Recall the definition of the cross product with respect to the unit vectors:
i × i = j × j = k × k = 0
i × j = k
j × k = i
k × i = j
and that the product is anticommutative, so that for any two vectors u and v, we have u × v = - (v × u). (This essentially takes care of part (b).)
Now, given a = 8i + j - 2k and b = 5i - 3j + k, we have
a × b = (8i + j - 2k) × (5i - 3j + k)
a × b = 40 (i × i) + 5 (j × i) - 10 (k × i)
… … … … - 24 (i × j) - 3 (j × j) + 6 (k × j)
… … … … + 8 (i × k) + (j × k) - 2 (k × k)
a × b = - 5 (i × j) - 10 (k × i) - 24 (i × j) - 6 (j × k) - 8 (k × i) + (j × k)
a × b = - 5k - 10j - 24k - 6i - 8j + i
a × b = -5i - 18j - 29k
Answer:
Explanation:
If a = 8i + j - 2k and b = 5i - 3j + k show that a) a x b = -5i - 18j - 29k b) b X a = 50 + 18j +29k
knives, axe ,blades and nails are examples of
knives, axe ,blades and nails are examples of potential energy
or sharp objects
what is a non-economic benefit to international trade
Answer:
non economic benefits to international trade means not being too much profit not selling too much things /items in international trade
A cylindrical rod formed from silicon is 16.8 cm long and has a mass of 2.17 kg. The density of silicon is 2.33 g/cm3 . What is the diameter of the cylinder
Answer:
We are given the length, the mass and the density of the cylinder. First let us calculate for the volume by dividing the mass by the density.
volume = mass /density
where mass = 2.17 kg = 2170 g, therefore:
volume = 2170 g / (2.33 g/cm^3)
volume = 931.33 cm^3
We know that the volume of a cylinder has the formula:
volume = π r^2 h
since h = 16.8 cm, therefore calculating for radius:
931.33 cm^3 = π r^2 (16.8 cm)
r^2 = 17.646 cm^2
r = 4.2 cm
Hence the diameter (d) is:
d = 2 r
d = 8.4 cm
Explanation:
The diameter of the cylindrical rod is approximately 0.382 cm.
To find the diameter of the cylindrical rod, we can use the formula for the volume of a cylinder and then solve for the diameter.
The formula for the volume of a cylinder is:
V = π[tex]r^{2}[/tex]h,
where V is the volume, r is the radius, and h is the height (or length) of the cylinder.
In this case, we know the length of the cylinder (h) is 16.8 cm. We need to find the radius (r) in order to calculate the diameter.
The mass of the cylinder can be related to its volume and density using the formula:
m = ρV,
where m is the mass, ρ is the density, and V is the volume.
Rearranging this formula, we can solve for V:
V = m / ρ.
Now we have two equations:
V = π[tex]r^{2}[/tex]h,
V = m / ρ.
Setting these two equations equal to each other, we can solve for r:
π[tex]r^{2}[/tex]h = m / ρ.
Substituting the given values:
π[tex]r^{2}[/tex] * 16.8 cm = 2.17 kg / (2.33 g/[tex]cm^3[/tex]).
Let's solve this equation for r:
[tex]r^{2}[/tex] = (2.17 kg / (2.33 g/[tex]cm^3[/tex])) / (π * 16.8 cm).
[tex]r^{2}[/tex] ≈ 0.036775 [tex]cm^2[/tex].
Taking the square root of both sides:
r ≈ 0.191 cm.
Finally, we can find the diameter (d) by multiplying the radius by 2:
d ≈ 2 * 0.191 cm.
d ≈ 0.382 cm.
Therefore, the diameter of the cylindrical rod is approximately 0.382 cm.
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An object weighs 573.0 N on planet Xyleneer. If the object's mass is 92.1 kg, what is the acceleration due to gravity on planet Xyleneer?
Answer:
a = 6.22 m//s²
Explanation:
F = ma
a = F/m
a = 573.0 / 92.1
a = 6.221498...
Answer:
[tex]\boxed {\boxed {\sf 6.22 \ m/s^2}}[/tex]
Explanation:
We are asked to find the acceleration due to gravity on another planet.
Weight is the measure of the force of gravity. Therefore, we can use the following version of the force formula:
[tex]F_g=mg[/tex]
In this formula, [tex]F_g[/tex] is the weight, m is the mass, and g is the acceleration due to gravity.
The object weights 573.0 Newtons (or 573.0 kg*m/s²) on the planet. The object has a mass of 92.1 kilograms.
[tex]F_g[/tex]= 573.0 kg* m/s²m= 92.1 kgSubstitute these values into the formula.
[tex]573.0 \ kg*m/s^2 = 92.1 \ kg * g[/tex]
We are solving for g, so we must isolate the variable. It is being multiplied by 92.1 kilograms. The inverse of multiplication is division, so divide both sides of the equation by 92.1 kg.
[tex]\frac {573.0 \ kg*m/s^2}{92.1 \ kg}= \frac{92.1 \ kg*a}{92.1 \ kg}[/tex]
[tex]\frac {573.0 \ kg*m/s^2}{92.1 \ kg}=a[/tex]
The units of kilograms cancel.
[tex]6.22149837 \ m/s^2=a[/tex]
The original measurements of weight and mass have 4 and 3 significant figures. Our answer must have the least number of sig figs, or 3. For the number we found, that is the hundredth place. The 1 in the thousandths place tells us to leave the 2 in the hundredth place.
[tex]6.22 \ m/s^2=a[/tex]
The acceleration due ot gravity on planet Xyleneer is approximately 6.22 meters per second squared.
builder places a 3kg hammer on the top of a ladder, which is 4m above the ground. Calculate the gravitational potential energy of the hammer while on the ladder.
Answer:
[tex]E=mgh[/tex]
[tex]m=3kg[/tex]
[tex]h=4m[/tex]
[tex]g=9.8m/s^{2}[/tex]
[tex]E= 3*4*9.8=117.6J[/tex]
Explanation:
Only substitute amounts to formula.
Hope this helps ;)
Cheers :D
Croquet ball A moving at 8.3 m/s makes a head on collision with ball B of equal mass and initially at rest. Immediately after the collision ball B moves forward at 6.4 m/s .
What fraction of the initial kinetic energy is lost in the collision?
Answer:
0.25
Explanation:
That is the right answer.
The fraction of the initial kinetic energy is lost in the collision is 35.3%.
The given parameters:
Initial velocity of ball A = 8.3 m/sInitial velocity of ball B = 0Final velocity of ball B = 6.4 m/sThe initial kinetic energy of the system collision is calculated as follows;
[tex]K.E_i = \frac{1}{2} mv_1_i^2 + \frac{1}{2} mv_2_i^2\\\\K.E_i = \frac{1}{2} (m)(8.3)^2 + \frac{1}{2} (m) (0)^2\\\\K.E_i = 34.445 m[/tex]
The final velocity of ball A after collision is calculated as follows;
[tex]u_1 + v_1 = u_2 + v_2\\\\8.3 + v_1 = 0 + 6.4\\\\v_1 = 6.4 - 8.3\\\\v_1 = -1.9 \ m/s[/tex]
The final kinetic energy of the system after collision is calculated as follows;
[tex]K.E_f = \frac{1}{2} m(-1.9)^2 + \frac{1}{2} m(6.4)^2\\\\K.E_f = 22.285 \ m \[/tex]
The fraction of the initial kinetic energy is lost in the collision is calculated as follows;
[tex]= \frac{K_i - K_f}{K_i} \\\\= \frac{34.445 - 22.285}{34.445} \\\\= 0.353\\\\= 35.3\%[/tex]
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The Greek root astro means "stars." Use the context clues to choose the correct definition of the word astronomer. According to the astronomer, the bigger the telescope, the more detail we can see in the images. O A. a person who studies astronauts O B. a person who studies the stars O C. a person who tells the future O D. a person who studies other people
Answer:
b, it's a pretty easy explanation
:)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
Good morning dear...
Have a beautiful and joyful day ahead.
What is the potential energy when a 100 kg object is raised 4.00 m straight up?
Answer:
100kg x 4 x 10 = 4000J
Explanation:
A 0.015 kg marble sliding to the right at 0.225 m/s on a frictionless surface makes an elastic head-on collision with a 0.015 kg marble moving to the left at 0.180 m/s. After the collision, the first marble moves to the left at 0.180 m/s. Find the velocity of the second marble after the collision.
Explanation:
[tex]if \: the \: masses \: of \: the \:two \: marbles\: equal \\ then \: each \: velocity \: sharing \: with \: other \: velocity[/tex]
I tossed a ball straight up into the air and timed how long it took to return to the height I tossed it from. It took 4.2s. How fast did I throw the ball into the air?
Explanation:
[tex]v = u + at \\ 0 = u + ( - 10 { ms}^{ - 2}) \times 4.2s \\ u = 42 {ms}^{ - 1} [/tex]
Question 3 of 20 :
Select the best answer for the question.
3. Which of the following accurately describes the behavior of water when subjected to
temperature change?
A. The volume of water will decrease if heated from 6°C to 7°C.
B. The volume of water will increase if cooled from 3°C to 2°C.
O C. A mass of water will contract if cooled from 1°C to 0°C.
D. A mass of water will expand if heated from 0°C to 2°C.
As water cools the volume expands.
Answer: B. The volume of water will increase if cooled from 3°C to 2°C.
A conductor is a material that ?
conducts electricity (keeps it running)
Answer:
The material which allow heat and electricity to pass through them are called conductor.
Eg. In solids- copper, silver, gold etc
In liquids The liquid that conduct electricity are solutions of acid bases and salts in water. For example: Solution of sulphuric acid ,hydrochloric acid in water conduct electricity. Vinegar contains acetic acid and lemon juice contain citric acid also conduct electricity.
Explanation:
If you like my answer than please mark me brainliest thanks
How much force must be applied to push a 1.35 kg book across the desk at constant speed if the coefficient of sliding friction is 0.30?
The magnitude of the force that must be applied to push the book across the desk is 3.97 N.
The given parameters;
mass, m = 1.35 kgcoefficient of friction, μ = 0.3The acceleration of the book across the desk is calculated as follows;
a = μg
where;
g is acceleration due to gravitya = 0.3 x 9.8
a = 2.94 m/s²
The magnitude of the force that must be applied is calculated as follows;
F = ma
F = 1.35 x 2.94
F = 3.97 N
Thus, the magnitude of the force that must be applied to push the book across the desk is 3.97 N.
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what are people words in english
Answer: Plenty
Explanation:
some words are Hi, Banana, Dude and many more
A load of 20N is lifted through a height of 8m by a machine.If the effort of 80N moves a distance of 6m.Calculate the efficiency percentage of the machine
A load of 20N is lifted through a height of 8m by a machine.If the effort of 80N moves a distance of 6m.Calculate the efficiency percentage of the machine
Explanation:
A load of 20N is lifted through a height of 8m by a machine.If the effort of 80N moves a distance of 6m.Calculate the efficiency percentage of the machine
Answer:

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Join / LoginQuestionIn a lifting machine an effort of 500 N is to be moved by a distance of 20 m to raise a load of 10000 N by a distance of 0.8 m Determine the velocity ratio and mechanical advantage
Determine the velocity ratio and mechanical advantageA
Determine the velocity ratio and mechanical advantageA10 and 35
Determine the velocity ratio and mechanical advantageA10 and 35B
Determine the velocity ratio and mechanical advantageA10 and 35B20 and 35
Determine the velocity ratio and mechanical advantageA10 and 35B20 and 35C
Determine the velocity ratio and mechanical advantageA10 and 35B20 and 35C10 and 25
Determine the velocity ratio and mechanical advantageA10 and 35B20 and 35C10 and 25D
Determine the velocity ratio and mechanical advantageA10 and 35B20 and 35C10 and 25D25 and 20
Determine the velocity ratio and mechanical advantageA10 and 35B20 and 35C10 and 25D25 and 20Easy
Determine the velocity ratio and mechanical advantageA10 and 35B20 and 35C10 and 25D25 and 20EasyOpen in App
Determine the velocity ratio and mechanical advantageA10 and 35B20 and 35C10 and 25D25 and 20EasyOpen in AppSolution
Determine the velocity ratio and mechanical advantageA10 and 35B20 and 35C10 and 25D25 and 20EasyOpen in AppSolution
Determine the velocity ratio and mechanical advantageA10 and 35B20 and 35C10 and 25D25 and 20EasyOpen in AppSolutionVerified by Toppr
Determine the velocity ratio and mechanical advantageA10 and 35B20 and 35C10 and 25D25 and 20EasyOpen in AppSolutionVerified by TopprCorrect option is
Determine the velocity ratio and mechanical advantageA10 and 35B20 and 35C10 and 25D25 and 20EasyOpen in AppSolutionVerified by TopprCorrect option isD
Determine the velocity ratio and mechanical advantageA10 and 35B20 and 35C10 and 25D25 and 20EasyOpen in AppSolutionVerified by TopprCorrect option isD25 and 20
Determine the velocity ratio and mechanical advantageA10 and 35B20 and 35C10 and 25D25 and 20EasyOpen in AppSolutionVerified by TopprCorrect option isD25 and 20Distance moved by effort is 20m,that of load is 0.8m
Determine the velocity ratio and mechanical advantageA10 and 35B20 and 35C10 and 25D25 and 20EasyOpen in AppSolutionVerified by TopprCorrect option isD25 and 20Distance moved by effort is 20m,that of load is 0.8mVR=LdEd
Determine the velocity ratio and mechanical advantageA10 and 35B20 and 35C10 and 25D25 and 20EasyOpen in AppSolutionVerified by TopprCorrect option isD25 and 20Distance moved by effort is 20m,that of load is 0.8mVR=LdEdVR=0.820
Determine the velocity ratio and mechanical advantageA10 and 35B20 and 35C10 and 25D25 and 20EasyOpen in AppSolutionVerified by TopprCorrect option isD25 and 20Distance moved by effort is 20m,that of load is 0.8mVR=LdEdVR=0.820VR=25
Determine the velocity ratio and mechanical advantageA10 and 35B20 and 35C10 and 25D25 and 20EasyOpen in AppSolutionVerified by TopprCorrect option isD25 and 20Distance moved by effort is 20m,that of load is 0.8mVR=LdEdVR=0.820VR=25the load is 10,000N and effort=500N
MA=effortdloadd
MA=effortdloaddMA=50010000
MA=effortdloaddMA=50010000MA=20
A merry-go-round rotates from rest with an angular acceleration of 1.08 rad/s2. How long does it take to rotate through (a) the first 3.74 rev and (b) the next 3.74 rev
Answer:
Let ω1 be the initial angular speed and ω2 the final angular speed:
α = (ω2- α1) / t
corresponding to a = (v2 - v1) / t
S (distance corresponds to theta)
1 rev = 2 pi and 3.74 rev = 7.48 pi = 23.5 radians
S = 1/2 a t^2 linear or S = 1/2 α t^2 angular acceleration
23.5 = 1/2 * 1.08 t^2 and t = 6.60 sec for first 3.84 rev
b) ω1 = 1.08 * 6.6 = 7.13 rad/sec initial speed for second 3.74
23.5 = 7.13 t + .54 t^2 compare to S = v1 t + 1/2 a t^2
.54 t^2 + 7.13 t - 23.5 = 0
t^2 + 13.2 t - 43.5 = 0
t = 2.7 sec for next 3.74
Check:
7.13 * 2.7 + .54 * 2.7^2 = 23.2 rad = 3.7 rad
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You are traveling along a freeway at 65 mi/h. You suddenly skid to a stop because of congestion in traffic. Where is the energy that your car once had as kinetic energy before you stopped
The work and energy theorem allows finding the result for where the kinetic energy of the car is before stopping is:
The energy becomes:
An important part in work on discs. A part in non-conservative work due to friction.
Work is defined by the scalar product of force and displacement.
W = F . d
Where the bold indicate vectors, W is work, F is force and d is displacement.
The work energy theorem relates work and kinetic energy.
W = ΔK = [tex]K_f - K_o[/tex]
In this case the vehicle stops therefore its final kinetic energy is zero, consequently the work is:
W = - K₀
Therefore, the initial kinetic energy that the car has is converted into work in its brakes. In reality, if assuming that there is friction, an important part is transformed into non-conservative work of the friction force, this work can be seen in a significant increase in the temperature of the discs on which the work is carried out.
In conclusion, using the work-energy theorem we can find the result for where the kinetic energy of the car is before stopping is:
The energy becomes:
An important part in work on the discs. A part in non-conservative work due to friction.
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Example 4.16
An object of mass 3 kg rests on a plane. The coefficient of static friction and that of kinein
friction are given by Hs = 0.3 and pk = 0.2.
The plane is inclined at angle o to the horizontal.
(i) Find the maximum value of 0 for which the object remains at rest on the plane.
(ii) Find the acceleration of the object if it started sliding from rest down the plane at
angle Omax to the horizontal.
(ii) How long does it take the object to move, from rest, a distance of Imetre under the
conditions of (ii).
Answer:
Explanation:
(i) μs = F/N = mgsinθ/mgcosθ = tanθ
tanθ = 0.3
θ = 16.7°
(ii) a = F/m
a = (mgsinθ - (μk)mgcosθ) / m
a = g(sinθ - (μk)cosθ)
a = 9.8(sin16.7 - (0.2)cos16.7)
a = 0.94 m/s²
(iii) s = ½at²
t = √(2s/a)
t = √(2(1)/0.94)
t = 1.5 s
If the total translational kinetic energy of the molecules of oxygen in a container is 15 J at room temperature, what is the total rotational kinetic energy of these molecules
Answer:
zero(0)
Explanation:
if a molecule is moving along a straight path, there is zero rotational speed and that component give zero moment in the direction of the molecule's driving force
The ratio of total rotational kinetic energy to the total translational kinetic energy is 3 : 2. Thus, the rotational kinetic energy of oxygen with translational kinetic energy of 15 J is 10 J.
What is rotational kinetic energy?Rotational kinetic energy is the energy generated by virtue of the rotational motion of a molecule. The degree of freedom of a compound or molecules is the sum of its translational degree of freedom, rotational degree of freedom and vibrational degree of freedom.
For a diatomic molecule, there are three translational degrees of freedom along x, y and z directions. Similarly there will be two rotational degree of freedom along the molecular axis.
The ratio of rotational degree of freedom to that of translational motion is 3/2.
Thus Te / Re = 3/2
15 J/ Re = 3/2
Rotational kinetic energy Re = 30/3 =10 J.
Therefore, the rotational kinetic energy oxygen would be 10 J.
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An empty plastic or glass dish being removed from a microwave oven is cool to the touch. How can this be possible
Light bulbs produce useful energy in the form of light and waste energy in the form of heat. What kind of light bulb would you use
to incubate eggs?
A. low-efficiency light bulbs, because they produce more light
B. low-efficiency light bulbs, because they produce more heat
C. high-efficiency light bulbs, because they produce more heat
D. high-efficiency light bulbs, because they produce more light
Answer:
C) high efficiency light bulbs, because they produce more heat
Light bulbs produce useful energy in the form of light and waste energy in the form of heat, the kind of light bulb would you use to incubate eggs are low-efficiency light bulbs, because they produce more heat, therefore the correct answer is option B.
What is thermal energy?It can be defined as the form of the energy in which heat is transferred from one body to another body due to their molecular movements, thermal energy is also known as heat energy.
The type of light bulb you would use to incubate eggs is a low-efficiency light bulb since they produce more heat; consequently, option B is the right response. Light bulbs produce useful energy in the form of light and waste energy in the form of heat.
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the temperature of ice will rise until melting state select true or false
Answer:
True
Explanation:
I have learned that in grade schoolI have known that for quite awhile now alsoURGENTLY NEED HELP!!!!!!
the stretch of a spring and the force it exerts are inversely proportional.
Select one:
O True
O False
Answer:
False.
Explanation:
What's the kinetic energy of an object that has a mass of 12 kilograms and moves with a velocity of 10 m/s?
Answer:
600 JExplanation:
Given,
Mass (m) = 12 kgVelocity (v) = 10 m/sAs we know,
Kinetic Energy,
[tex] E_{k} \: = \frac{1}{2} m {v}^{2} [/tex]Therefore ,
Kinetic energy of the object is,
[tex] = \frac{1}{2} \times 12 \: kg \times 10 \: m {s}^{ - 1} \times 10 \: m {s}^{ - 1} [/tex]
(On dividing 12 by 2 we get 6)= (6 × 10 × 10) J [As 'J' stands for 'joule']
= 600 J (Ans)
Danny is competing in the high jump. When he is in the air, his body has _______ energy due to its height, and it has _______ energy due to its motion.
Answer:
Gravitational potential energy
kinetic energy
A body at higher temperature contains more heat? Is this true ?
the momentum of a car before the crash is 22500kg m/s. the car stops in 0.14s. what is the average force on the car during the crash?
Answer:
what is the full questio n because I can't see the momentum
13. Which of the following lines (of latitude or longitude) would be represented by 0° Latitude?
14. Which of the following lines (of latitude or longitude) would be represented by 90° North
Latitude?
15. Which of the following lines (of latitude or longitude) would be represented by 90° South
Latitude?
16. Which of the following lines (of latitude or longitude) would be represented by 0° Longitude?
a. south pole b. equator c. prime meridian d. north pole
Answer:
14. Which of the following lines (of latitude or longitude) would be represented by 90° North Latitude?
ANSWER: D. North Pole
15. Which of the following lines (of latitude or longitude) would be represented by 90° South Latitude?
ANSWER: A. South Pole
16. Which of the following lines (of latitude or longitude) would be represented by 0° Longitude?
ANSWER: C. Prime Meridian
Answer:
A
Explanation:
