A 12 N [E] force is applied to a toy train with a mass of 2.7 kg. The toy train is attached by a light string to a wagon with a mass of 1.8 kg which is attached to a second wagon with a mass of 1.0 kg. If the train is pulled on a surface with a coefficient of kinetic friction of 0.05, determine the tension in the string between the first and the second wagon. (6T, 3C) Include free body diagrams for the three masses involved in the acceleration. (3 Comm.)
See the attached diagram for reference and free body diagrams. The acceleration a of each body will be the same since each connecting string is in tension.
By Newton's second law, we have
• net force on the train:
- - horizontal
[tex]\sum F = F - F_{k,T} - T_1 = m_Ta[/tex]
(where F = 12 N)
- - vertical
[tex]\sum F = N_T - m_Tg = 0[/tex]
• net force on wagon 1:
- - horizontal
[tex]\sum F = T_1 - T_2 - F_{k,1} = m_1a[/tex]
- - vertical
[tex]\sum F = N_1 - m_1g = 0[/tex]
• net force on wagon 2:
- - horizontal
[tex]\sum F = T_2 - F_{k,2} = m_2a[/tex]
- - vertical
[tex]\sum F = N_2 - m_2g = 0[/tex]
We want to determine T₂, the tension in the string connecting the two wagons.
For each body, the corresponding normal force has magnitude
N = mg
where m is the respective mass, and the kinetic friction has magnitude
Friction = 0.05 N = 0.05mg
So if µ = 0.05, then the frictional force on each body is
[tex]F_{k,T} = 0.05 (2.7\,\mathrm{ kg}) g = 1.323\,\mathrm N[/tex]
[tex]F_{k,1} = 0.05 (1.8\,\mathrm{ kg}) g = 0.882\,\mathrm N[/tex]
[tex]F_{k,2} = 0.05 (1.0\,\mathrm{ kg}) g = 0.49\,\mathrm N[/tex]
which leaves us with the system of equations,
[1] … 12 N - 1.323 N - T₁ = (2.7 kg) a
[2] … T₁ - T₂ - 0.882 N = (1.8 kg) a
[3] … T₂ - 0.49 N = (1.0 kg) a
Adding [1] and [2] eliminates T₁ :
(12 N - 1.323 N - T₁) + (T₁ - T₂ - 0.882 N) = (2.7 kg) a + (1.8 kg) a
[4] … 9.795 N - T₂ = (4.5 kg) a
Divide through both sides of [3] by 1.0 kg to solve for a :
a = (T₂ - 0.49 N) / (1.0 kg)
Substitute this into [4] and solve for T₂ :
9.795 N - T₂ = (4.5 kg) (T₂ - 0.49 N) / (1.0 kg)
(9.795 N - T₂) (1.0 kg) = (4.5 kg) (T₂ - 0.49 N)
9.795 N - T₂ = 4.5 T₂ - 2.205 N
12 N = 5.5 T₂
T₂ = (12 N) / 5.5 ≈ 2.1818 N ≈ 2.2 N
You flip a coin straight up if the coin reaches a high point of 0.25 m above where you released it what was the initial speed?
Answer: 2.21 m/s
Explanation:
Given
Coin reaches a height of 0.25 m above the launch point
Suppose u is the initial speed of the coin
Using the equation of motion
[tex]\Rightarrow v^2-u^2=2as\\[/tex]
Putting values
[tex]\Rightarrow 0^2-u^2=2\times g\times s=2\times (-9.8)\times 0.25\\\Rightarrow u^2=4.9\\\Rightarrow u=2.21\ m/s[/tex]
Thus, the initial velocity is 2.21 m/s
What is released when rocks shift or move along a tectonic plate boundary?
(It is a science question)
Answer:
juuhu
Explanation:
jjj
who invented Pascal??
An organism with the alleles Aa is called __________, while one with AA or aa is called __________.
A. heterozygous, hom/ zygous
B. heterozygous, homo/zygous
Answer:
Hetefrozygous, homofzygous
What is the acceleration of a 24 kg mass pushed by an 8 N force?
Answer:
0.25 m/s squared
Explanation:
Mass of the body (m)= 24kg
Applied force on the body(F)= 6N
Acceleration of the body (a)= ?
Solution
F = ma
a = F/m
a = 6N/24kg
a = 0.25m/s^2
Answer: The acceleration of the body is 0.25m/s^2
I hope this helps
Answer:
[tex]\boxed {\boxed {\sf a=\frac {1}{3} \ m/s^2}}[/tex]
Explanation:
Force is the product of mass and acceleration.
[tex]F=ma[/tex]
The mass is 24 kilograms and the force is 8 Newtons. Let's convert the Newtons to make the problem easier.
1 Newton is equal to 1 kilogram meter per square second. The force of 8 N equals 8 kg*m/s²Substitute the known values into the formula.
[tex]8 \ kg*m/s^2= (24 \ kg )*a[/tex]
Since we are solving for a, we must isolate the variable. It is being multiplied and the inverse of multiplication is division. Divide both sides by 24 kilograms.
[tex]\frac {8 \ kg*m/s^2}{24 \ kg}= \frac{(24 \ kg )*a}{24 \ kg}[/tex]
The kilograms will cancel, hence our earlier unit conversion.
[tex]\frac {8 \ m/s^2}{24 }= a[/tex]
[tex]\frac {1}{3} \ m/s^2=a[/tex]
The acceleration is 1/3 meter per square second.
A centrifuge used in DNA extraction spins at a maximum rate of 7000rpm producing a "g-force" on the sample that is 6000 times the force of gravity. If the centrifuge takes 10 seconds to come to rest from the maximum spin rate: a) What is the angular acceleration of the centrifuge? b)what is the angular displacement of the centrifuge during this time
Answer:
A) a = 73.304 rad/s²
B) Δθ = 3665.2 rad
Explanation:
A) From Newton's first equation of motion, we can say that;
a = (ω - ω_o)/t. We are given that the centrifuge spins at a maximum rate of 7000rpm.
Let's convert to rad/s = 7000 × 2π/60 = 733.04 rad/s
Thus change in angular velocity = (ω - ω_o) = 733.04 - 0 = 733.04 rad/s
We are given; t = 10 s
Thus;
a = 733.04/10
a = 73.304 rad/s²
B) From Newton's third equation of motion, we can say that;
ω² = ω_o² + 2aΔθ
Where Δθ is angular displacement
Making Δθ the subject;
Δθ = (ω² - ω_o²)/2a
At this point, ω = 0 rad/s while ω_o = 733.04 rad/s
Thus;
Δθ = (0² - 733.04²)/(2 × 73.304)
Δθ = -537347.6416/146.608
Δθ = - 3665.2 rad
We will take the absolute value.
Thus, Δθ = 3665.2 rad
Plzzz help!! A stationary speed gun emits a
microwave beam at 2.10x1010 Hz. It
reflects off a car and returns 1030 Hz
higher. What is the speed of the car?
(Unit = m/s)
Answer:
The speed of the car is 14.7m/second or 15 m/second approximately.
Explanation:
A microwave beam at [tex]2.10\times10^1^0Hz[/tex] is generated by a stationary speed gun. It bounces off a car and returns at a higher frequency of 1030 Hz. The car's observed frequency would be the product of adding the two frequencies. That is to say,
F =[tex]2.1\times10^1^0+1030[/tex] =[tex]2.100000103\times10^1^0Hz[/tex]
Using doppler effect formula
[tex]F=\frac{C}{C-V}\times f[/tex]
Where
F = observed frequency
f = source frequency
C = speed of light = [tex]3\times10^8[/tex]
V = speed of the car
Putting the values in the formula -
[tex]2.100000103\times10^1^0=\frac{3\times10^8}{3\times10^8-V}\times2.1\times 10^1^0[/tex]
[tex]\frac{2.100000103\times10^1^0}{2.1\times10^1^0}[/tex] [tex]=\frac{3\times10^8}{3\times10^8-V}[/tex]
[tex]1.000000049=\frac{3\times10^8}{3\times10^8-V}[/tex]
by cross multiplication ,
300000014.7 - 1.000000049V = [tex]3\times10^8[/tex]
Collect the like terms
1.000000049V = 14.71429
Make V the subject of formula
V = [tex]\frac{14.71429}{1.000000049}[/tex]
V = 14.7 m/s
Therefore , the speed of the car is 15m/second approximately.
Regina is making observations of waves from different sources. She wants to classify the waves as either mechanical or electromagnetic. Which question will BEST help Regina to classify the waves?
A.
Can the wave transfer matter?
B.
Can the wave transfer energy?
C.
Can the wave travel through a vacuum?
D.
Can the wave travel through a liquid?
Answer:
A. Can the wave transfer matter?
Explanation:
EMW is made by vibrations of the charged particles and they work on a mechanical waveform. The energy is transferred through a vacuum and thus they need a medium to pass the energy. Thus in order to transport the energy from one place to another, such as a sound wave. Hence first she should have knowledge about the chemical and physical properties of the waves such as can they transfer matter.Select the correct answer from each drop-down menu.
Photosynthesis is a process in which plants prepare food using carbon dioxide, chlorophyll, and water in the presence of sunlight.
During photosynthesis,(blank)
energy is transformed into(blank)
1.Chemical,electrical,kinetic, Solar ?
2.Chemical, Electrical, Kinetic, Solar
Answer:
During photosynthesis solar energy is converted into chemical energy
Explanation:
During photosynthesis solar energy is converted into chemical energy in the form of energy rich bond of ATP molecule.
ATP (Adenosine triphosphate) and ADP (Adenosine diphosphate) molecules are termed currency of energy. ADP molecule is converted into ATP molecules, whenever energy is available in certain exothermic reactions of metabolism.
ATP molecules are store- house of energy. ATP molecule is broken down into ADP molecule in presence of enzyme ATPase, releasing energy whenever energy is required.
The synthesis of ATP molecules, utilizing solar energy during photosynthesis, is termed photo-phosphorylation.
These ATP molecules produced during light reaction of photosynthesis are utilized in dark reaction of photosynthesis (Calvin cycle).
ATP molecules synthesized during photo-phosphorylation may also be used in other metabolic reactions.
Photo-phosphorylation is of 2 types, i.e. Cyclic and Non-cyclic photo-phosphorylation.
Chlorophyll molecules entrap solar energy . There are 2 types of photo-systems in chlorophyll. These are photo-system -I and photo-system-II .
The electrons of chlorophyll molecule of photo-system I get excited which pass through series of electron carriers in electron transport system arranged in the order of decreasing energy level.
During the passage of electrons from carriers of higher energy level to the carriers of lower energy level, the energy is lost which is utilized for converting ADP molecule into ATP molecule.
Photo-system I is concerned with light reaction of photosynthesis only, constituting cyclic photo-phosphorylation.
The electron transport during Photo-system II results in the synthesis of NADPH2 in presence of enzyme NADP reductase. NADPH2 is used in reduction reaction of Calvin cycle.
Both Photo-systems participate in non-cyclic photo-phosphorylation that results in the synthesis of NADPH2 in addition to the synthesis of ATP molecules.
3. Determine the units of the quantity described by the following com-
binations of units:
a. kg (m/s) (1/s)
b. (kg/s) (m/s2)
c. (kg/s) (m/s)
d. (kg/s) (m/s)
Define heat according to molecular theory .
I think ....... the answer will be ......
like a theory
How much power is needed to lift a 20-kg object to a height of 4.0 m in 2.5 seconds?
Answer:
313.92w
Explanation:
Formula for power:
P=W/∆t = Fv
Givens:
m=20kg
∆y=4.0m
∆t=2.5s
a=9.81m/s²
In order to find power, we first need to solve for work.
W=Fd (force*displacement), f=mg
W=mg∆y
W=(20kg)(9.81m/s²)(4.0m)
W=784.8J
P=W/∆t
P=784.8J/2.5s
P=313.92 watts
An ant walks 15 m east, then 40 m north, and finally 20 m west. What is the total displacement from the starting point
Answer: 40.311 m
Explanation:
Given
Ant walks 15 m east
then 40 m North and finally 20 m west
from the figure, ant is 40 m North and 5 m west
Using Pythagoras, we can write
[tex]\Rightarrow d=\sqrt{40^2+5^2}\\\Rightarrow d=\sqrt{1625}=40.311\ m[/tex]
Neptune and Uranus are called the "ice giants" due to the presence of ice on their surface. Which is a reasonable explanation for why there aren't any ice giants in the group of terrestrial planets? A. They have rocky surfaces. B. They do not have rings. C. They are too close to the sun.
Answer:
C. They are too close to the sun.
Explanation:
Due to their relative location the gas giant such as neptune and Uranus are mostly cold and icy planets as they are located deep into the solar system and have large distance firm the sun.As compared to those of the earth and other rocky planets. Due to their distance they consist of primitive atmosphere and have slow rotation and movement.Pls helppp. Is this right?
Answer:
yes you are totally right
3. How does the wavelength of green different from violet-indigo?
Answer:
As the full spectrum of visible light travels through a prism, the wavelengths separate into the colors of the rainbow because each color is a different wavelength. Violet has the shortest wavelength, at around 380 nanometers, and red has the longest wavelength, at around 700 nanometers.
Explanation:
1. Which of the following decreases with an increase in altitude?
a. air pressure
b. visibility
c. water vapor
d. none of the above
Answer: air pressure
Explanation:
which lever is human arm
Answer:
The human arm is a class 3 lever
Explanation:
Answer:
A bent arm is a Class 3 lever. The pivot is at the elbow and the forearm acts as the lever arm. The biceps muscle provides the effort (force) and bends the forearm against the weight of the forearm and any weight that the hand might be holding.
Explanation:
Una bola se lanza verticlamente de la parte superior de un edificio con una velocidad inicial 25 m/s la bola impacta al suelo en la base del edificio 7 segundos despues de ser lanzada ¿que altura subio la bola
Answer:
S = 415.1 meters
Explanation:
Dados los siguientes datos;
Velocidad inicial = 25 m/s
Tiempo, t = 7 segundos
Para encontrar la altura (desplazamiento) de la pelota, usaríamos la segunda ecuación de movimiento;
[tex] S = ut + \frac {1}{2}at^{2}[/tex]
Dónde;
S representa el desplazamiento o altura medida en metros.
u representa la velocidad inicial medida en metros por segundo.
t representa el tiempo medido en segundos.
a representa la aceleración medida en metros por segundo cuadrado.
Sustituyendo en la ecuación, tenemos;
[tex] S = 25*7 + \frac {1}{2}*(9.8)*7^{2}[/tex]
[tex] S = 175 + 4.9*49 [/tex]
[tex] S = 175 + 240.1 [/tex]
S = 415.1 meters
A force of 1000 N is exerted on a golf ball for 0.005 s. The change in momentum of the golf ball is - a 200,000 kg m//s b 50 kg m//s c 5,000 kg m//s d 5 kg m//s
Answer:
d) 5 Ns
Explanation:
Impulse = Ft = 1,000(0.005) = 5
A block of size 100cmX50cm applies a force of 100N on the ground. Calculate the pressure
exerted by the block on the ground.
(2 Points)
Answer:
200 N/m²
Explanation:
Pressure = Force / Area
Force =100N
Area = 100cm x 50 cm= 5000cm² =0.5m²
Hence Pressure = 100N / 0.5m²
Pressure = 200N/m²
objects through which light can pass are referred to as dash objects
Answer:
Those objects are called transparent objects...
Explanation:
If only some light can pass through them ,it is called translucent....
If no light can pass through them ,it is called opaque.
Answer:
hii good morning
hey i am not good player but i wanted to give a triel to play duo in ff
If the pelican was traveling 8.79 m/s but was only 2.7 m above the water, how far would the fish travel horizontally before hitting the water below?
Answer:
6.52m
Explanation:
The horizontal distance travelled is known as its range. This is expressed as;
Range = u* √2H/g
u is the speed of the pelican
H is the maximum height
g is the acceleration due to gravity
Range = 8.79*√2(2.7)/9.8
Range = 8.79 * √5.4/9.8
range = 8.79*√0.5510
Range = 8.79*0.7423
Range = 6.52
Hence the fish will travel 6.52m before hitting the water below
You ride your bike 5 miles east to school, then 2 miles east to Wawa, return to school, then ride 2 miles west to the library to work on your homework. What is your displacement?
Answer:
3 miles
Explanation:
5 + 2 - 2 - 2 = 3 miles
i really really need help with this so please help me for a better grade asap
Answer :
Imma just put it in the explanation
Explanation:
Electric to sound : Radio
Chemical to thermal+radiant+sound+kinetic : Fireworks
Gravitational to kinetic+sound : Waterfall
Chemical to thermal+kinetic : Drinking water (not sure what last answer is called but its supposed to match the girl drinking water lol)
hope this helps
Question 2
What measurements are needed to calculate your BMI?
A. Weight and shoe size
B. Height and weight
C. heart and breathing rate per minute
D. core temperature and height
Answer:
B
Explanation:
two children of masses m1 = m2 = 20 kg , ride on the perimeter of a small merry-go- round . the merry -go-round us a disk of mass M = 30 kg answer
Answer:
c
Explanation:
When the C4 key on a piano keyboard is pressed, a string inside the piano is struck by a hammer and begins vibrating back and forth at approximately 260 cycles per second.
a. What is the frequency in Hertz of the sound wave?
b. What is the wavelength of the wave?
Answer:
Frequency = 260 Hz and wavelength = 1.31 m
Explanation:
Given that,
A hammer begins vibrating back and forth at approximately 260 cycles per second.
(a) The frequency of an object is the number of vibrations per unit time. The frequency of the sound wave is 260 Hz.
(b) The speed of sound in air is 343 m/s. So,
[tex]v=f\lambda\\\\\lambda=\dfrac{v}{f}\\\\\lambda=\dfrac{343}{260}\\\\\lambda=1.31\ m[/tex]
Hence, this is the required solution.
A potato is which part of the plant?
root
stem
leaf
flower