Answer:
1) x_{cm} = 5 m , 2) I = 168.32 kg m²
Explanation:
1) An important concept of center of mass is
[tex]x_{cm} = \frac{1}{M} \sum x_{i} m_{i}[/tex]
where M is the total mass of the system
Let's apply this equation to our case, suppose that all masses are equal and are worth 1 kg
[tex]x_{cm}[/tex] = ⅓ (1 0 + 1 5 + 1 10)
x_{cm} = 5 m
2) In this para indicates that there is an axis of rotation at the point xo = 3.8 m and they ask to calculate the moment inertia.
Let's use the parallel axes theorem
I = I_{cm} + M D
where I_{cm} is the moment of inertia with respect to the center of mass, D the distance between the two axes of rotation and M the total mass of the system
Let's look for the moment of inertia of the center of mass
[tex]I_{cm}[/tex] = 1 0 + 1 5² + 1 10²
I_{cm} = 125 kg m²
the total moment of inertia is
I = 125 + 3 3.8²
I = 168.32 kg m²
The moment of inertia of the 3-mass system about the new axis is 54.32 kgm/s².
We have three masses each of mass = 1kg such that they are in line with mass m at origin, m at 5m and m at 10m
(a) The center of mass:
[tex]X=\frac{m_1x_1+m_2x_2+m_3x_3}{m_1+m_2+m_3} \\ \\ X =\frac{ 1*0+1*5+1*10}{1+1+1}\\ \\ X = 5m[/tex]
Hence the center of mass of the system is at x = 5m.
(b) The moment of inertia about the axis passing through x = 3.8m
from the parallel axis theorem:
[tex]I = I_{cm} + Md^2[/tex]
where, [tex]I_{cm}[/tex] is the moment of inertial along an axis passing through the center of mass of the system, M is the total mass of the system and d is the distance of the given axis from center of mass.
M = 3kg
d = 5 - 3.8 = 1.2m
[tex]I_{cm}=1*5^2+1*0+1*5^2\\\\ I_{cm}=50 kgm/s^2[/tex]
Md² = 3×(1.2)²
Md² = 4.32 kgm/s²
I = 50 + 4.32
I = 54.32 kgm/s² is the moment of inertial about the given axis.
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types of magnetic resonance image
Answer: ur mom
Explanation:
Since astronauts in orbit are apparently weightless, a clever method of measuring their masses is needed to monitor their mass gains or losses to adjust diets. One way to do this is to exert a known force on an astronaut and measure the acceleration produced. Suppose a net external force of magnitude 59.0 N is exerted and the magnitude of the astronaut's acceleration is measured to be 0.852 m/s2. Calculate her mass.
Answer:
The value is [tex]m = 69.24 \ kg[/tex]
Explanation:
From the question we are told that
The value of the external force is [tex]F = 59.0 \ N[/tex]
The magnitude of the astronaut's acceleration is [tex]a = 0.852 \ m/s[/tex]
Generally Newton's Second Law of Motion from the mass of the astronauts is mathematically represented as
[tex]m = \frac{F}{a}[/tex]
=> [tex]m = \frac{59 }{0.852 }[/tex]
=> [tex]m = 69.24 \ kg[/tex]
(a) Calculate the linear acceleration of a car, the 0.220-m radius tires of which have an angular acceleration of 11.0 rad/s2. Assume no slippage.
Answer:
The value is [tex]a_t = 2.42 \ m/s^2[/tex]
Explanation:
From the question we are told that
The radius of the tires is [tex]r = 0.22 \ m[/tex]
The angular acceleration is [tex]\alpha = 11.0 \ rad/s^2[/tex]
Generally the linear acceleration is mathematically represented as
[tex]a_t = r * \alpha[/tex]
=> [tex]a_t = 0.22 * 11[/tex]
=> [tex]a_t = 2.42 \ m/s^2[/tex]
A girl rides her bike at 15 m/s for 20 s. How far does she travel in that time?
We are given:
Initial Velocity(u) = 15 m/s
Time interval(t) = 20s
Solving for the distance covered:
Since the girl keeps riding her bike at 15 m/s, her speed is constant and hence, acceleration of the bike is 0 m/s²
acceleration(a) = 0 m/s²
We know that:
s = ut + 1/2(at²) [second equation of motion]
s = (15)(20) + 1/2(0)(400) [plugging the values]
s = 150 + 0
s = 300 m
Hence, the girl covered 300 m in 20 seconds
Using a scale of 1 cm to represent 10 N, find the size and direction of the resultant of forces of 50 N
and 30 N acting at the angle of 45 O to each other.
Answer:
[tex]74.31\ \text{N}[/tex]
[tex]16.59^{\circ}[/tex]
Explanation:
P = 50 N
Q = 30 N
[tex]\theta[/tex] = Angle between the vectors = [tex]45^{\circ}[/tex]
Resultant is given by
[tex]R=\sqrt{P^2+Q^2+2PQ\cos\theta}\\\Rightarrow R=\sqrt{50^2+30^2+2\times 50\times 30\times \cos45^{\circ}}\\\Rightarrow R=74.31\ \text{N}[/tex]
Angle of resultant
[tex]\phi=\tan^{-1}\dfrac{Q\sin\theta}{P+Q\cos\theta}\\\Rightarrow \phi=\tan^{-1}\dfrac{30\times \sin45^{\circ}}{50+30\cos45^{\circ}}\\\Rightarrow \phi=16.59^{\circ}[/tex]
Magnitude of the resultant is [tex]74.31\ \text{N}[/tex]
Direction of the resultant is [tex]16.59^{\circ}[/tex]
A 2.0 kg bucket is attached to a horizontal ideal spring and rests on frictionless ice. You have a 1.0 kg mass
that you must drop into the bucket. Where should the bucket be when you drop the mass (so it is moving
purely vertically when it lands in the bucket) if your goal is to:
(a) Maximize the amplitude of the oscillation of the resulting 3.0 kg mass and spring system.
(b) Minimize the amplitude of the oscillation of the resulting 3.0 kg mass and spring system.
Answer:
x = A cos (w \sqrt{2y_{o}/g})
a) maximun Ф= \sqrt{\frac{2}{3} \frac{2 y_{o} }{g} }
b) minimun Ф = [tex]\frac{\pi }{2}[/tex] - \sqrt{\frac{2}{3} \frac{2 y_{o} }{g} }
Explanation:
For this exercise let's use kinematics to find the time it takes for the mass to reach the floor
y = y₀ + v₀ t - ½ g t²
as the mass is released from rest, its initial velocity is zero (vo = 0) and its height upon reaching the ground is zero (y = 0)
0 = y₀ - ½ g t²
t = [tex]\sqrt{2y_{o}/g}[/tex]
The bucket-spring system has a simple harmonic motion, which is described by
x = A cos wt
in this expression we assumed that the phase constant (Ф) is zero
let's replace the time
x = A cos (w \sqrt{2y_{o}/g})
this is the distance where the system must be for the mass to fall into it.
a) The new system has a total mass of m ’= 3.0 kg, so its angular velocity changes
w = [tex]\sqrt{k/m}[/tex]
In the initial state
w = \sqrt{k/2}
When the mass changes
w ’= \sqrt{k/3}
the displacement in each case is
x = A cos (wt)
for the new case
x ’= A cos (w’t + Ф)
the phase constant is included to take into account possible changes due to the collision of the mass.
we see that this maximum expressions when the cosine is maximum
cos (w´t + Ф) = 1
w’t + Ф = 0
Ф = -w ’t
Ф = - [tex]\sqrt{k/3}[/tex] [tex]\sqrt{2y_{o}/g}[/tex]
\sqrt{\frac{2}{3} \frac{2 y_{o} }{g} }
b) the function is minimun if
cos (w’t + fi) = 0
w’t + Ф = π / 2
Ф = π / 2 - w ’t
Ф = [tex]\frac{\pi }{2}[/tex] - \sqrt{\frac{2}{3} \frac{2 y_{o} }{g} }
What is the resistance of a wire with "p" of .25, a length "L" of 11.2, and an area "A" of 1.26?
Answer:
Resistance = 2.2 Ohms.
Explanation:
Given the following data;
Resistivity, P = 0.25
Length, L = 11.2
Area, A = 1.26
To find the resistance.
Resistance is given by the formula below;
Resistance = PL/A
Substituting into the equation, we have;
Resistance = (0.25*11.2)1.26
Resistance = 2.8/1.26
Resistance = 2.2 Ohms.
Therefore, the resistance of the wire is 2.2 Ohms.
Help please I would appreciate it
Answer:
i think the red runner travels greater distance ie.40 m
Explanation:
although ,the blue one travels 21 m but in the backward direction .so the correct ans is "the red runner travels 40 m"
What is net force?
A. The sum of all the forces acting on an object
B. The difference between the largest and smallest forces acting on
an object
C. The largest force acting on an object
D. The smallest force acting on an object
Answer:
A. The sum of all the forces acting on an object.
Explain how a fish is able to enjoy 180° field of view when in a pond.
Answer:
Time
An explanation of basic pond measurements that are vital to basic pond management practices.
Save For Later Print
Pond Measurements: Area, Volume and Residence Time - Articles UPDATED: OCTOBER 29, 2015
Pond Measurements: Area, Volume and Residence Time
The importance of getting an accurate estimation of your pond surface area cannot be overestimated. The majority of pond owners visually estimate their pond area, which usually results in an overestimate of the true pond surface area. Pond area and water volume should be calculated based on some simple measurements. The effort necessary to estimate pond surface area is directly related to your pond's shape and uniformity. The simplest method--using basic equations for common shapes--can be applied if your pond closely resembles a circle, square, rectangle, or trapezoid in shape.
Pond Shapes
Circular
pond shape can be estimated by measuring the distance around the pond shoreline in feet. Square the shoreline distance and divide by 547,390 to get the pond area in acres. For example, a pond that is 450 feet around the shoreline would have an area = (450 feet)2 / 547,390 or 0.37 acres.
Explanation:
i looked this up
A spiral spring of 8cm extended to 9.2cm when a load of 1.6N is applied. what is the force constant of the spring, provided the elastic is not exceeded.
Explanation:
By Hooke's Law, Fe = kx.
Since Fe = 1.6N and x = 9.2cm - 8cm = 1.2cm,
k = Fe/x = 1.6N/1.2cm = 1.33N/cm.
What is the change in potential energy in moving a 10kg box from the floor to a table 1 m high?
Explanation:
potential energy formula is 1/2 mv2(this 2 is square).m means mass and v means velocity.
now, you can calculate
The change in potential energy in moving a 10kg box from the floor to a table 1 m high is 98 Joules.
To find the potential energy, the given values are,
Mass of the box = 10Kg
Height h = 1 m
What is Potential energy?The potential energy can be defined as the energy that is stored and that can be determined through various parts in a particular system.
Also, the energy will gets stored when the object is not moving.
For example: Spring. Even when the spring is not stretched or contracted it stores energy.
The formula for Potential energy PE= mgh joules.
m is the Mass,
g is the acceleration due to gravity = 9.8 m/s²,
h is the height.
Substituting all the given values,
Potential Energy= 10 (9.8)(1)
PE= 98 J
Thus the potential energy of the box= 98 J.
To learn more about the potential energy,
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2) Two railway tracks are parallel to west east direction. Along one track, train A moves with a speed of 45 m/s from
west to east, while along the second track, train B moves with a speed of 60 m/s from east to west calculate speed of
Bw.rt. A
Answer:
[tex]Relative\ Velocity = 105m/s[/tex]
Explanation:
Given
[tex]V_A = 45m/s[/tex]
[tex]V_B = 60m/s[/tex]
Required
Determine the speed of B w.r.t A
The question implies that, we determine the relative velocity of B w.r.t A
Because both trains are moving towards one another, the required velocity is a [tex]sum\ of\ velocities\ of[/tex] both trains:
This is shown below:
[tex]Relative\ Velocity = V_A + V_B[/tex]
[tex]Relative\ Velocity = 45m/s + 60m/s[/tex]
[tex]Relative\ Velocity = 105m/s[/tex]
How long( in hours, will it take for 500 000 C of charge to flow through a diode if it requires
0.05 Amp to operate it.
Answer:
277.78 hours
Explanation:
The formula for calculating the amount of charge is expressed as;
Q = It
I is the current
t is the time
Given
I =0.05A
Q = 50,000C
Required
Time t
Recall that: Q = It
t = Q/I
t = 50,000/0.05
t = 1,000,000secs
Convert to hours
1,000,000secs = 1,000,000/3600
1,000,000secs = 277.78 hours
Hence it will take 277.78 hours for the charge to flow through the diode
A street bridge is 5.5m long if the linear expansion of steel is 0.00001 oc How much will it expand when temperatures is by 10oc? Give answer in Cm
Answer:
[tex]l_o=550.055\ cm[/tex]
Explanation:
Given that,
Length of a street bridge, l = 5.5 m
The coefficient of bridge, [tex]\alpha =0.00001 ^0 C[/tex]
We need to find how much will it expand when temperatures is by 10°C.
The change in length per unit original length is given by :
[tex]\dfrac{\Delta l}{l}=\alpha \Delta T\\\\\Delta l = l\alpha \Delta T\\\\=5.5\times 0.00001 \times 10\\\\\Delta l=0.00055\\\\(l_o-l)=0.00055\\\\l_o=0.00055+5.5\\\\=5.50055\ m\\\\l_o=550.055\ cm[/tex]
Hence, the length will expanded 550.055 cm.
2. Two identical spheres having charges Q and -
2Q experience a force F at a certain distance
If the spheres are kept in contact and then
placed at same initial distance, the force
between them will be
force between the two charges (+q1 and +q2),if they are at a distance 'a' is
F1=1/4pieEo q1q2/d^2................ (1)
when the metal spheres are in contact the charge flow from one sphere to another till both the sides acquires the same charge. here q1 and q2 are of same sign,hence after contact each sphere will have a charge
[tex] \binom{q1 + q2 }{2} [/tex]
now,the force between them,
f2=1/4pieEo
(q1+q2/2)^2/d^2
from eq (1)and eq (2)
f2=f1 (q1+q2)^2/4q1q2
Briefly describe the Rutherford atomic model
Answer:
The Rutherford model was made by Ernest Rutherford, to describe a atom. That is a brief explanation
Explanation:
A rifle is aimed at a target 40m away. The bullet hits the target 2.2cm below the horizontal plane (ignore wind and rotational effects).
(a) What is the time of flight for bullet?
(b) What is the muzzle velocity (velocity of bullet when it leaves the rifle)?
Answer:
The value is [tex]u_x = 597 \ m/s[/tex]
Explanation:
From the question we are told that
The distance of the target from the riffle is [tex]d = 40 \ m[/tex]
The height at which the bullet hit the target is [tex]y = 2.2 \ cm = 0.022 \ m[/tex]
Considering the vertical motion
Generally from kinematic equations we have that
[tex]y = u_y t + \frac{1}{2} * gt^2[/tex]
At the initial stage the velocity is zero i.e [tex]u_y = 0 \ m/s[/tex]
=> [tex]0.022 = 0 * t + \frac{1}{2} * 9.8 t^2[/tex]
=> [tex]t = 0.067 \ s[/tex]
Generally the velocity of the bullet when it leaves the riffle is mathematically represented as
[tex]u_x = \frac{ d}{t}[/tex]
=> [tex]u_x = \frac{40 }{ 0.067 }[/tex]
=> [tex]u_x = 597 \ m/s[/tex]
i just got hit on the head by a basketball.
story of my life.
Season Leaders
Go to Stats
Points Per Game
1.
Talen Horton-Tucker
26.0
2.
Nikola Jokic
26.0
3.
Zion Williamson
26.0
4.
Giannis Antetokounmpo
24.5
5.
Patty Mills
24.0
Rebounds Per Game
1.
Rudy Gobert
14.0
2.
Harry Giles III
13.5
3.
Clint Capela
13.0
4.
Nikola Vucevic
13.0
5.
Giannis Antetokounmpo
12.0
Assists Per Game
1.
Ja Morant
9.0
2.
Bam Adebayo
8.0
3.
T.J. McConnell
7.5
4.
DeMar DeRozan
7.0
5.
Spencer Dinwiddie
7.0
More Leaders
Hustle Leaders
Advanced Leaders
All Time Leaders
How large a net force is required to accelerate a 1,586-kg SUV from rest to a speed of 10.4 m/s in a distance of 212 m?
Answer:
F = 404.6 N
Explanation:
Mechanical Force
According to the second Newton's law, the net force exerted by an external agent on an object of mass m is:
F = m.a
Where a is the acceleration of the object.
On the other hand, the equations of the Kinematics describe the motion of the object by the equation:
[tex]v_f=v_o+a.t[/tex]
Where:
vf is the final speed
vo is the initial speed
a is the acceleration
t is the time
Another useful equation for speeds and distance X is:
[tex]V_f^2=V_o^2+2aX[/tex]
To calculate the acceleration, we solve for a:
[tex]\displaystyle a=\frac{V_f^2-V_o^2}{2X}[/tex]
The SUV starts from rest (vo=0) to vf=10.4 m/s traveling a distance of X=211 m, thus the acceleration is:
[tex]\displaystyle a=\frac{10.4^2-0^2}{2(212)}[/tex]
[tex]\displaystyle a=\frac{108.16}{424}[/tex]
[tex]a=0.26 \ m/s^2[/tex]
The force needed to accelerate the SUV of mass m=1,586 Kg is:
F = 1,586*0.26
F = 404.6 N
calculate the force necessary to keep a mass of 2 kg moving on a circular path of radius 0.2 m with a period of 0.5 second. what is the direction of this force
A little girl pushes a 5.0 kg toy baby stroller at constant speed 7.0 m across the floor. She pushes on the handle with a force of 40 N at an angle of 30o with the horizontal. All parts are 4 points each.
Complete Question
1 a A little girl pushes a 5.0 kg toy baby stroller at constant speed 7.0 m across the floor. She pushes on the handle with a force of 40 N at an angle of 30o with the horizontal. How much work is done by the girl on the wagon?
1b A farmhand pushes 20 ㎏ bale of hay 4m across the floor of the barn if she exerts a horizontal force of 60 N on the hay, how much work is done? (5 pts)
All parts are 4 points each
Answer:
1a
[tex]W = 242.5 \ J[/tex]
1b
[tex]W = 240 \ J[/tex]
Explanation:
Considering question a
From the question we are told that
The mass of the toy baby stroller is [tex]m = 5.0 \ kg[/tex]
The distance covered is [tex]d = 7.0\ m[/tex]
The force the girl applies on the handle is [tex]F = 40 \ N[/tex]
The angle at which this force is applied is [tex]\theta = 30^o[/tex]
Generally the workdone is mathematically represented as
[tex]W = F_x * d[/tex]
Here [tex]F_x[/tex] is the force along the horizontal axis , this is mathematically represented as
[tex]F_x = F cos (\theta )[/tex]
=> [tex]F_x = 40 * cos(30 )[/tex]
=> [tex]F_x = 34.64 \ N[/tex]
So
[tex]W = 34.64 * 7[/tex]
=> [tex]W = 242.5 \ J[/tex]
Considering question b
From the question we are told that
The mass of the toy baby stroller is [tex]m = 20 \ kg[/tex]
The distance covered is [tex]d = 4 \ m[/tex]
The force the girl applies on the handle is [tex]F = 60 \ N[/tex]
Generally the workdone is mathematically represented as
[tex]W = F * d[/tex]
=> [tex]W = 60 * 4[/tex]
=> [tex]W = 240 \ J[/tex]
Can you help with this question please thanks
Answer:
no .the blue runner began 16 m ahead of the red runner
What kind of energy is produce when sun reaches solar panel?
Answer:
Radient to ElEcTrIcAAl
Explanation:
The FitnessGram Pacer Test is a multistage aerobic capacity test that progressively gets more difficult as it continues. The 20 meter pacer test will begin in 30 seconds. Line up at the start. The running speed starts slowly, but gets faster each minute after you hear this signal. A single lap should be completed each time you hear this sound. Remember to run in a straight line, and run as long as possible.
what are the very small particles that make up matter
Answer:
The very small particles that make up matter are I) Atoms
Matter - Anything that have mass and occupies space is called matter . it is made up of atoms and molecules
Atoms - The smallest part of matter is called atom.
Molecule - Group of atoms combine together to form a molecule.
More to know - Atom is made up of even smaller particles called neutron, proton and electron. Electron moves around nucleus ( nucleus is made up of neutron and proton) Different types of atom combine and form molecule ( Nitrogen dioxide No2 has 1 atom of nitrogen and 2 atoms of oxygen)which is NOT true of the Big Bang Theory?
1. it explains what’s happening in the universe now
2. it explains what caused the big bang.
3. it explains what the universe was like in the beginning
4. it stages that the universe is expanding
Answer:
1. it explains what's happening im the universe now
Which term best describes the motion of the rope particles in relation to the motion of the rope wave shown in the photograph
Answer:
A: Perpendicular
Explanation:
The question is incomplete as it lacks the image of the rope wave motion.
However, as found on "estudyassistant", the options are;
A) Perpendicular
B) Circular
C) Longitudinal
D) Parallel
From all that, we can say that;
The rope's are moving simultaneously in the same pattern without touching each other.
This is therefore a mechanical wave being created with the motion having oscillations that are perpendicular to the direction of energy transfer of the ropes.
This is a definition of transverse waves because the rope particle motion is perpendicular to the wave motion.
Answer:
A: Perpendicular
Explanation:
Read above explanation.
А
Each sentence describes potential and kinetic energy
at various locations on a slide. Complete each
statement by selecting the position of the object on the
slide.
An object at position has all kinetic energy
An object at position has all potential energy
An object at position has about half potential energy
and half kinetic energy.
B
с
Answer:
C. A. B.
Explanation:
Credit to Lainey in the comments for the answer!
Answer:
1] C
2] A
3] B
Explanation:
PLEASE HELP! what kind of electricity does electrical heat burners make
Answer:
Electrical to Thermal
Wavelength is a measurement of ___________ , while period is a measurement of ___________ . *
Speed; time
Time; speed
Distance; time
Time; distance
Distance; speed
Speed; distance
distance ; time
Explanation:
wavelength is in metres [m]
period is in seconds [s]