The object as point particles is [tex]r_{cm} =0.5909 m, 0.6364 m.[/tex]
What is the center of mass of a system of particles?A place at which the entire mass of the body or all the masses of a system of particles appears to be concentrated is known as the center of mass of a body or system of particles. According to physics, the center of mass is a location where the total of the weighted relative positions of the distributed mass's points in space equals zero.a)
The center of mass of a three-particle system is expressed as
[tex]r_{cm}=[/tex] [tex]$$r_{c m}=\frac{\sum_{i=1}^{3} m_{i} r_{i}}{\sum_{i=1}^{3} m_{i}} \Rightarrow \frac{m_{1} r_{1}+m_{2} r_{2}+m_{3} r_{3}}{m_{1}+m_{2}+m_{3}}$$[/tex]
When the system is only on [tex]$\mathrm{x}$[/tex]-axis (i.e. [tex]$\mathrm{y}=0$[/tex] )
[tex]$$\begin{aligned}x_{c m} &=\frac{m_{1} x_{1}+m_{2} x_{2}+m_{3} x_{3}}{m_{1}+m_{2}+m_{3}} \\x_{c m} &=\frac{(5.0 \times 0.5)+(2.0 \times 0)+(4.0 \times 1.0)}{5.0+2.0+4.0} \\x_{c m} &=0.5909 \mathrm{~m} \\\text { Therefore } r_{c m}=(0.5909 \mathrm{~m}, 0)\end{aligned}$$[/tex]
b)
When the two particles are shifted
[tex]\begin{aligned}&x_{c m}=\frac{m_{1} x_{1}+m_{2} x_{2}+m_{3} x_{3}}{m_{1}+m_{2}+m_{3}} \\&x_{c m}=\frac{(5.0 \times 0.5)+(2.0 \times 0)+(4.0 \times 1.0)}{5.0+2.0+4.0} \\&x_{c m}=0.5909 \mathrm{~m} \\&y_{c m}=\frac{m_{1} y_{1}+m_{2} y_{2}+m_{3} y_{3}}{m_{1}+m_{2}+m_{3}} \\&y_{c m}=\frac{(5.0 \times 1.0)+(2.0 \times 0)+(4.0 \times 0.5)}{5.0+2.0+4.0} \\&y_{c m}=0.6364 \mathrm{~m}\end{aligned}[/tex]
Therefore [tex]r_{cm} =0.5909 m, 0.6364 m.[/tex]
The object as point particles is [tex]r_{cm} =0.5909 m, 0.6364 m.[/tex]
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Two drums are rolling down a hill. The drums are the same size and mass.
Drum #1 has most of its mass concentrated at the rim, while drum #2 has
most of its mass concentrated in the center. Which of the following
statements are correct? Select all that apply.
Drum #1 will reach the bottom of the hill first because its moment of inertia is
greater.
Drum #1 will have a greater center of mass speed and reach the bottom of the
hill first.
Drum #2 will have a greater center of mass speed and reach the bottom of the
hill first.
Drum #2 will reach the bottom of the hill first because its moment of inertia is
smaller.
Hi there!
Drum #2 will have a greater center of mass speed and reach the bottom of the hill first.
The moment of inertia can be thought of as inertia for rotation.
If mass is concentrated at the rim, the drum has a GREATER moment of inertia compared to if the mass is more concentrated towards the center.
Using the Rotational Equivalent of Newton's Second Law:
[tex]\Sigma \tau = I\alpha[/tex]
**Sum of torques = Moment of inertia * angular acceleration
From this equation, we know that if 'I' increases, 'α' decreases, and thus, the speed of the object's center of mass decreases and it will reach the bottom later.
Therefore, drum #2 with the smaller moment of inertia (mass concentrated at the center) will have a greater angular acceleration ⇒ greater center of mass speed ⇒ read the bottom first.
What climate zone are you in temperatures are always very warm Where is this zone located on Earth
Answer:
Warm weather may be found in the tropical zone since the sun's heat is concentrated in regions close to the equator. At 23.5 degrees north of the equator and 23.5 degrees south of the equator, this area is nearly in the middle of the world. It has a monthly average temperature of 18 degrees Celsius or higher.
Explanation:
is power and voltage the same thing yes or no
Many astronomers have spent their entire career attempting to definitively answer the question "Are we alone?". To date, we have found no other life forms. Discuss the type of efforts made to date to answer this question and the results of those efforts. Within our solar system, what are the best candidates for harboring life? Aside from the scientific evidence, what are your views regarding life beyond Earth and the basis for why you feel that way?
Answer:
Astrobiologists have put in tremendous efforts till now in the search for extra-terrestrial life. They are searching not only for tremendously developed life forms like humans, but also for microbes that are found to inhabit even the harshest of environments on Earth. Due to the tremendous development in technology, the odds of finding life beyond Earth are increasing day by day. Nasa's Kepler mission was launched to hunt for Earth like planets beyond our Solar System, and till now this mission has established the presence of 2,337 exoplanets, along with 1,284 new planets. This hugely increases the chances of finding another Earth like planet outside the limits of our Solar system. NASA's Astrobiology researchers are presently studying the most severe environments on Earth for improved understanding of the kind of conditions that would be able to support life in every part of the universe. Moreover, programs for instance SETI are keeping an eye on the galaxy for electromagnetic communications occurring or situated between stars from the societies on new worlds.
There is still a tremendous possibility to find life in our solar system. By the discovery of life forms in the extreme environments here on Earth, scientists have realized that the presence of solar energy is not an absolute necessity for the subsistence of life. Energy from chemical reactions can also trigger the organic elements to interact and start the formation of life. In the Solar system, Jupiter's moons Io and Europa and Saturn's moons Enceladus and Titan have been realized to the very strong candidates for the presence of microscopic life forms.
Explanation:
I hold a very optimistic view on the presence of life beyond Earth. It is highly probable that life on Earth is not an exceptional case but it should be a general one in the Universe. While we are always excited to imagine that we might encounter species as much developed or more highly developed than us, there is very good chance that the Universe is teeming with microscopic life forms. Also, to discover another intelligent life form would also be highly welcome.
4 Four objects are stiuated along the y axis as follow: a 20 kg object is at +3 m, a 3 kg object is at +2.5 m, a 2.5 kg object is at origin, and a 4 kg object is at -5 m. What is the center of mass of these objects?
Answer: 1.348 meters
Explanation: Although the sign is missing from the location of the 4.00 kg object, it is assumed to be positive. The net moment of all the objects about the center of mass must be zero. Let the center of mass be on the y axis at a point c . Adding the four moments together, we get:
(2.00)(3.00−c)+(3.00)(2.50−c)+(2.50)(0−c)+(4.00)(0.500−c)=0
6.00−2.00c+7.50−3.00c+0−2.50c+2.00−4.00c=0
11.5c=15.50
c= 1.348 metres
The center of mass is on the y axis at y = 1.348 metres.
Circle the anomalous result in the table below. An anomaly is a piece of data that doesn't
fit in with the rest of the data.
1. Concentration of
sucrose (M)
0.25
0.5
1
1.5
2
2. Change in mass of piece of potato (g)
Group B's
Group A's
measurements
0.02
0.05
0.12
0.17
0.21
3. measurements
0.03
0.05
2.3
0.14
0.2
Average?
Pls help I need to get this done really soon otherwise I will get a detention for two hours after school with my least fave teacher plss it’s for a test!!!!!!
Answer:
Explanation:
yes
A car with a mass of 1000 kg accelerates from 0 to 90 km/h in 10 seconds. a) What is its acceleration? b) What is the net force on the car?
Answer:
v
f=90km/h=25m/s
v_{_{i}}=0v
i=0
t=10\;\mathrm{s}t=10s
m=1000\;\mathrm{kg}m=1000kg
The acceleration of the car is 2.5 m/s². The net force acting on the car is 2500 Newtons (N). The correct answers are 2.5 m/s², 2500 Newtons (N).
Given:
Mass of the car (m) = 1000 kg
Acceleration (a) = 2.5 m/s²
a) The acceleration of the car is:
Acceleration (a) = Change in velocity / Time taken
Final velocity (v(f)) = 90 × 0.27778 = 25 m/s
Acceleration (a) = (Final velocity - Initial velocity) / Time taken
Acceleration (a) = (25 - 0 ) / 10
Acceleration (a) = 2.5 m/s²
Therefore, The acceleration of the car is 2.5 m/s².
b) Newton's second law of motion:
F = m × a
F = 1000 × 2.5
F = 2500 N
The net force acting on the car is 2500 Newtons (N).
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Particles that are __________ can transfer heat energy as they vibrate.
A. The same size
B. The same color
C. Very close together
D. Very far apart
Consider the f(x) = cos(Bx) function shown in the figure in blue color. What is the value of parameter B for this function? This parameter is called angular frequency in physics and it is denoted by ω.
As a reference the g(x) = cos(x) function is shown in red color, and green tick marks are drawn at integer multiples of π.
The value of parameter B (angular frequency) for this function is 2.7.
What is amplitude of a wave?
The amplitude of a wave is the maximum displacement of the wave. It can also be described at the maximum upward displacement of a wave curve.
f(x) = Acos(Bx)
where;
A is amplitude of the waveB is angular frequency of the waveWhat is angular frequency of a wave?Angular frequency is the angular displacement of any element of the wave per unit time.
From the blue color; at y = -0.9, x = -7.5 cm
-0.9 = cos(-7.5B)
7.5B = arc cos (0.9)
7.5B = 2.7
B = 7.5/2.7
B = 2.7
Thus, the value of parameter B (angular frequency) for this function is 2.7.
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Suppose you need your silicon circuit element to run continuously for 3 minutes before it shuts off long enough to cool back down to its initial temperature. If the circuit element can withstand a temperature change of 5.1 ∘C without being damaged, what is the maximum rate at which energy can be added to the circuit element?
The maximum rate at which energy can be added to the circuit element mathematically given as
[tex]MER=5.044 \times 10^{-4} \mathrm{~J} / \mathrm{sec}[/tex]
What is the maximum rate at which energy can be added to the circuit element?Generally, the equation for P is mathematically given as
[tex]P=\ln s \frac{\Delta T}{\Delta t}[/tex]
Therefore
[tex]Rate\ of\ Change\ of\ Temp =\frac{p}{lnS}[/tex]
[tex]\frac{p}{lnS}=\frac{7.4 \times 10^{-3}}{23 \times 10^{-6} \times 705}[/tex]
[tex]\frac{p}{lnS}=0.456^{\circ \mathrm{c}} / \mathrm{sec}[/tex]
Max temp Change
[tex]MaxT=5.6^{\circ} \mathrm{C}[/tex]
[tex]\text { time }=3 \times 60[/tex]
t=180s
In conclusion, Max Energy Rate
[tex]MER =23 \times 10^{-6} \times \frac{301 \times 5.6}{180}[/tex]
[tex]MER=5.044 \times 10^{-4} \mathrm{~J} / \mathrm{sec}[/tex]
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a motorist drives along a straight road at a constant speed of 15 m/s. just as she passes aparked motorcycle police officer , the officer starts to accelerate at 2m/s2 to over take her. assuming the officer maintains this acceleration,
a) determine the time it takes the police to reach the motorist the speed and
b) the total displacement of the officer as he overtakes the motorist
Explanation:
Distance traveled by motorist =(15.0m/s)t
Distance traveled by policeman =1/2(2.00m/s2)t2
(a) Intercept occurs when 15.0t =t2or t=15.0s.
(b) x(officer)=1/2(2.00m/s2)t2= 225m
As the resistance increases, what happens to the slope on the current vs voltage graph?
A. It gets steeper
B. It gets flatter
C. It keeps a constant slope
D. Not enough info
B. As the resistance increases, the slope on the current vs voltage graph gets flatter.
What is resistance?Resistance is the opposition to the follow of current in electrical material.
The mathematical relationship between resistance, current and voltage is given by Ohm's law.
R = V/I
where;
R is resistance, measured in ohmsV is voltage, measured in voltsI is current, measured in ampereFrom the equation above, increase in resistance means an increase in voltage or decrease in current.
In Current vs voltage graph, the following will occur;
The current decreases - the vertical axis decreasesThe voltage increases - the horizontal axis becomes largerThus, as the resistance increases, the slope on the current vs voltage graph gets flatter.
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A certain force F has an c component of 46N and a y component of 80N. Find the magnitude of this force. A- 73.8N B- 103.8N C 92.3N D-67.6N E-none
Answer:
X component= 46 N
Y component= 80 N
Magnitude =( 46 ^2 + 80^2 )^0.5 = 92.3 N
The mass of a coin is measured to be 12.5±0.1 g. The diameter is 2.8±0.1 cm and the thickness 2.1 ±0.1 mm. Calculate the average density of the material from which the coin is made with its uncertainty. Give your answer in kg m-³.
with proper explanation
answer only if u know or else u know the consequences
The average density of the material from which the coin is made is 9.67 g/cm³.
Volume of the coinThe volume of the coin at the given diameter is calculated as follows;
V = Ah
where;
A is area of the coinh is the thickness of the coinV = πd²/4 x h
V = π(2.8)²/4 x (0.21 cm)
V = 1.293 cm³
average density of the coinThe average density of the material from which the coin is made is calculated as follows;
density = mass/volume
density = 12.5 g / (1.293 cm³)
density = 9.67 g/cm³
Thus, the average density of the material from which the coin is made is 9.67 g/cm³.
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what is barometer ???
Answer:
an instrument measuring atmospheric pressure, used especially in forecasting the weather and determining altitude.
Explanation:
hope it helps ya
A 5 Ω and a 5 Ω resistor are in parallel. What is their total resistance?
A. 10 Ω
B. 2.5 Ω
C. 25 Ω
D. 5 Ω
Answer:
B. 2.5 Ω
Explanation:
[tex]\frac{1}{5} +\frac{1}{5}=0.4[/tex]
Put a one on top of the 0.4
[tex]\frac{1}{0.4} =2.5[/tex]
i. Which of the following formula gives definition of relative density? d d B. A. C. d water at 4°C d d mercury at 4°C D. d water at 40°C d d alcohol at 4°C
Answer:
water at 4°c that's abnormal stage of water
Which diagram best represents the relationship between these terms?
Quantum
Mechanics
Uses Solid-
State Physics
Has
Applications
Crystallography
is a pot plant a closed system?
Answer:
No because a pot plant system must interact with its surroundings (air, water, etc) and these are not closed systems.
Only if the pot plant were completely enclosed, say in a large glass jar would the system be closed.
A triangular plate with a non-uniform areal density has a mass M=0.500 kg. It is suspended by a pivot at P and can oscillate as indicated below. Its center of mass is a distance d=0.300 m from the pivot axis and its moment of inertia about an axis through the CM and parallel to the pivot axis is ICM=9.00×10-3 kg m2.
The plate is released from an angle θ=15°. Calculate the period of the oscillations.
The period of the oscillations.T = 1.2042s
Opposition is the process of any quantity or measure fluctuating repeatedly about its equilibrium value throughout time. This process is referred to as oscillation. Oscillation, a periodic fluctuation of a substance, can also be described as alternating between two values or rotating around a central value.
Typically, the mathematical formula for the moment of inertia is
T = 2 π √(I / mgd)
Therefore, a moment of inertia
I = 9.00×10-3 + md^2 ;
I=9.00*10^{-3}+ 0.5 * 0.3^2
I=0.054
T=2[tex]\pi \sqrt{0.5*9.8*0.3}[/tex]
T=1.2042s
The period of the oscillations.T = 1.2042s
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I = 30A and R = 30; what is V?
A. 900v
B.90v
C.10v
D.0.1v
Answer:
[tex]V = 900\; {\rm V}[/tex] for a resistor where [tex]I = 30\; {\rm A}[/tex] and [tex]R = 30\; {\rm \Omega}[/tex].
Explanation:
By Ohm's Law, if the electric resistance of a resistor is [tex]R[/tex] and the current going through that resistor is [tex]I[/tex], the voltage across that resistor would be [tex]V = I\, R[/tex].
Note that electric resistance is typically measured in Ohms, where [tex]1\; {\rm \Omega} = 1\; {\rm V \cdot A^{-1}}[/tex].
Given that [tex]I = 30\; {\rm A}[/tex] and [tex]R = 30\; {\rm \Omega}[/tex] for the resistor in this question, apply the formula [tex]V = I\, R[/tex] to find the voltage [tex]V[/tex] across this resistor:
[tex]\begin{aligned} V &= I\, R \\ &= 30\; {\rm A} \times 30\; {\rm \Omega} \\ &= 30\; {\rm A} \times 30\; {\rm V \cdot A^{-1}} \\ &= 900\; {\rm V} \end{aligned}[/tex].
The oxygen–hemoglobin dissociation curve depicts the relationship between the partial pressure of oxygen (pao2) and the:__________
The oxygen–hemoglobin dissociation curve depicts the relationship between the partial pressure of oxygen (pao2) and the arterial oxygen.
What does the oxygen–hemoglobin dissociation curve depicts?The oxygen-hemoglobin dissociation curve (OHDC) indicates the relationship between the oxygen saturation of hemoglobin and the partial pressure of arterial oxygen. This curve can change its position or shifted to another level depending on various factors.
So we can conclude that the oxygen–hemoglobin dissociation curve depicts the relationship between the partial pressure of oxygen (pao2) and the arterial oxygen.
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Three professional wrestlers are fighting over a champion’s belt, and each exerts a force on the belt. Wrestler 1 exerts a force F1=40.0 N in the +x-direction, wrestler 2 exerts a force F2=80.0 N in the negative y-direction, and wrestler 3 exerts a force F3=60.0 N at an angle of 36.9° counterclockwise (anticlockwise) from the +x-direction.
The resultant force of the three professional wrestlers on the championship belt is 98.35 N.
Component of the forces in x - direction
The component of the forces in x -direction is calculated as follows;
Fx = 40 N + 60(cos 36.9)
Fx = 40 N + 47.98 N
Fx = 87.98 N
Component of the forces in y - directionThe component of the forces in y -direction is calculated as follows;
Fy = -80 N + 60(sin 36.9)
Fy = -43.95 N
Resultant forceR = √Fx² + Fy²
R = √( 87.98² + 43.95²)
R = 98.35 N
Thus, the resultant force of the three professional wrestlers on the championship belt is 98.35 N.
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A simple pendulum suspended in a rocket ship has a period [tex]T_{0}[/tex]. Assume that the rocket ship is near the earth in a uniform gravitational field.
True or false:
1. If the ship moves upward with a constant velocity, the period increases.
2. If the length of the pendulum is doubled, the new period will be: square root of 2 times [tex]T_{0}[/tex].
3. If the ship accelerates upward, the period increases.
4. If the ship accelerates downward at 9.81 [tex]m/s^{2}[/tex], the pendulum will no longer oscillate.
5. If the mass of the pendulum is halved, the period decreases.
(1) If the ship moves upward with a constant velocity, the period increases, false.
(2) If the length of the pendulum is doubled, the new period will be: square root of 2 times T₀. true.
(3) If the ship accelerates upward, the period increases, true.
(4) If the ship accelerates downward at 9.81 m/s² , the pendulum will no longer oscillate, false.
(5) If the mass of the pendulum is halved, the period decreases, false.
Period of a simple pendulum
The period of a simple pendulum is given as;
T = 2π√(L/g) ------- (1)
where;
L is length of the pendulumg is acceleration due to gravityWhen the ship moves upward with a constant velocity, the period will not change.
When the length of the pendulum is doubledT ∝√L
when, L = 2L₀
T = T₀√2
Thus, if the length of the pendulum is doubled, the new period will be: square root of 2 times T₀.
when ship accelerates upwardt = √2h/g
when the height increases, time or period increaseswhen mass of the pendulum is halvedT = √I/mgd
where;
m is mass of the pendulumwhen the mass is halved, the period increases.
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Why does Usain bolt run?
Answer:
because he's fast and speedy
Explanation:
• An object of mass 2.0 kg moves in uniform circular motion on a horizontal friction less table. The radius of the circle is 0.75 m and the centripetal force is 10.0 N. The work done by this force when the object moves through one-half of a complete revolution is
Answer:
23.562
Explanation:
First it is good to work out the circumference:
2 pi r
2 pi .75
circumference = 4.7124
Next we need half of this because it is half a resolution. This will be our distance travelled.
half = 2.3562
word done = force x distance
work done = 10 x 2.3562
work done = 23.562
(I didn't see the need for mass...)
?
A motorboat travels east with a velocity of 4 meters/second relative to the
water when it encounters a current with a velocity of 7.0 meters/second
north relative to the shore. What is the resultant speed (magnitude of
velocity) for the boat relative to the shore?
Answer:[tex]\sqrt{65} m/s[/tex]
Explanation:
a ball rolls off a platform that is 12 m above ground. The ball's horizontal velocity as it leaves the platform is 5 m/s. How much time it takes for the ball to hit the ground
The time it takes for the ball to hit the ground from the platform is determined as 1.56 seconds.
Time of motion of the ball
The time of motion of the ball is calculated as follows;
h = vt + ¹/₂gt²
where;
v is initial vertical velocity = 0t is time of motionh is height of fall of the ballh = 0 + ¹/₂gt²
h = ¹/₂gt²
t = √(2h/g)
t = √(2 x 12 / 9.8)
t = 1.56 seconds
Thus, the time it takes for the ball to hit the ground from the platform is determined as 1.56 seconds.
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Glucose solution is administered to a patient in a hospital. The density of the solution is 1.308 kg/l. If the blood pressure in the vein is 35.7 mmHg, then what is the minimum necessary height of the IV bag above the position of the needle?
The minimum necessary height of the IV bag above the position of the needle is 0.37 m.
Minimum necessary heightThe minimum necessary height of the IV bag above the position of the needle is calculated as follows;
P = ρgh
where;
ρ is density = 1.308 kg/L = 1308 kg/m³g is acceleration due to gravity = 9.8 m/s²p is pressure = 35.7 mmHg = 4759.609 Pah is height, (m) = ?Substitute the given parameters and solve for minimum height
h = P/ρg
h = (4759.609) / (9.8 x 1308)
h = 0.37 m
Thus, the minimum necessary height of the IV bag above the position of the needle is 0.37 m.
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Explain the mechanism by which an open fracture could result in shock.
Answer:
an open fracture contains some sort of water which if it comes in contact with electrons could result to a shock