
ΔU= Q - W
where the heat absorbed and the work done by the system on the environment are considered positive.
Taking these considerations into account, in this case:
Q= 500 cal= 2,092 J (being 1 cal=4.184 J) W=500 JReplacing:
ΔU= 2,092 J - 500 J
ΔU= 1,592 J whose closest answer is 1,595 J
The change in the internal energy of the gas 1,595 J
Given that "mass" multiply by constant “k” is equal to "energy" divided by
“height”. Determine, by using dimensions of each, which physical quantity is
represented by “k”?
Answer:
K must be an acceleration
Explanation:
Recall that unit of energy consists the following dimensions:
mass * length^2 / time^2
then if we have : mass * K = energy / length
then the units of K can be obtained by replacing the units of energy by (mass * length^2 / time^2), and then dividing by units of mass:
K = (mass * length^2 / time^2)/ (length * mass)
where we cancel out units of mass, and one unit of length resulting in units of length divided units of time squared. and such are units of acceleration. Therefore K must be an acceleration.
A bicycle mechanic is checking a road bike's chain. He applies force F = 48 N to a pedal at the angle shown in (Figure 1) while keeping the wheel from rotating. The pedal is 17 cm from the center of the crank; the gear has a diameter of 16 cm.
Answer:
T = 102.3 ≈ 100
Explanation:
r(pedal) = 17 cm = 0.017 m
r(gear) = 16 cm / 2 = 8 cm = 0.008 m
θ = 180°-110° = 70°
F = 48 N
T = ?
τ₁ = r(pedal)*F*cosθ = (0.017 m)(48 N)cos(70°) = 0.28 N*m (*negative because it is applied clockwise)
τ₂ = -τ₁ = -(-0.28 N*m) = 0.28 N*m
τ₂ = r(gear)*T*cosθ
T = τ₂÷(r(gear)*cosθ) = 0.28 N*m ÷ (0.008 m * cos(70°))
T = 102.3 ≈ 100 ( 2 sig figs)
your sister has gained admission into your former school write a letter giving her information about the school and advise her to behave well while in school
Answer:
Find the letter below.
Explanation:
5183 Richmond Avenue,
Houston City,
Texas, U.S.A.
16th November 2020.
Dear Jane,
I received with joy the news of your admission into Texas City High School, my alma mater. This is a big feat and evidence of your hard work and commitment to your academics. To excel in this school, there are certain points which I would like you to note.
First, this is a new phase of your life and it would be important for you to clearly keep your purpose for going to school in mind. Your foremost purpose is to study and gain the needed knowledge that would help you in life.
Secondly, the school is a very sociable environment with lots of interesting activities such as sports, dancing, literary groups, and so many others. Find a group that appeals to you and participate actively in it. Extracurricular activities would help you socialize with your mates and teachers. It would also help you meet interesting people who might later serve some useful purpose in your life after graduation.
The teachers at Texas City High School are very kind and willing to help you excel in your academics and other chosen fields. Be sure to respect them and meet them when you have difficulties in any area of concern. There are also counselors that guide you and help you to remain on the path to excellence.
My dear Jane, life in Texas City High School would not always be rosy as there are bullies in school who would want to intimidate you or get you into fights. Avoid them by all means. Be cordial to all. Report any cases of harassment to the relevant authorities for they are seasoned in handling such matters maturely.
The cafeteria is also an interesting feature of the school. There you can find different kinds of snacks that I know you would love given how much you love snacks. I would only recommend that you make healthier choices so that you do not become overweight or fall ill due to overindulgence in unhealthy meals.
My dear baby girl, be assured of my love and kind wishes as you move on to this next stage of your life. Always know that I am here to give you my advice when you need it. Be a good girl my dear sister. Do have a lovely time at school.
Yours lovingly,
Queen Walters.
explain what the emitter does in CT
the emitter of x-rays rotates around the patient and the detector, placed in diametrically opposite side, picks up the image of a body section (beam and detector move in synchrony)
i believe that should be ur answer =) good luck !
the force of attraction between any two objects that have mass is
Answer:
gravitational force
Explanation:
Gravitational force -an attractive force that exists between all objects with mass; an object with mass attracts another object with mass; the magnitude of the force is directly proportional to the masses of the two objects and inversely proportional to the square of the distance between the two objects
A potential difference of 107 mV exists between the inner and outer surfaces of a cell membrane. The inner surface is negative relative to the outer surface. How much work is required to eject a positive sodium ion (Na ) from the interior of the cell?
Answer:
The workdone is [tex]W = 1.712 *10^{-20 } \ J[/tex]
Explanation:
From the question we are told that
The potential difference is [tex]V = 107 mV = 107 *10^{-3} \ V[/tex]
Generally the charge on [tex]Na^{+}[/tex] is [tex]Q_{Na^{+}} = 1.60 *10^{-19 } \ C[/tex]
Generally the workdone is mathematically represented as
[tex]W = Q_{Na^{+}}V[/tex]
=> [tex]W = 1.60 *10^{-19 } * 107 *10^{-3}[/tex]
=> [tex]W = 1.712 *10^{-20 } \ J[/tex]
why is The sum of two vectors has the smallest magnitude when the angle between these two vectors is 180t
Answer:
C = A - B
Explanation:
The addition of vectors takes into account the magnitude of each vector and its direction, so when adding two vectors, the result depends on the direction of the vectors.
* If the vectors have the same direction the result is maximum
C = A + A
* if the vectors have 90 between them, the magnitude of the result is given by the Pythagorean Theorem
C = √(A² + B²)
* if the vectors have 180º between them the result is minimal
C = A - B
We can also perform this sum graphically, where the resulting vector goes from the origin of the first vector to the tip of the last one, it can clearly be seen that when the vectors are antiparallel (180º angle) the magnitude is minimal
Imagine you are running PE class. You run the first 1000 meters in 3 minutes and then get tired and run the last 600 meters in 5 minutes. What was your *average* speed?
Answer:
200 meters per minute
Explanation:
You run the 1600 meters in a total of 8 minutes, so the average speed if 200 meters per minute.
Help!!! Need answer ASAP.
Answer:
a = 11.03 [m/s²]
Explanation:
To solve this problem we must use Newton's second law which tells us that the sum of forces is equal to the product of mass by acceleration.
ΣF = m*a
where:
F = force = 160000 [N]
m = mass = 14500 [kg]
a = acceleration [m/s²]
160000 = 14500*a
a = 11.03 [m/s²]
A crate is pulled due south with a force of 350. N. What other force must be applied if the
net force on the crate is 425 N due north? Enter the magnitude (with units) and direction
(north, south, east, west).
Answer:
775 N due North.
Explanation:
If the crate is pulled South with 350 N force, and the net force on the crate results into 425 N due North, then the other force (F) acting must be larger than the 350 N, and pointing North:
F - 350 N = 425 N
F = 425 N + 350 N = 775 N due North.
FOR THIS QUESTION, solve as if you are on the moon and use moon gravity (g = 1.7 m/s^2)
An astronaut stands on top of a lunar lander, which is 2.4 meters tall, and putts golf balls off the side with an initial velocity of 4.5 meters per second. How far in the horizontal direction will they travel?
A.) 12.6 m
B.) 2.8 m
C.) 1.7 m
D.) 7.7 m
Answer:the answer is D
Explanation: I just took the quiz
Is a windmill that is not running, potential or kinetic?
When you sweat, what is the external stimuli? I need help asap.
Answer:
An External Stimulus is a stimulus that comes from outside an organism. Examples: You feel cold so you put on a jacket. When you sweat, the external stimulus is either you're anxious or hot.
Explanation:
hope it helps! <3
When does acceleration due to gravity equal 9.8 m/s downward?
Select one:
a. always
b. when an object has been dropped downward
c. when an object has been thrown upward
d. at the peak of a thrown object's flight
Answer:
b
Explanation:
i took the quiz i think its right
Which is increased when the string of a stringed instrument is tightened?
timbre
pitch
wavelength
loudness
When the string of the instrument is tightened then the length of the string decreases hence the pitch and frequency will increase so, option B is correct.
What is pitch?The frequency at which the sound waves that create a sound vibrate determines its pitch. High-frequency sound waves produce high-pitched noises, and low-frequency sound waves make low-pitched noises. The ability to discern between harsh and flat sounds is known as pitch.
A string will vibrate at a varied frequency depending on its length. Higher frequency and higher pitch are produced by shorter strings.
The pitch rises as the anxiety does as well. A string's length is also crucial. A string vibrates and makes music when it is supported at two points and pulled. The pitch of this string will, however, rise if the length is shortened.
To know more about the pitch:
https://brainly.com/question/12244387
#SPJ2
A motorcycle moving at a constant velcoity suddenly accelerates at a rate of 4.0 m/s/s to a speed of 35 m/s in 5.0 s. What was the initial speed of the motorcycle?
Answer:
15 m/s
Explanation:
v = u+ at
35 = u + 20
35-20 = u
u= 15 m/s
A gas has 4.99*10^27 molecules. How many moles is that?
Answer: 8280
Explanation: This is the answer that my online school curriculum said was right.
God loves you!!!
Answer:
This isn't an answer, but rather a question for the answer that was given (which was correct! Thank you so much!) I was trying to figure out how to comment because I am in no way trying to steal points or anything like that, but I have a genuine question that I couldn't figure out any other way to ask...
How did you come up with 8280? Whenever I do it I get 8289....
I would like to know the process for future reference. Thank you for your help and again, I apologize for taking these points with no answer to contribute.
Which of the following best describes a solid?
A
matter is made of atoms so tightly packed together that they cannot move around
B
takes the shape and volume of its container
C
has a definite volume, but takes the shape of its container
A motorcycle moving at a constant velocity suddenly accelerates at a rate of 4.0 m/s^2 to a speed of 35 m/s in 5.0 s. What was the initial speed of the motorcycle?
Answer:
15m/sExplanation:
Step one:
given data
acceleration a=4m/s^2
final velocity v=35m/s
time t=5 seconds
Step two:
Required
initial velocity u=?
Applying the first equation of motion
v=u+at
substituting we have
35=u+4*5
35=u+20
u=35-20
u=15 m/s
The initial velocity is 15m/s
Squid use jet propulsion for rapid escapes. A squid pulls water into its body and then rapidly ejects the water backward to propel itself forward. A 1.5 kg squid (not including water mass) can accelerate at 20 m/s2 by ejecting 0.15 kg of water. Part A What is the magnitude of the thrust force on the squid
Answer: see attachment
Explanation:
Please help me! Will give brainliest.
Answer:
B. Boats need to float.
What will happen to the charge and potential difference if the plate area were increased while the plate separation remains unchanged?
Answer:
Potential difference and charge will also increase.
Explanation:
Asking that :
What will happen to the charge and potential difference if the plate area were increased while the plate separation remains unchanged?
The charge is directly proportional to area of the plate. That is, increase in area of the plate of a capacitor will lead to the increase in the charges between the plates.
And since charge is also proportional to the magnitude of potential difference between the plates from the definition of capacitance of a capacitor which says that:
Q = CV
Therefore, increase in the area of the plate will also lead to increase in potential difference between the plates.
Therefore, if the plate area were increased while the plate separation remains unchanged, the charge and potential difference between them will also increase.
At 20 oC the densities of fresh water and ethyl alcohol are, respectively, 998 and 789 kg/m3. Find the ratio of the adiabatic bulk modulus of fresh water to the adiabatic bulk modulus of ethyl alcohol at 20 oC.
Answer:
The ratio is [tex]\frac{B_1}{B_2} = 1.265[/tex]
Explanation:
From the question we are told that
The density of fresh water is [tex]\rho__{f}} = 998 \ kg/m^3[/tex]
The density of ethanol is [tex]\rho_{e} = 789 \ kg /m^3[/tex]
Generally speed of a wave in a substance is mathematically represented as
[tex]v = \sqrt{\frac{B}{\rho} }[/tex]
Here B is the adiabatic bulk modulus of the substance while [tex]\rho[/tex] is the density of the substance
So at constant wave speed
[tex]\sqrt{\frac{B_1}{\rho_1} } = \sqrt{\frac{B_2}{\rho_2} }[/tex]
=> [tex]\frac{B_1}{\rho_1} = \frac{B_2}{\rho_2}[/tex]
=> [tex]B_1 \rho_2 = B_2\rho_1[/tex]
=> [tex]\frac{B_1}{B_2} = \frac{\rho_1}{\rho_2}[/tex]
Here [tex]\rho_1 =\rho__{f}} = 998 \ kg/m^3[/tex] and [tex]\rho_2 = \rho_{e} = 789 \ kg /m^3[/tex]
So
=> [tex]\frac{B_1}{B_2} = \frac{998}{789}[/tex]
=> [tex]\frac{B_1}{B_2} = 1.265[/tex]
A 5 kg projectile is shot with an initial velocity of 8 m/s from a height of 10 meters. If the acceleration due to gravity is 9.8 m/s^2, what is the total initial energy of the projectile?
Answer: 650 joules
Explanation:
Total energy (kinetic + potential)
1/2×mv^ + mgh
1/2×5×8×8+ 5×9.8×10
1/2×320 + 5×98
320/2 + 480
320/2 + 980/2 (multipling to make the denominator equal)
1300/2 = 650 joules
Hope it helps, if you don't understand try doing it yourself with the formula.
:)