Need help with dot product

Answer:

Assuming there are no energy losses due to friction or drag, the gravitational potential energy will change into kinetic potential energy as the car reaches the bottom of the slope.

G.P.E = m*g*h

K.E = (m*v^2)/2

where

m = mass of toy car (kg)

g = gravity (m/s^2)

h = heigh of your car from the bottom (m)

v = velocity of the toy car as it reaches the bottom (m/s)

Equate K.E to G.P.E

G.P.E = K.E

m*g*h = (m*v^2)/2

make v the subject of the formula

v = (2*g*h)^(1/2)

Substitute g = 9.81 m/s^2 and h = 2m into the equation to get v

v = (2*9.81*2)^(1/2)

v = 6.264 m/s

Answer:

Small particles of dust and pollution in the air can contribute to (and sometimes even enhance) these colors, but the primary cause of a blue sky and orange/red sunsets or sunrises is scattering by the gas molecules that make up our atmosphere. Large particles of pollution or dust scatter light in a way that changes much less for different colors.

Explanation:

The energy in the system is given by the initial potential energy at the point 1.

The linear velocity at point 3, is approximately 33.59 m/s.

Reasons:

The parameters are;

Height at point 1, h₁ = 83 m

Radius of the ring = 8 cm

Mass of the ring, M = 8 kg

Height at point 2, h₂ = 32 m

At point 2, we have;

Change in potential energy = Kinetic energy

Which gives;

(83 - 32) × 9.81 × 8 = 0.5 × 8 × v² + 0.5 × 8 × 0.08² × (v/0.08)²

Which gives;

v ≈ 22.37 m/s

At point 3, the rotational kinetic energy remains constant while the

translational kinetic energy increases as follows;

K.E. at point 3 = Initial kinetic energy + Change in potential energy

Which gives;

K.E. at point 3 = 0.5 × 8 × v₃³ ≈ 0.5×8×22.37² + 32×9.81×8

[tex]v_3^2 = \dfrac{0.5 \times 8 \times 22.37^2 + 32 \times 9.81 \times 8}{0.5 \times 8} = 1128.15[/tex]

v₃ ≈ √(1128.15) ≈ 33.59

The linear velocity at point 3, v₃ ≈ 33.59 m/s

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The probable question parameters as obtained from a similar question online are;

Height at point 1, h₁ = 83 m

Radius of the ring = 8 cm

Mass of the ring, M = 8 kg

Height at point 2, h₂ = 32 m

The answer is C) kilogram

The SI unit in the given options is kilogram, the correct option is C.

The most common unit of measurement is the standard unit. These units are standardized, which means that everyone understands an object's size, weight, and other properties.

Standard Units of Measurement have fixed values that cannot be changed.

The International System of Units, abbreviated SI in all languages and sometimes pleonastically as the SI system, is the modern version of the metric system and the world's most widely used measurement system.

The SI is a coherent system of units of measurement that begins with seven base units: the second (symbol s, the unit of time), the metre (m, length), the kilogram (kg, mass), the ampere (A, electric current), and so on.

Thus, the correct option is C.

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Answer: A , D & F

Explanation:

The angular speed of the merry-go-round reduced more as the sandbag is

placed further from the axis than increasing the mass of the sandbag.

The rank from largest to smallest angular speed is presented as follows;

[m = 10 kg, r = 0.25·R]

              [tex]{}[/tex] ⇩

[m = 20 kg, r = 0.25·R]

              [tex]{}[/tex] ⇩

[m = 10 kg, r = 0.5·R]

              [tex]{}[/tex] ⇩

[m = 10 kg, r = 0.5·R] = [m = 40 kg, r = 0.25·R]

              [tex]{}[/tex] ⇩

[m = 10 kg, r = 1.0·R]

Reasons:

The given combination in the question as obtained from a similar question online are;

1: m = 20 kg, r = 0.25·R

2: m = 10 kg, r = 1.0·R

3: m = 10 kg, r = 0.25·R

4: m = 15 kg, r = 0.75·R

5: m = 10 kg, r = 0.5·R

6: m = 40 kg, r = 0.25·R

According to the principle of conservation of angular momentum, we have;

[tex]I_i \cdot \omega _i = I_f \cdot \omega _f[/tex]

The moment of inertia of the merry-go-round, [tex]I_m[/tex] = 0.5·M·R²

Moment of inertia of the sandbag = m·r²

Therefore;

0.5·M·R²·[tex]\omega _i[/tex] = (0.5·M·R² + m·r²)·[tex]\omega _f[/tex]

Given that 0.5·M·R²·[tex]\omega _i[/tex] is constant, as the value of  m·r² increases, the value of [tex]\omega _f[/tex] decreases.

The values of m·r² for each combination are;

Combination 1: m = 20 kg, r = 0.25·R; m·r² = 1.25·R²

Combination 2: m = 10 kg, r = 1.0·R; m·r² = 10·R²

Combination 3: m = 10 kg, r = 0.25·R; m·r² = 0.625·R²

Combination 4: m = 15 kg, r = 0.75·R; m·r² = 8.4375·R²

Combination 5: m = 10 kg, r = 0.5·R; m·r² = 2.5·R²

Combination 6: m = 40 kg, r = 0.25·R; m·r² = 2.5·R²

Therefore, the rank from largest to smallest angular speed is as follows;

Combination 3 > Combination 1 > Combination 5 = Combination 6 >

Combination 2

Which gives;

[m = 10 kg, r = 0.25·R] > [m = 20 kg, r = 0.25·R] > [m = 10 kg, r = 0.5·R] > [m =

10 kg, r = 0.5·R] = [m = 40 kg, r = 0.25·R] > [m = 10 kg, r = 1.0·R].

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Answer:

b Shiny

Explanation:

Trust me it's right

Answer:

Explanation:

s = s₀ + v₀t + ½at²

50 = 0 + 0(4) + ½a(4²)

50 = 8a

a = 50/8 = 6.25 m/s²

Answer:

Explanation:

0.120 rev/s(2π rad/rev) = 0.24π rad/s

At the highest point of the arc, gravity must supply the required centripetal acceleration. As the normal force is 1/4 of his normal weight, then 3/4 of gravity acceleration must be used as centripetal acceleration

0.75g = ω²R

R = 0.75(9.81) / (0.24π)²

R = 12.942198...

R = 12.9 m

The radius of the circle is equal to 12.95m which is rotating with an angular velocity of 0.120 rev/s.

A body spins in a vertical circle so that its motion at different points is different from the motion of the body is said to be vertical circular motion.

The velocity and tension vary in maximum magnitude from the lowest to the highest position because of the effect of the gravitational force of the earth.

Given, the angular velocity of the Ferris wheel, ω = 0.120 rev/s

ω = 0.120 rev/s × 2π rad/rev

ω= 0.7536 rad/s

If r is the radius of the circle and 'm' is the mass of the jack.

From newton's second law of motion, the net force will be equal to

mg - N = mrω²

mg - (mg/4) = mrω²

r = 3g/4ω²

r = 3×9.81 / (4× 0.7536)

r = 12.95 m

Therefore, the radius of the circle in which the jack travels is equal to 12.95m.

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Your question is incomplete, most probably the complete question was,

Jack sits in the chair of a Ferris wheel that is rotating at a constant 0.120 rev/s. As Jack passes through the highest point of his circular part, the upward force that the chair exerts on him is equal to one-fourth of his weight. What is the radius of the circle in which Jack travels?

Answer:

how many feet?

Explanation:

Answer:

Explanation:

Radio waves

Radio waves have photons with the lowest energies. Microwaves have a little more energy than radio waves. Infrared has still more, followed by visible, ultraviolet, X-rays and gamma rays.

Answer:

Instrument Use

Accelerometer Measures acceleration

Altimeter Measures altitude of an aircraft

Ammeter Measures electric current in ampere

Anemometer Measures wind speed

Answer:

Explanation:

I've been doing these types of problems for many years and I don't think I've ever seen an "efficiency" rating on a ramp.

I'm going to ASSUME that 20% efficient means that 80% of the Potential energy that gets converted becomes system internal heat energy.

Potential energy at the start of a 2.0 m slide

PE = mgh = mg2sin30 = mg2(½) = mg J

0.8mg J gets converted to heat and 0.2mg converts to kinetic energy

0.2mg = ½mv²

v² = 0.4g

v = √(0.4(9.8)) = 1.979898... ≈ 2.0 m/s

Answer:

The data suggest that the true mean HAZ depth is larger when the current setting is higher.

Answer:

Explanation:

s = s₀ + v₀t + ½at²

s = 0 + 0(15) + ½(6)(15²)

s = 675 m

Not sure what the free fall acceleration is needed for, but if the object is dropped from a high enough point, it will travel in 15 seconds

s = ½10(15²) = 2250 m  if air resistance is ignored

Answer:

At the highest point when you toss a ball into the air.

Explanation:

At the higest point of a trajectory of a ball, the velocity is zero for a split second and there is no speed and direction. However, there still is acceleration of -10 m/s^2 because the force of gravity is still acting upon it at that point.

Hi there!

An example of this could be when a ball is thrown vertically into the air and reaches the TOP of its trajectory.

When an object is thrown with a vertical velocity, the acceleration due to gravity results in a decrease in its positive (upward) velocity until it reaches its highest point, where the instantaneous velocity = 0 m/s and the object begins to fall back down (negative velocity).

Additionally, throughout its entire trajectory, the ball experiences an acceleration due to gravity of g = 9.8 m/s², even at its highest point where there is a velocity = 0 m/s.

Answer:

it would decrease

Explanation:

f=1/T

Find the distance the ball travels:

3.4 meters - 1.5 meters = 1.9 meters

Now divide the distance the ball travels by the speed:

1.9 meters / 4.4 m/s = 0.43 seconds

Answer:

Explanation:

s = s₀ + v₀t + ½at²

There are an infinite number of solutions to this question as posed because we are not told the direction of the initial velocity.

Assuming ground is level and origin and UP the positive direction

The shortest amount of time possible is when the initial velocity is straight down

1.5 = 3.4 - 4.4t + ½(-9.8)t²

0 = -4.9t² - 4.4t + 1.9

t = (4.4 ±√(4.4² - 4(-4.9)(1.9))) / (2(-4.9))

positive answer is

t = 0.32 s

The longest amount of time possible is when the initial velocity is straight up.

1.5 = 3.4 + 4.4t + ½(-9.8)t²

0 = -4.9t² + 4.4t + 1.9

t = (-4.4 ±√(4.4² - 4(-4.9)(1.9))) / (2(-4.9))

positive answer

t = 1.22 s

If the initial velocity is horizontal, meaning no vertical velocity

1.5 = 3.4 + 0t + ½(-9.8)t²

-4.9t² = -1.9

t² = 0.38775...

t = 0.62 s

Any angle between UP and Down will have a different initial vertical velocity and result in a different time to catch height.

It appears from the comments on the other answer, that I have shown you how to arrive at three of the four possible solutions.  The initial direction is very important.

Answer:

340

Explanation:

Sorry I don't know how to do this one yet, I just found the answer in a textbook.

The angle that vector a makes with the +x axis is closest to 23.

The direction of a vector is represented tangent of angle equal to the ratio of the y component and the x component of the vector quantity.

tangent of angle = y/x

angle = tan⁻¹ (-2.3/5.3)

angle = 23.46°

Thus, the angle that vector makes with +x is 23.

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Hi there!

A.

We can calculate the gravitational field strength using the following equation:

[tex]g = \frac{Gm_p}{r^2}[/tex]

G = Gravitational Constant

mp = mass of planet (kg)

r = radius (m)

Plug in the given values:

[tex]g = \frac{(6.67*10^{-11})*(5.68*10^{24})}{(6.03*10^7)^2} = \boxed{0.104 N/kg}[/tex]

B.

The force can be calculated using:

[tex]F_g = \frac{Gm_1m_2}{r^2}[/tex]

Plug in the values:

[tex]F_g = \frac{(6.67*10^{-11})(5.68*10^{24})(50)}{(6.04*10^7)^2} = \boxed{5.209N}[/tex]

Answer:

[tex]\boxed {\boxed {\sf g=0.104 \ N/kg \ and \ F_g= 5.2 \ N }}[/tex]

Explanation:

A. Gravitational Field Strength

The gravitational field strength can be calculated using the following formula:

[tex]g= \frac{Gm}{r^2}[/tex]

G, or the universal gravitational constant, is 6.67 × 10⁻¹¹ N*m²/kg². The mass of Saturn is 5.68 × 10²⁴ kilograms. The radius of Saturn is 6.03×10⁷ meters.

Substitute these values into the formula.

[tex]g= \frac{ (6.67 \times 10^{-11} \ N*m^2/kg^2) (5.68 \times 10^{24} \ kg)}{(6.03 \times 10^{7} \ m )^2}[/tex]

Multiply the numerator and square the denominator.

[tex]g= \frac{ 3.78856 \times 10^{14} \ N *m^2/kg }{3.63609 \times 10^{15} \ m^2}[/tex]

Divide.

[tex]g= 0.1041932405 \ N/kg[/tex]

The original measurements of mass and radius have 3 significant figures, so our answer must have the same. For the number we found, that is the thousandth place. The 1 in the ten-thousandth place tells us to leave the 4 in the thousandth place.

[tex]\boxed {g \approx 0.104 \ N/kg}[/tex]

B. Force of Gravity

The force of gravity is calculated using the following formula:

[tex]F_g= mg[/tex]

The mass of the object is 50 kilograms. We just calculated the gravitational field strength, which is 0.104 Newtons per kilogram. Substitute these values into the formula.

[tex]F_g= (50 \ kg)(0.104 \ N/kg)[/tex]

Multiply. The units of kilograms cancel.

[tex]\boxed {F_g=5.20 \ N}[/tex]

What is the acceleration of the cart at t=8 seconds?

Hence the answer us letter a) 0 m/s^2.

That's all I know, Hope it help :)

Answer:

626m

Explanation:

Answer:

batteries in parallel connection and bulbs in serial connection

To get the dimmest bulb with two batteries and two bulbs you would connect the batteries in parallel and the bulbs in series.

When two-terminal components and electrical networks that can be connected in series or parallel. This will result in two terminals in the electrical network, and may themselves participate in a series or parallel topology. When a two-terminal "object" is an electrical component or electrical network is a matter of perspective.

A circuit is said to be in series when the same current flows through all the components in the circuit where the current has only one path. A circuit is said to be parallel when there are multiple paths for the electric current to flow through it where the components which are part of the parallel circuit will have a constant voltage across all their ends.

Thus, to get the dimmest bulb with two batteries and two bulbs you would connect the batteries in parallel and the bulbs in series.

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Answer:

The race car will crash into the outer wall

Explanation:

max fr = μsN = 1.1 mg = 11 m

mv2/R = m(100)2/(400) = 25 m > fr

Answer: for part A Its A the ANSWER for part B its D

Explanation:

Answer:

a and b

Explanation:

Answer/Explanation:

It False, because if You Round Both of them..

1.25= 1.30

1.04= 1.00

it's like, 1 dollar and 4 cents; compared to 1 dollar and 25 cents. Obviously 25 cents is a lot more than 4 cents.

Answer:

everything will float up and go up to space and die

Explanation:

gravity keeps us down and once it stops everything will float up. And if it were to stop everywhere everything and everyone will die and everything will be destroyed.