Three objects of identical shape and mass, m, are attached to a rod of length l and negligible mass its moment of inertia is ML^2/2.
Mass of object = m
Distance between them=l
objects have equal mass so center of mass will be at the axis
Distance of object from center of mass d=l/2
Moment of inertia=mass *distance between them^2
Total momentum of inertia = moment of inertia of object 1
+ moment of inertia of object 1
I=Md^2+Md^2
I=M(L/2)^2+M(L/2)^2
I=ML^2/2
Moment of inertia, is a quantitative measure of the rotational inertia of a body—i.e., the opposition that the body exhibits to having its speed of rotation about an axis altered by the application of a torque (turning force). The axis may be internal or external and may or may not be fixed depending on the situation.
SI unit: kg⋅m2
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A ball with an initial velocity of 9.6 m/s rolls up a hill without slipping.
a)Treating the ball as a spherical shell, calculate the vertical height it reaches in m. b) Repeat the calculation for the same ball if it slides up the hill without rolling in m.
(a) The vertical height (the ball with an initial velocity of 9.6 m/s rolls up a hill without slipping) reaches = 7.836 m
(b) The calculation for the same ball if it slides up the hill without rolling in = 4.70 m
As the ball begins to roll up the hill, its kinetic energy begins to change into gravitational potential energy, and by the time it reaches its maximum height on the hill, it has been completely converted into gravitational potential energy. Because the ball is rolling up, it has both translational and angular kinetic energy: As a result of energy conservation, we have:
Potential energy = Kinetic energy trans + Kinetic energy rotation
mgh = ½ mv² + ½ Iw²
Hence,
(a) the vertical height:
h = 5v² / 6g
= 5 (9.6)² / (6 x 9.81)
= 460.8 / 58.8
= 7.836 m
(b) If the ball slide up without rolling, it means the angular velocity is zero.
Hence,
h' = v² / 2g
= (9.6)² / (2 x 9.8)
= 92.16 / 19.6
= 4.70 m
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Two identical loudspeakers 1.75 m apart are emitting sound waves into a room where the speed of sound is 340 m/s. Boss Hog is standing 4.5 m in front of one of the speakers, perpendicular to the line joining the speakers. A. How far from the other speaker is Boss Hog? (This is a geometry question.) B. If Boss Hog hears a maximum in the sound intensity, indicating constructive interference, what is the lowest possible frequency of the sound? C. If he hears no sound at that location, what is the lowest possible frequency the speakers are playing that can heard by a human?
A) The other speaker is 4.83 m from the Boss hog, B) Lowest possible frequency heard by Boss Hog is 1030.3 Hz, C) Lowest possible frequency if he hears no sound is 515.2 Hz.
Distance between two speakers = 1.75 m
Distance between Boss Hog from one speaker, = 4.5 m
Distance of other speaker from Boss Hog, d = √(1.75² + 4.5²) = 4.83 m
Path length difference, L = 4.83 - 4.5 = 0.33 m
For constructive interference, L = nλ
0.33 = 1 × λ [For lowest frequency, n=1]
So the lowest frequency f₁ = speed/wavelength = 340/0.33
f₁ = 340/0.33 = 1030.3 Hz
For destructive interference, L = (n + 1/2)λ
0.33 = 1/2 × λ [For lowest possible frequency, n= 0]
λ = 0.33/0.5 = 0.66
So lowest frequency, f₂ = 340/0.66 = 515.2 Hz
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A 10g bullet moving 70ms-¹ penetrate a block of wood 5cm before stopping determine the kinetic energy of the bullet, the average stopping force
Answer:
-490 Newtons
Solution:
The work is attached
Label the locations on the Earth where high tides and low tides would be found relative to the position of the Moon. The Earth rotates in a counterclockwise manner when viewed from above the North Pole. Begin by labeling the location closest to the Moon.
Starting from top and moving clockwise:
First low tide
Second High Tide
Second Low Tide
First High Tide
Starting from top and moving clockwise:
First low tide
Second High Tide
Second Low Tide
First High Tide
When and where do high and low tides occur?
They are caused by the moon’s and, to a lesser extent, the sun’s gravitational influences on the earth. A high tide occurs when the highest point of the wave, or the crest, hits a coast. A low tide occurs when the lowest point, or the trough, hits a coast.
The world’s highest tides may be found in Canada near the Bay of Fundy, which connects New Brunswick and Nova Scotia. With tidal ranges of over 30 feet, the highest tides in the United States may be found around Anchorage, Alaska. Tidal highs and lows are affected by a variety of variables.
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1. Define the law of conservation of momentum in your own words.
2. Which of Newton's laws explains how momentum is conserved in all interactions between objects?
3. What do you know about the forces involved in an interaction between two objects?
4. Is momentum a vector or a scalar quantity? Based on your answer, which other value is important
besides the numerical value of momentum?
5. How do you find the total momentum of objects in a system?
6. If objects are traveling in opposite directions, what do you know about the signs of their momenta?
7. What characteristics are required for a system to be considered closed and isolated?
8. What forces are considered when we examine interactions between two objects in a closed, isolated
system?
9. If two objects begin at rest, what is the total momentum of the system before they push off from one
another? What is the momentum of the system after they push off from one another?
1. Total momentum of an isolated system before collision is always equal to total momentum after collision is called conservation of momentum.
2. Newton's third law explains how momentum is conserved in all interaction between objects.
3. Force is an unopposed interaction between two or more bodies that apply the shift in the objects state of motion. The action and reaction are two interacting forces that we called as Newton's third law of motion. There are two forces acting on two interacting objects in any interaction.
4. Momentum is a vector quantity and has the same direction as velocity. It is the product of mass (a scalar quantity) and velocity (a vector quantity).
5. To find total momentum of the system , add their individual momentums together. Calculate momentum for each object by using formula P=mv, where P is momentum, m is mass, v is velocity.
6. If the objects are travelling in opposite direction, then the overall momentum will be zero. They have same mass and velocity, when their momentum vectors add up to exactly zero when added together.
7. Closed system in which the exchange of only energy with its surroundings takes place. An isolated system in which no exchange of matter or energy takes place.
8. The internal forces are considered when we examine interaction between two objects in a closed and isolated system because these forces cause momentum of the system to be transferred between one object to another.
9. Before the push-off, the total initial momentum is zero. The total momentum after the push-off should also be zero.
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Calculate the magnitude of the electric field at the origin due to the following distribution of charges: -q at (x,y) = (a,a), -q at (a,-a), +q at (-a,-a) and +q at (-a,a). Where q = 3.95 × 10-7 C and a = 2.40 cm.
The magnitude of the electric field at the origin due to this distribution of charges is [tex]2.81 X 10^{5} N/C[/tex]
The electric field at the origin can be calculated using Coulomb's law
E = k * (q1/r1^2 + q2/r2^2 + q3/r3^2 + q4/r4^2),
where k is the Coulomb constant (9x10^9 Nm^2/C^2), q1, q2, q3, and q4 are the charges, and r1, r2, r3, and r4 are the distances from the origin to the charges.
By substituting the given values, we get:
r1 = r2 = sqrt((a^2)+(a^2)) = sqrt(2a^2) = sqrt(2) * a
r3 = r4 = sqrt((a^2)+(a^2)) = sqrt(2a^2) = sqrt(2) * a
q1 = q2 = -q = -3.95 × 10^-7 C
q3 = q4 = q = 3.95 × 10^-7 C
Hence, the magnitude of the electric field at the origin is:
E = k * ((-q1/r1^2) + (-q2/r2^2) + (q3/r3^2) + (q4/r4^2))
= 9x10^9 Nm^2/C^2 * ((-3.95 × 10^-7 C)/(sqrt(2) * a)^2 + (-3.95 × 10^-7 C)/(sqrt(2) * a)^2 + (3.95 × 10^-7 C)/(sqrt(2) * a)^2 + (3.95 × 10^-7 C)/(sqrt(2) * a)^2)
= 9x10^9 Nm^2/C^2 * ((-3.95 × 10^-7 C)/(2 * (a^2)) + (-3.95 × 10^-7 C)/(2 * (a^2)) + (3.95 × 10^-7 C)/(2 * (a^2)) + (3.95 × 10^-7 C)/(2 * (a^2)))
= 9x10^9 Nm^2/C^2 * (4 * 3.95 × 10^-7 C)/(2 * (2.40 cm)^2)
= (9x10^9 Nm^2/C^2) * (4 * 3.95 × 10^-7 C)/(2 * (0.024 m)^2)
= (9x10^9 Nm^2/C^2) * (4 * 3.95 × 10^-7 C)/(2 * 0.000576 m^2)
= (9x10^9 Nm^2/C^2) * (4 * 3.95 × 10^-7 C)/(0.001152 m^2)
=[tex]2.81 X 10^{5} N/C[/tex]
Therefore, the magnitude of the electric field at the origin due to this distribution of charges is [tex]2.81 X 10^{5} N/C[/tex].
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1) A bowling ball is rolling down a lane at a bowling alley. How can you know that a force has acted on the bowling ball?
a-by determining a change in the direction of the bowling ball as it rolls down the alley
b-by determining the direction of the bowling ball
c-by timing how long the bowling ball takes to reach the end of the lane
d-by measuring the mass of the bowling ball
2) What is the advantage of using a simple machine to do work?
a-A simple machine reduces the force needed to do the work.
b-A simple machine reduces the time needed to do the work.
c-A simple machine reduces the displacement required to do the work.
d-A simple machine reduces the work that has to be done.
3)Students measure how much work it takes to lift an object two meters. They use an inclined plane that is 3 meters long, an inclined plane that is 4 meters long, and a compound pulley. Which statement is correct?(1 point)
a-The 3-meter plane will require the least amount of work.
b-All three simple machines will require the same amount of work.
c-The compound pulley will require the least amount of work.
d-The 4-meter plane will require the least amount of work.
4) What is the advantage of using an inclined plane to move boxes into a truck?
a-You will use less force.
b-You will need to do less work.
c-You will walk less distance.
d-You will use less energy.
5) How can the mechanical advantage of a lever be calculated?
a-Divide the length of the effort arm by the length of the load arm.
b-Divide the length of the load arm by the length of the effort arm.
c-Divide the input force by the output force.
d-Divide the output distance by the input distance.
6) A student makes a class 1 lever to lift a box, but he finds that he cannot apply enough force to lift the box. How can he modify the lever to reduce the amount of force he needs?
a-He can lengthen the part of the lever he pushes on.
b-He can shorten the part of the lever he pushes on.
c-He can lengthen the part of the lever bearing the load.
d-He can use a taller fulcrum.
7) Using a class 1 lever, students lift a bucket of water 0.3 meters. They push on the lever a distance of 1.8 meters. If they use 312 Newtons of force, how much force would they need to lift the bucket without the lever?(1 point)
1,872 N
52 N
561.6 N
93.6 N
8) Which equation shows the relationship between work and energy?
a-W=Eo/Ei
b-W=Eo×Ei
c-W=ΔE
d-W=Eo+Ei
9) A gardener uses a lever to pry a rock out of the ground. She presses the lever down 0.9 meters and applies 30 Newtons of force. How much work does she do?(1 point)
a-29.1 J
b-27 J
c-270 J
d-30.9 J
10) A robot vacuum cleaner cleans the Potters’ front room. Which is the vacuum cleaner’s useful output energy?
a-electric energy that recharges the robot’s battery
b-thermal energy that warms the robot
c-kinetic energy that moves the robot and its brush
d-sound energy that makes a whirring noise
11) A worker uses a pulley to lift a bale of hay from a truck into a barn. If she expends 390 Joules of energy, and 358 Joules lift the box, what is the pulley’s efficiency?
a-91.8%
b-108.9%
c-0.918
d-8.2%
12) A worker uses a pulley to lift a bale of hay from a truck into a barn. If she expends 390 Joules of energy, and 358 Joules lift the box, what is the pulley’s efficiency?
a-8.2%
b-0.918
c-108.9%
d-91.8%
13) Nadia pushes a box up an inclined plane. She expends 2,000 Joules of energy, but only 1,540 Joules are applied to the box. What happens to the other 460 Joules of energy?
a-They are converted to other forms of energy.
b-They are destroyed.
c-They are transferred to another simple machine.
d-They are transferred back into Nadia.
14) Students invent a game that uses a lever to flip beanbags toward a target. How could they make the lever more efficient?
a-Make the target larger.
b-Use lighter beanbags.
c-Use a fulcrum with a sharper point.
d-Use a taller fulcrum.
1) by determining a change in the direction of the bowling ball as it rolls down the alley
2) A simple machine reduces the force needed to do the work.
3) The compound pulley will require the least amount of work.
4) You will need to do less work.
5) Divide the input force by the output force.
6) He can lengthen the part of the lever he pushes on.
7) 561.6 N
8) W=ΔE
9) -27 J
10) kinetic energy that moves the robot and its brush
11) 91.8%
12) -91.8%
13) They are converted to other forms of energy.
14) Use a fulcrum with a sharper point.
What is the mechanical advantage?Mechanical advantage is the ratio of output force to input force in a machine, used to determine its efficiency in doing work.
We know that the essence of the simple machine is that it helps to do more work in a short time.
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match the variable to its type. drag and drop options on the right-hand side and submit. for keyboard navigation...show more press space or enter to grab ordinal time spend studying for this class in hours press space or enter to grab nominal your federal tax bracket press space or enter to grab numerical the brand of your cell phone
The variable type is continuous then nominal then discrete and then again continuous and last ordinal again
Here, we must match the variable with the appropriate choices so that we may understand that a continuous variable is one that can take any value within a range.
Ordinal variables that can take only countable values in discrete orders and nominal variables that categorized data.
According to this it is clear that volume is continuous and leaf shape is nominal.
Count of grapes is discrete and time is continuous and fruit quality is ordinal.
According to the definition, qualitative data such as nominal and ordinal cannot have a numerical value.
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Enter an expression for the total time of flight of the ball: the time from when it is launched to when it lands back on the ground. Express this time in terms of vi and a. It suggested using the formula I entered for part c which was= ( vf2 - vi2 )/( 2a)
The expression for the total time of flight when the object is released from ground level is t = (2u sinθ ) / ( g ).
What is the expression for total time of flight?The expression for the total time of flight is calculated by applying second kinematic equation as shown below.
when the object is released from a height, h
h = vt + ¹/₂gt²
where;
h is the height of fall of the objectv is the initial vertical velocity of the objectg is acceleration due to gravityt is the time of flightwhen the object is released from ground level,
t = (2u sinθ ) / ( g )
where
u is the initial velocityθ is the direction of the velocityg is acceleration due to gravityThus, the time of flight of an object is the total time spent in air by the object.
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A skateboarder starts up a 3.0-m-long ramp at 4.0 m/s.
What is the maximum height of the ramp for which the skateboarder goes off the end rather than rolling back down?
Answer:
below
Explanation:
The Kinetic Energy (1/2 mv^2) is to be converted to the maximum Potential Energy ( mgh)
1/2 mv^2 = mgh divide through by m
1/2 v^2 = gh solve for 'h'
1/2 v^2 / g = h Plug in the numbers
1/2 (4^2)/9.81 = h = .815 m = 81.5 cm
In a race two horses start from rest and each maintains a constant acceleration. In the same elapsed time Silver Bullet runs 1.20 times farther than Shotgun. According to the equations of kinematics, which one of the following is true concerning the accelerations of the horses?
A. aSilver Bullet = 1.44 aShotgun
B. aSilver Bullet = aShotgun
C. aSilver Bullet = 0.72 aShotgun
D. aSilver Bullet = 2.40 aShotgun
E. aSilver Bullet = 1.20 aShotgun
According to the equations of kinematics, concerning the accelerations of the horses will be E. aSilver Bullet = 1.20 aShotgun.
ABOUT KINEMATICSKinematics is a part of physics that deals with motion. Then how can an object be said to move.
The answer is if the object changes position.
If we move position within a certain time we call it velocity. Then our speed changes every time we call it acceleration.
Position, velocity, and acceleration are quantities in physics that have a close relationship with kinematics.
This quantity is a vector quantity which has magnitude and direction. Kinematics itself has several types, namely motion kinematics and particle dynamics.
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Is tension the same on both sides of a rope?
The tension of an "ideal cord" that runs through an "ideal pulley" is the same on both sides of the pulley (and at all points along the cord).
Yes, the tension of an "ideal cord" that runs through an "ideal pulley" is the same on both sides of the pulley
What is force?It is the physical magnitude that expresses the effort necessary to move the mass of one kilogram with an acceleration of one meter per second squared, this is expressed in units of the international system in Newton.
We can tell that the tension is the magnitude of contact force between different segment of a string, rope or wire. As an ideal cord has zero mass and zero weight, the tension will be the same in all points along the cord.
The tension of a body could be expressed by:
T = mg + ma
Where:
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For the below figure, the coordinates of the particles are:
Q1 (-2, 0)
Q2 (2m, 0)
Q3 (0,2m)
01-02-1nC
Determine the charge magnitude for Q3 to ensure the net force on Q3 is facing down the Y axis with a net magnitude of 5.9 Micro N
Q3
D
Y axis
08
x axis
Answer:
To determine the charge magnitude for Q3, we need to use Coulomb's Law, which states that the force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them.
The net force on Q3 is given as F_net = F_12 + F_13 + F_23
The force between Q1 and Q3 is given as F_13 = (1/(4πε)) * (Q1*Q3)/(D^2)
The force between Q2 and Q3 is given as F_23 = (1/(4πε)) * (Q2*Q3)/((2m-D)^2)
The force between Q1 and Q2 is given as F_12 = (1/(4πε)) * (Q1*Q2)/(2m)^2
where ε is the electric constant and D is the distance between Q3 and Q1 along the Y-axis
By equating the net force to the given value of 5.9 Micro N we can solve for Q3.
Explanation:
Above
A particle travels between two parallel vertical walls separated by 23 m. It moves toward the opposing wall at a constant rate of 9.6 m/s. It hits the opposite wall at the same height. a=9.8. What will be its speed when it hits the opposing wall? At what angle with the wall will the particle strike?
The particle is moving toward the wall and is being deflected at the same time.
What is Vertical walls?The time to reach the wall will be 18.4/7.2 =2.56 sec. The direction of the acceleration is not specified but since the ask for how high we will assume it is upward. S=1/2 at^2 t= 2.56.
s = 0.5X 1.7 m/s 2 x 2.56*2.56 = 5.5 meters. Two velocities on x one way the up velocity is 1.7*2.56 = 4.3 m/s or the arctan of 4.3/7.2 =30.8 degrees.
Vertical gardens, sometimes known as "green walls," are large-scale plant arrangements that are affixed to wall-mounted structures. They serve as an effective ornamental element while also being quite practical because they improve the indoor air quality and the comfort level of the surrounding area.
Therefore, The particle is moving toward the wall and is being deflected at the same time.
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Determine the resultant internal loadings in the beam at cross sections through points D and E. Point E is just to the right of the 16-kN load.Shear ForceShear force is the total effective force or resultant force vertical to the shaft or beam. Normal force is perpendicular to the shear force. The magnitude of the shear force depends on the vertical load applied to the beam.
The resultant internal loadings in the beam at cross sections through point D and E are 15.12 kN upwards and 34.88 kN upwards respectively.
To calculate the internal loading at point D and E, first we need to calculate the support reaction at A and C, by taking the moment about reaction A.
R₁ + R₂ = 25×4 + 15 = 115 kN
R₂ × 7 = 15 × 5.5 + 100 × (4×2/3)
R₂ = 349.167/7 = 49.88
R₁ = 115 - 49.88 = 65.12 kN
Internal loading at D = 65.12 - 25×2 = 15.12 kN upwards
Internal loading at E = 49.88 - 15 = 34.88 kN upwards
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--The given question is incomplete, the complete question is:
"Determine the resultant internal loadings in the beam at cross sections through points D and E in the given figure. Point E is just to the right of the 15-kN load."--
From a stationary hot-air balloon 500 feet above the ground, two sightings of a lake are made (see the figure). How long is the lake?
The length of the lake is 839.1 ft, if the height of the hot-air balloon is 500 ft.
Angle of depression of the farthest end, θ₁ = 25°
Angle of depression of the nearest end, θ₂ = 65°
Height of the balloon, h = 500 ft
The distance between the bottom of the balloon and the farthest end of the lake, x = 500/tan25 = 1072.25 ft
The distance between the bottom of the balloon and the nearest end of the lake, y = 500/tan65 = 233.2 ft
The length of the lake, l = 1072.25 - 233.2 = 839.1 ft
--The given question is incomplete, the complete question is:
"From a stationary hot-air balloon 500ft above the ground, two sightings of a lake are made. One at the farthest end of the lake at an angle of depression of 25 degrees and another at the nearest end of the lake at an angle of depression of 65 degrees. How long is the lake?"--
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The half-life of a radioactive material is the time required for an amount of this material to decay to one-half its original value. Show that for any radioactive material that decays according to the equation Q? = -rQ, the half-life tau and the decay rate r satisfy the equation rtau = ln 2.
The half-life of a radioactive material is the time required for an amount of this material to decay to one-half its original value. The half-life tau and the decay rate r satisfy the equation r tau = ln 2.
Given the equation Q' = -rQ, where Q is the amount of the radioactive material present at time t and r is the decay rate.
The half-life tau is defined as the time it takes for the amount of the material to decay to one-half its original value, which can be expressed as:
Q(tau) = Q(0)/2, where Q(0) is the initial amount of the material.
Substituting into the decay equation and solving for tau, we get:
-rQ(tau) = -r(Q(0)/2)
-r(Q(0)/2) = -rQ(0)/2
ln(Q(0)/2) = -r tau
ln 2 = -r tau
r tau = ln 2
Therefore, the half-life tau and the decay rate r satisfy the equation rtau = ln 2.
Half-life is the amount of time it takes for half of the radioactive atoms in a sample to decay. It is a characteristic property of a radioactive substance and is used to describe its decay over time. The half-life of a radioactive material is the time required for half of the original amount of the material to decay. This property can be used to determine the age of ancient artifacts, to determine the age of rocks and minerals, and to predict the behavior of radioactive isotopes in various applications, such as medicine and power generation.
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A voltage drop test can find excessive resistance in a circuit that may not be detected using an ohmmeter.TrueFalse True
It is accurate to say that a voltage drop test might uncover excessive resistance in a circuit that an ohmmeter could miss.
Does a voltage decrease indicate resistance?Voltage drop in electronics is the decline in electric potential along a current's path as it flows through a circuit. Because some of the energy supplied is lost, voltage drops between conductors, contacts, and connectors are undesired.Voltage drop testing is a straightforward but efficient diagnostic technique to find high-resistance issues in a circuit rapidly. The voltage drop across a load, device, or conductor can be measured using the DC voltage scale on your Digital Volt Ohm Meter (DVOM) or Digital Multi-meter.It is accurate to say that a voltage drop test might uncover excessive resistance in a circuit that an ohmmeter could miss.To learn more about voltage drop test refer to:
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three cables are used to tether a balloon as shown. determine the vertical force p exerted by the balloon at a knowing that the tension in the cable ad is 481 n.
The vertical force p exerted by the balloon is 926 N.
What is Velocity ?
Velocity is a vector quantity that describes the rate of change of an object's position. It is equal to the displacement of an object divided by the time interval over which the displacement occurred. Velocity has both magnitude and direction, and its units are typically meters per second (m/s). The velocity of an object can change over time due to acceleration, and if an object is moving in a circular path, it also has a component of velocity perpendicular to its direction of motion, known as centripetal velocity.
[tex]$$Tensions in vector form are;$$\begin{aligned}& \vec{T}_{A B}=T_{A B}\left[\frac{\vec{r}_{A B}}{\left|r_{A B}\right|}\right] \\& \Rightarrow \vec{T}_{A B}=T_{A B}\left[\frac{-4.20 \hat{i}-5.60 \hat{j}}{\sqrt{4.20^2+5.60^2}}\right] \\& \Rightarrow \vec{T}_{A B}=-0.6 T_{A B} \hat{i}-0.8 T_{A B} \hat{j}\end{aligned}$$and[/tex]
[tex]$$\begin{aligned}& \vec{T}_{A C}=T_{A C}\left[\frac{\vec{r}_{A C}}{\left|r_{A C}\right|}\right] \\& \Rightarrow \vec{T}_{A C}=T_{A C}\left[\frac{2.40 \hat{i}-5.60 \hat{j}+4.20 \hat{k}}{\sqrt{2.40^2+5.60^2+4.20^2}}\right] \\& \Rightarrow \vec{T}_{A C}=0.3243 T_{A C} \hat{i}-0.7568 T_{A C} \hat{j}+0.5676 T_{A C} \hat{k}\end{aligned}\\\\and[/tex]
[tex]\begin{aligned}& \vec{T}_{A D}=T_{A D}\left[\frac{\vec{r}_{A D}}{\left|r_{A D}\right|}\right] \\& \Rightarrow \vec{T}_{A D}=(481)\left[\frac{-5.60 \hat{j}-3.30 \hat{k}}{\sqrt{5.60^2+3.30^2}}\right] \\& \Rightarrow \vec{T}_{A D}=-414.4 \hat{j}-244.2 \hat{k}\end{aligned}$$[/tex]
[tex]$$Vertical force at $A$ is:$$\vec{F}_A=F_A \hat{j}$$[/tex]
[tex]$$By equilibrium of $z$-forces ( $k$ components);$$\begin{aligned}& \sum F_2=0 \\& \Rightarrow 0.5676 T_{A C}-244.2=0 \\& \Rightarrow T_{A C}=430.2571 \mathrm{~N}\end{aligned}$$[/tex]
[tex]$$By equilibrium of $x$-forces (i components);$$\begin{aligned}& \sum F_x=0 \\& \Rightarrow-0.6 T_{A B}+0.3243 T_{A C}=0 \\& \Rightarrow-0.6 T_{A B}+0.3243(430.2571)=0 \\& \Rightarrow T_{A B}=232.5714 \mathrm{~N}\end{aligned}$$By equilibrium of $y$-forces (j components):$$\begin{aligned}& \sum F_y=0 \\& \Rightarrow-0.8 T_{A B}-0.7568 T_{A C}-414.4+F_A=0 \\& \Rightarrow-0.8(232.5714)-0.7568(430.2571)-414.4+F_A=0 \\& \Rightarrow F_A=926 \mathrm{~N}\end{aligned}$$[/tex]
Thus, the vertical force p exerted by the balloon is 926 N.
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which one of the following statements concerning the electric field is false? the si unit of the electric field is the newton per meter (n/m). the magnitude of the electric field at a particular location due to a particular charged particle is inversely proportional to the square of the distance of the particle from that location. at a given point, a charged particle will experience a force, if an electric field is present at that location. if a positively charged particle is placed at a location where the electric field is directed due north, it will be accelerated due north. the electric field is a vector quantity.
The statement that is false is:
"if a positively charged particle is placed at a location where the electric field is directed due north, it will be accelerated due north."
A charged particle will experience a force in the direction of the electric field, but it may not necessarily be accelerated in the same direction. The acceleration of a charged particle depends on other factors such as the mass of the particle, the strength of the electric field, and any other forces acting on the particle. So, a positively charged particle may not be accelerated due north, even if the electric field is directed due north. The electric field is a fundamental concept in physics and is used to describe the force that a charged particle experiences in a given electric field. It is a vector quantity that represents the force per unit charge and is defined as the force that a charged particle would experience if placed at a given point in space.
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when a ball thrown straight upwards reaches the very top of its path, its magnitude of acceleration is
when a ball thrown straight upwards reaches the very top of its path, its magnitude of acceleration is equal to acceleration due to gravity (g).
What is a Freely Falling Body?
A body is considered to be falling freely when it is dropped from a height under the influence of earth's gravity without being given any initial velocity.The body has no starting velocity.The body is subjected to an acceleration that is downward and equal to the earth's gravitational pull.The gravitational attraction of the earth causes the ball to become stationary when it reaches the highest point. When it eventually comes back, the speed is equivalent to the speed of gravity.Free fall causes an item to accelerate by -9.8 m/s². Free fall is any motion of a body in which gravity is the only force acting on it according to Newtonian mechanics. A body in free fall experiences no force according to general relativity, which reduces gravitation to a space-time curvature.To learn more about Free Fall from the given link
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The magnetic structure of figure 1.21 was built with cast steel. As the final flux density is low, the relative magnetic permeability may be taken as 1000.
determine: a. the reluctance of all legs of the structure;
Magnets are one of the objects that are widely used in human life today, because of their ability to attract metal so that they can be used in everyday life. Magnets can be used in making electric motors, power plants and so on.
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John Glenn's 1300 kg Mercury capsule orbited at 7800 m/s (Eastward) velocity, before retrorockets pushed westward: 4450 N for 5 s, 8900 N for 10 s, 4450 N for 5s.
b) what was the total Impulse from the retro-rockets?
b) what was the quickest acceleration caused by the retrorockets? (ignore gravity here)
Answer:
b) The total impulse from the retro-rockets is the sum of the impulse from each individual engine firing. The impulse from each firing is the force applied multiplied by the duration of the firing. Therefore, the total impulse is (4450 N x 5 s) + (8900 N x 10 s) + (4450 N x 5 s) = 22,250 Ns + 89,000 Ns + 22,250 Ns = 133,500 Ns.
b) The quickest acceleration caused by the retrorockets is the change in velocity divided by the duration of the retrorocket firing. Since the retrorocket firing is done in three stages, we need to find the acceleration for each stage and then take the maximum value. The first stage acceleration is (4450 N)/(1300 kg)= 3.4 m/s^2, the second stage acceleration is (8900 N)/(1300 kg)= 6.8 m/s^2, the third stage acceleration is (4450 N)/(1300 kg)= 3.4 m/s^2. So the quickest acceleration is 6.8 m/s^2.
suppose the mass of a fully loaded module in which astronauts take off from the moon is 11,500 kg. the thrust of its engines is 26,000 n. (assume that the gravitational acceleration on the moon is 1.67 m/s2.) (a) Calculate its the magnitude of acceleration in a vertical takeoff from the Moon. (b) Could it lift off from Earth? If not, why not? If it could, calculate the magnitude of its acceleration.
Vertical takeoff from the moon will experience an acceleration of 0.6 m/s2. No, it couldn't leave the ground and launch.
Determination of magnitude of acceleration:Upward force = 26000 N
Mass of the module = 11,500 kg
Now, acceleration = 26000/11500 - 1.67
Therefore, acceleration = 0.6 m/s²
Why was it unable to fly off the ground from earth?They would accelerate at a negative 7.54 meters per second squared if they were on Earth, where the acceleration would be calculated as follows: 26,000 kg divided by 11,500 kg minus 9.8 meters per second squared. They would therefore not be able to escape the Earth if they were in the air near it since the acceleration would be downward and in the direction of the Earth.
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Three charged particles are located at the positions shown below. Find the total force on sphere B please.
As depicted in an equilateral triangle has three charged particles at each corner. Ion refers to an atom with a charge on it.
How do charged particles work?
The negatively charged components of an atom are called electrons. A typical atom is nonpolar because the negative electrode of its electrons balance the charge of its protons with in atomic nucleus. Ions are created when an atom receives or loses an electron. A positive charge is created when an atom loses an electron, and a negative charge is created when it gets an electron.
Ions are what?
An ion is an electrical charges atom or molecule that is created when an electron is lost or gained. Cation refers to the ion created when an electron is lost. For instance, magnesium ion (Mg2+)
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A car travels at 75 km/h on a level road in the positive direction of an x axis. each tire has a diameter of 69 cm. relative to a woman riding in the car, what are the following values?
(a) the velocity v at the center of each tire
( __ m/s)
(b) the velocity v at the top of each tire
( ___ m/s)
(c) the velocity v at the bottom of each tire
( __m/s)
(d) the magnitude a of the acceleration at the center of each tire
__m/s2
(e) the magnitude a of the acceleration at the top of each tire
__m/s2
(f) the magnitude a of the acceleration at the bottom of each tire
__m/s2
Relative to a hitchhiker sitting next to the road, what are the following values?
(g) the velocity v at the center of each tire
( __ m/s)
(h) the velocity v at the top of each tire
( __m/s)
(i) the velocity v at the bottom of each tire
( __m/s)
(j) the magnitude a of the acceleration at the center of each tire
__m/s2
(k) the magnitude a of the acceleration at the top of each tire
__ m/s2
(l) the magnitude a of the acceleration at the bottom of each tire
__ m/s2
The conversion factor from km/h to m/s is 1000/3600 m/s/km/h.
So, the velocity of the car relative to the woman riding in the car is 75 km/h x (1000/3600 m/s/km/h) = 20.83 m/s.
(a) The velocity at the center of each tire is the same as the velocity of the car relative to the woman riding in the car, which is 20.83 m/s.
(b) The velocity at the top of each tire is 20.83 m/s + (π x (69/2) cm x 2π radians/s /s) = 20.83 m/s + 27.77 m/s = 48.60 m/s.
(c) The velocity at the bottom of each tire is 20.83 m/s - (π x (69/2) cm x 2π radians/s /s) = 20.83 m/s - 27.77 m/s = -6.94 m/s.
(d) The acceleration at the center of each tire is 0 m/s2.
(e) The acceleration at the top of each tire is (π x (69/2) cm x 2π radians/s^2) = 869.68 m/s^2.
(f) The acceleration at the bottom of each tire is - (π x (69/2) cm x 2π radians/s^2) = -869.68 m/s^2.
Relative to the hitchhiker sitting next to the road, the velocity of the car is negative, i.e., -20.83 m/s.
(g) The velocity at the center of each tire relative to the hitchhiker is -20.83 m/s.
(h) The velocity at the top of each tire relative to the hitchhiker is -20.83 m/s + 27.77 m/s = -6.94 m/s.
(i) The velocity at the bottom of each tire relative to the hitchhiker is -20.83 m/s - 27.77 m/s = -48.60 m/s.
(j) The acceleration at the center of each tire relative to the hitchhiker is 0 m/s2.
(k) The acceleration at the top of each tire relative to the hitchhiker is 869.68 m/s^2.
(l) The acceleration at the bottom of each tire relative to the hitchhiker is -869.68 m/s^2.
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What conclusion does the student most likely make based on this data?
The conclusion that the student will most likely make based on this data is that tightly packed particles in solids slow down the light waves, however, sound waves make particles bounce into each other, so they travel faster in solids which is denoted as option D.
What is a Wave?This is referred to as a propagation of disturbances from place to place in a regular and organized way.
Sound waves make particles bounce into each other, so they travel faster in solids and is as a result of the vibrations of kinetic energy which move along by being passed from one molecule to another thereby making option D the correct choice
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The full question:
What conclusion does the student most likely make based
on this data?
Light waves always travel the same speed; however, the speed of sound is determined by the medium that it travels throughAll sound waves always have the same energy, so the temperature of the medium does not affect wave speed.Light needs to vibrate particles, so it travels fastest in tightly packed solids, while sound does not need a medium, so it travels fastest in a gas.Tightly packed particles in solids slow down the light waves, however, sound waves make particles bounce into each other, so they travel faster in solids.a 2.00-kg ball a moves at 3.00 m/s toward the right. it collides elastically with a 4.0-kg ball b that is initially at rest. the velocities of the balls after the collisions are
The velocity of ball a after the collision is 1.33 m/s and the velocity of ball b after the collision is 1.67 m/s.
The velocity of the balls after the impact may be calculated using the momentum conservation rule.
The system's momentum before the collision equals the system's momentum after the impact.
Each ball's momentum before the contact is determined by its mass and velocity.
Let us refer to the velocity of ball a following the collision as va' and the velocity of ball b following the collision as vb'.
The law of conservation of momentum may thus be stated as follows:
m1 * v1 + m2 * v2 = m1 * v1' + m2 * v2'
where m1 is the mass of ball a, v1 is its velocity before the collision,
m2 is the mass of ball b, and
v2 is its velocity before the collision.
Since ball b was initially at rest, v2 = 0 m/s.
Plugging in the given values, we get:
2.00 kg * 3.00 m/s + 4.00 kg * 0 m/s
= 2.00 kg * va' + 4.00 kg * vb'
Solving for va' and vb', we get:
va' = (4.00 kg * 0 m/s + 2.00 kg * 3.00 m/s) / (2.00 kg + 4.00 kg)
= 1.33 m/s
vb' = (2.00 kg * 3.00 m/s) / (2.00 kg + 4.00 kg)
= 1.67 m/s
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At the core of all examples of Pavlovian conditioning is:Please choose the correct answer from the following choices, and then select the submit answer button. A.rewards.
B.association..
C.punishments.
D.neurogenesis.
At the core of all examples of Pavlovian conditioning is association. So option B is correct.
Pavlovian conditioning, also known as classical conditioning, is a type of learning that occurs when a neutral stimulus becomes associated with a stimuli that naturally evokes a response, such as food or a sound. The neutral stimulus becomes a conditioned stimulus and elicits the same response as the natural stimulus.
This process occurs through the repeated pairing of the two stimuli, and the formation of an association between them. The core of all examples of Pavlovian conditioning is therefore the establishment of an association between two stimuli, leading to a learned response.
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If you throw a ball straight downward (in the absence of air resistance), after leaving your hand its acceleration isSelect one:a. less than 10 m/s2.b. greater than 10 m/s2.c. 10 m/s2.
After the ball leaved the hand its acceleration is: 10 m/s2
What is vertical launch?In physics vertical launch is the motion described by an object that has been launched vertically in which the acceleration is the earth's gravitational force.
In the vertical launch downward movements, the acceleration due to the gravity is always acting downward and its value is 10 m/s2, this is because of attraction that the earth exerts on all bodies pulling them toward its center
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