A metal bar is in the xy-plane with one end of the bar at the origin, [tex]\[r = (3.87 \, \text{m}) \mathbf{i} + (3.21 \, \text{m}) \mathbf{j}\][/tex], [tex]\theta\approx 55.16^\circ\][/tex], magnitude of torque is 22.58 Nm.
a) Position Vector r can be calculated as:
Given:
[tex]\(x = 3.87 \, \text{m}\)[/tex]
y = 3.21 m
The position vector r for the point where the force is applied is:
[tex]\[r = (3.87 \, \text{m}) \mathbf{i} + (3.21 \, \text{m}) \mathbf{j}\][/tex]
b) Magnitude of Torque can be calculated as:
Magnitude of r:
[tex]\[|r| = \sqrt{(3.87 \, \text{m})^2 + (3.21 \, \text{m})^2} \approx 5.019 \, \text{m}\][/tex]
Magnitude of F:
[tex]\[|F| = \sqrt{(6.82 \, \text{N})^2 + (-3.24 \, \text{N})^2}\\\\ \approx 7.610 \, \text{N}\][/tex]
Calculate the dot product of r and F:
[tex]\[r \cdot F = (3.87 \, \text{m}) (6.82 \, \text{N}) + (3.21 \, \text{m}) (-3.24 \, \text{N})\\\\ \approx 16.658 \, \text{N} \cdot \text{m}\][/tex]
Calculate the angle [tex]\(\theta\)[/tex] using the dot product and magnitudes:
[tex]\[\cos(\theta) = \frac{r \cdot F}{|r| \cdot |F|} \\\\= \frac{16.658 \, \text{N} \cdot \text{m}}{(5.019 \, \text{m})(7.610 \, \text{N})}\\\\ \approx 0.5526\][/tex]
[tex]\[\theta \approx \cos^{-1}(0.5526)\\\\ \approx 55.16^\circ\][/tex]
Now calculate the magnitude of the torque using the sine of the angle:
[tex]\[|\tau| = |r| \cdot |F| \cdot \sin(\theta)\\\\ = (5.019 \, \text{m}) (7.610 \, \text{N}) \sin(55.16^\circ)\\\\ \approx 22.58 \, \text{N} \cdot \text{m}\][/tex]
c) Direction of Torque:
According to the right-hand rule, the torque points either into or out of the plane formed by r and F. Its direction is perpendicular to that plane. The sign of the angle determines the precise orientation.
In this case, since [tex]\(\theta \approx 55.16^\circ\)[/tex] is positive (counterclockwise rotation), the torque points out of the plane formed by r and F.
Thus, the direction of the torque is outward from the xy-plane.
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Your question seems incomplete, the probable complete question is:
A metal bar is in the xy-plane with one end of the bar at the origin. A force F=(6.82)i+ -3.24j is applied to the bar at the point x=3.87m , y=3.21m .
What is the position vector r for the point where the force is applied?
a Express your answer in terms of the unit vectors i and j .
b What are the magnitude of the torque with respect to the origin produced by F?
c What are direction of the torque with respect to the origin produced by F?
7. Why are cooking pans made of aluminum? {Explain using the specific heat value of
aluminum} it conducts heat well high thermal energy
How many ounces in a cup?
Answer:
8 oz
Explanation:
what is the frequency of a light wave that has a wavelength of 0.039 m?
Answer:
Convert your wavelength into meters. Divide the speed of light, ~300,000,000 m/s, by the wavelength in m. This gives you the wave's frequency
Explanation:
What is the direction of the normal contact force of the road on the wheels?
Tick one box.
Down
Left
Right
Up
The direction of the normal contact force of the road on the wheels is : ( B ) Left
Contact force
The contact force of the road on the wheels will act in a direction opposite to the movement of the wheel on the road. therefore as the wheel moves forward ( right ), the contact force will move backwards ( left ) of the direction of motion.
Hence we can conclude that the direction of the normal contact force of the road on the wheels is : ( B ) Left
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does a five pound ball weigh more or less 40000 miles above sea level
It would weigh less bc the higher you are the less gravity there is.
(What
pressure does water
exert at the bottom of
the container in the
Water
(1000 kg/m)
5m
adjoining figure?) (g
=9.8 m/s2)
Answer:
49,000 Pa
Explanation:
Pressure in liquid=depth x density x g
= 5 x 1000 x 9.8
= 49,000Pa
What happens to force when two charges move away?
If the distance between the two charges is doubled, the attraction or repulsion becomes weaker.
Explanation:
At a distance of 1.0 A.U. The earth takes 1.0 year to travel around the sun how far away is a planet that takes 64 years ro go around the sun
Answer:
This is from another brainly question so I hope this helps :)
The earth takes 1 year to orbit the sun and is about 150, 000, 000km. Given that, use the rule of 3 to find your answer:
1 - 150, 000, 000
64 - x
(150, 000, 000 * 64) / 1= x
9, 600, 000, 000 / 1
9, 600, 000, 000 km.
A planet located 9, 600, 000, 000 km from the sun takes about 64 years to complete its orbit around the sun.
A student measures the voltage and current between two points in an
electrical circuit. If the voltage is 120 V and the current is 0.5 A, what is the
resistance, according to Ohm's law?
A. 0.00402
Β. 240 Ω
C. 1200
D. 60.00
Answer:
B. 240Ω
Explanation:
The formula between voltage, current and resistance is:
voltage = current × resistance
So resistance = voltage ÷ current
Therefore resistance = 120 ÷ 0.5
Resistance = 240Ω
the earth exerts a gravitational force of 850N on John. What is Johns mass in kg
Answer:
86.73 kg
Explanation:
Remember that F=mg
Let's plugin our numbers
850N=m9.8m/s^2
850N=9.8m/s^2m
86.73=m
Velocity of an object of mass 5 kg increases from 3 m/s to 7 m/s on applying a force continuously for 2 s. Find out the force applied. If the duration for which force acts is extended to 5 s, what will be the velocity of the object then?
Answer:
Force=10N
Velocity=13m/s
Explanation:
Given,
Mass = 5kg
initial velocity=3m/s
Final velocity=7m/s
Time=2s
Now acceleration= v-u/t
=7-3/2
=4/2
=2m/s²
So, acceleration=2m/s²
Now,
F=ma
=5*2
=10N
The physical meaning of 220 volts
Answer:
a particular level of electical potential from a power source
What would happen if you placed a compass near an electromagnet when there is an electric current in the coil of the electromagnet? Why would this happen? What if you flipped the electromagnet around so the end that was closest to the compass is now farthest away?
Answer:
Here's the answer
Explanation:
since an electromagnet has a magnetic field, it will always follow the electromagnet.
Why wouldn’t you move during an earthquake?
Answer:
So you maybe don't fall, have something fall on you, and for a bunch of different reasons. EARFQUAKES are really dangrous.
Explanation:
Hope this helps you!
Which reaction connects the citric acid cycle to the electron‑transport chain and amino acid synthesis?
Conversion of succinylcoA to succinate is the reaction that link acid cycle to the electron‑transport chain and amino acid synthesis.
Conversion of succinylcoA to succinateSuccinylCoA is converted into succinate through the hydrolytic release of coenzyme A by succinyl-CoA synthetase Also succinyl-CoA is porphyrin synthesis, where it combine with glycine by ALA synthase to form δ-aminolevulinic acid.
Succinyl CoA is catalytically converted to succinate. The enzyme stimulates the hydrolysis of succinyl CoA into succinate and ATP and this represents a remarkable point of substrate level phosphorylation. After this, it link up to the electron transport chain via citric acid cycle.
Therefore, Conversion of succinylcoA to succinate is the reaction that link citric acid cycle to the electron‑transport chain and amino acid synthesis.
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The electron‑transport chain reaction connects the citric acid cycle to the electron‑transport chain and amino acid synthesis.
What is an electron‑transport chain reaction?The electron transport chain is a set of protein complexes that link redox processes to create an electrochemical potential that leads to the production of ATP in a process known as
Both photosynthesis and cellular respiration occur in mitochondria.
As a result, the process that connects the citric acid cycle to the electron transport chain and amino acid synthesis is succinyl-CoA to succinate conversion.
Hence the electron‑transport chain reaction connects the citric acid cycle to the electron‑transport chain and amino acid synthesis.
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If you create an equilibrium mixture from f e 3 and s c n − ions, adding c l − ions will choose. Highlight_off because choose. Highlight_off
Since chloride ions are not part of the ionic equilibrium, addition of chloride ions will only increase the concentration of the anions in the solution.
What is ionic equilibrium?An ionic equilibrium is an equilibrium that exists between two or more ions in an aqueous solution.
The ionic equilibrium between iron (iii) ion and thiocyanate ions is given below:
[tex]Fe^{3+}\rightleftharpoons SC \: N^{-}[/tex]
From the principle of equilibrium, addition of either ions in the ionic equilibrium will alter equilibrium position to the left or right.
Addition of chloride ions, Cl- which is not a part of the ionic equilibrium will only increase the concentration of the anions in the solution.
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The chloride ions are not part of the ionic equilibrium, adding them to the solution will merely raise the concentration of anions.
What is equilibrium?When a chemical reaction does not convert all reactants to products, it reaches equilibrium. Many processes attain a state of balance, or dynamic equilibrium, in which both reactants and products are present.
The following is the ionic equilibrium between iron (III) ion+ and thiocyanate ions:
[tex]\rm Fe^{3+} \rightleftharpoons SC \ N^{-}[/tex]
The addition of either ion in the ionic equilibrium will shift the equilibrium position to the left or right, according to the principle of equilibrium.
The inclusion of chloride ions, Cl-, which are not components of the ionic equilibrium, increases the levels of anions in the solution.
Thus, the chloride ions are not part of the ionic equilibrium, adding them to the solution will merely raise the concentration of anions.
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Assume that a gravitational anomaly in the solar system has shifted a field of asteroids into Earth’s orbit, and the field is now moving directly towards Earth. The asteroid field has a density of rho (asteroids/volume), and each asteroid has an average mass of m. The asteroid field stretches over a distance d in Earth’s path. Assume that the Earth moves with a velocity of v, the asteroids with u, and that be the radius of the Earth. The Earth collides with the asteroid field:
Show that the slow-down ∆v of the Earth due to the asteroid collisions is given by:
Answer:
An asteroid is a minor planet of the inner Solar System. Historically, these terms have been applied to any astronomical object orbiting the Sun.
If a satelite with a mass of 9 x 10^2 kg is placed in an orbit around a planet with a mass of 6 x 10^20 kg, at a speed of 17000 m/s, find the distance from the center of the planet to the satelite.
Hi there!
We can begin by deriving an equation for the orbital radius.
For an object orbiting the earth, it is experiencing a centripetal force due to the force of gravitation.
Recall Newton's Law of Universal Gravitation:
[tex]F_g = \frac{Gm_1m_2}{r^2}[/tex]
G = Gravitational Constant (6.67 × 10⁻¹¹ Nm²/kg²)
m = masses (kg)
r = radius (m)
This is equivalent to the satellite's centripetal force experienced:
[tex]F_c = \frac{m_sv^2}{r}[/tex]
[tex]m_s[/tex] = mass of satellite (kg)
v = velocity (m/s)
r = radius (m)
Set the two equal, and rearrange for the orbital radius of the satellite.
[tex]\frac{Gm_sm_p}{r^2} = \frac{m_sv^2}{r}\\\\\frac{Gm_p}{r} = v^2\\\\r = \frac{Gm_p}{v^2}[/tex]
Notice that the orbital radius of the satellite does NOT depend on the satellite's mass. (we canceled it out).
Now, plug in the given values.
[tex]r = \frac{(6.67\times 10^{-11})(6\times 10^{20})}{17000^2} = \boxed{138.478 m}[/tex]
11. Which of the following is a type of energy
that is not involved in the human body's
everyday processes?
A. mechanical energy
B. nuclear energy
C. thermal energy
D. chemical energy
Answer:
nuclear
Explanation:
A: a type of mechanical energy is kinetic, which comes from velocity/movement
C: people produce heat
D: converting food energy into usable energy within the body
Thunder is heard 7.2 seconds after a bolt of lightning is observed. if the speed of sound is 349 m/s, how far away did the lightning strike?
Answer:
2512.8 meters
Explanation:
s=d/t
by using speed formula
The driver of a pickup truck accelerated at a rate of -5 m/s2 in 2.0 seconds. What was his net change in velocity?
Explanation:
a= -5m/s^2 t=2s
a= v-u
-------
t
at=v-u
(-5x2)
= -10m/s
A weight of 200 n is hung from a spring with a spring constant of 2500 n/m and lowered slowly. How much will the spring stretch?
8n/m this is because 200×2500 all over 100 . 0's will cancile 0's living 200×2500×1 ,25 will go into 200 8 times ×1 =8n/m
The length by which the spring got stretched will be 0.08 m. The force is directly propotional to the distance by which the spring stretched.
What is spring force?The force required to extend or compress a spring by some distance scales linearly with respect to that distance is known as the spring force. Its formula is
F = kx
The given data in the problem is;
F is the spring force =200
K is the spring constant= 2500 N/m
x is the length by which spring got stretched =?
The stretch of the spring is found as;
[tex]\rm F=kx \\\\ x = \frac{F}{k} \\\\\ x= \frac{200}{2500} \\\\ x=0.08 \ m[/tex]
Hence the length by which the spring got stretched will be 0.08 m.
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A 1.2-kg hot iron sphere with heat capacity
576 J °C-1 is cooled by immersing it in a tank of
water (Fig g). (See the photo that I uploaded)The mass of the water is 3 kg and
its initial temperature is 12 °C. After 5 minutes,
both the iron sphere and the water reach a final
temperature of 15 °C.
(a) Find the energy gained by the water.
(b) Find the average rate of energy transfer from
the iron sphere to the water.
(c) What is the initial temperature of the iron
sphere?
Given the data from the question, the heat gained by the water, the rate of energy transfer and the initial temperature of the iron are:
A. The energy gained by the water is 37656 J
B. The average rate of energy transfer from
the iron sphere to the water is 125.52 J/s (Watts)
C. The initial temperature of the iron
sphere is 65.4° C
A. How to determine the heat gained Mass of water (M) = 3 Kg = 3 × 1000 = 3000 gInitial temperature (T₁) = 12 °C Final temperature (T₂) = 15 °Change in temperature (ΔT) = 15 – 12 = 3 °C Specific heat capacity (C) = 4.184 J/gºC Heat (Q) =?Q = MCΔT
Q = 3000 × 4.184 × 3
Q = 37656 J
B. How to determine the rate of energy transfer Heat (Q) = 37656 JTime (t) = 5 min = 5 × 60 = 300 sPower (P) =?Power = energy / time
Power = 37656 / 300
Power = 125.52 J/s (Watts)
C. How to determine the initial temperature of the iron Mass of iron (M) = 1.2 Kg = 1.2 × 1000 = 1200 gHeat capacity (C) = 576 J/ºC Heat (Q) = 37656 JTemperature (T) =?Q = CT
37656 = 576 × T
Divide both side by 576
T = 37656 / 576
T = 65.4° C
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3. Describe comets and their orbits in the solar system.
Comets have an extremely eccentric orbit around the Sun. They can travel hundreds of thousands of years through the solar system before returning to the Sun at perihelion. Comets, like all orbiting bodies, obey Kepler's Laws, which state that the closer they get to the Sun, the faster they move.
A comet is a dirty snowball many kilometers across that exists at a considerable distance from the Sun. However, when it gets closer to the Sun, the comet's surface warms up, causing its components to melt and vaporize, resulting in the comet's distinctive tail. The distance between the Earth and the Sun can be measured in comet tails.
With a class 1 lever, does mechanical advantage increase or decrease as the fulcrum is moved closer to the load? Explain why.
Answer:
L1 F1 = L2 F2 explains balancing torques
F1 = load = counterclockwise torque
F2 = applied force - clockwise torque
L represents distances from fulcrum to the applied forces
F2 = F1 * (L1 / L2) (I)
MA mechanical advantage = (L2 / L1) load over applied force
We can rewrite equation (I) as
load force / applied force = applied distance / load distance
As the fulcrum is moved closer to the load L1 decreases and L2 increases which corresponds to an increase in MA
explain why the age of the ocean floor bedrock increases as the distance from the mid-atlantic ridge increases?
Answer:
The age of the bedrock increases the further you get away from the mid atlantic ridge because it is at the ridge that the new bedrock is formed. At the Ridge, the diverging plates cause magma to rise up and harden, forming new bedrock. As this happens, the older bedrock is pushed outwards, further and further away from the Ridge.
Explanation:
Hope it helps.
A ball that has a mechanical energy of 65 J haas 10 j of kinetic energy. The ball has j of potential energy
Answer:
55 j
Explanation:
Mechanical energy = kinetic + potential
65 = 10 + P.E.
55 j = PE
If you wanted to melt ice, then heat it up, and get the water to just barely vaporize, how many equations would you need to solve for the energy used in this procedure?
Two equations will be needed to solve for the energy used in this procedure.
What is Energy?This is defined as the ability or capacity to do work. Ice being converted to vapor requires energy and the equations are seen below:
H₂O₍s₎ ⇒ H₂O₍l₎
H₂O₍l₎ ⇒ H₂O₍g₎
These are the equations which are used to calculate energy with heat being involved in both reactions.
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A builder drops a brick from a height of 15 m above the ground. The gravitational field strength g is 10 N/ kg. What is the speed of the brick as it hits the ground?
The speed of the brick dropped by the builder as it hits the ground is 17.32m/s.
Given the data in the question;
Since the brick was initially at rest before it was dropped,
Initial Velocity; [tex]u = 0[/tex]Height from which it has dropped; [tex]h = 15m[/tex]Gravitational field strength; [tex]g = 10N/kg = 10 \frac{kg.m/s^2}{kg} = 10m/s^2[/tex]Final speed of brick as it hits the ground; [tex]v = \ ?[/tex]
Velocityvelocity is simply the same as the speed at which a particle or object moves. It is the rate of change of position of an object or particle with respect to time. As expressed in the Third Equation of Motion:
[tex]v^2 = u^2 + 2gh[/tex]
Where v is final velocity, u is initial velocity, h is its height or distance from ground and g is gravitational field strength.
To determine the speed of the brick as it hits the ground, we substitute our giving values into the expression above.
[tex]v^2 = u^2 + 2gh\\\\v^2 = 0 + ( 2\ *\ 10m/s^2\ *\ 15m)\\\\v^2 = 300m^2/s^2\\\\v = \sqrt{300m^2/s^2}\\ \\v = 17.32m/s[/tex]
Therefore, the speed of the brick dropped by the builder as it hits the ground is 17.32m/s.
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name one type of energy the washing machine wastes when spinning the clothes
Answer:
Electrical Energy
The Electricity Rotates the spinning part of Washing machine and It spinns clothes.