4. Trilobites are animals that lived during the Paleozoic era. They populated all parts of the
ocean showed consistent evolution over time and left behind fossils that are large
enough to be studied without a microscope. All of these characteristics make trilobites
the ideal
a. Trace fossil
b. Keystone species
c. Index fossil
d. Reference point
dnreserve the remains of dead

The angular velocity of the wheel at the bottom of the incline is 4.429 rad/sec

The angular velocity (ω) of an object is the rate at which the object's angle position is changing in relation to time.

For a wheel attached to an incline angle, the angular velocity can be computed by considering the conservation of energy theorem.

As such the total kinetic energy (K.E) and rotational kinetic energy (R.K.E) at a point is equal to the total potential energy (P.E) at the other point.

i.e.

P.E = K.E + R.K.E

[tex]\mathbf{mgh = \dfrac{1}{2}m(r \times \omega)^2 + \dfrac{1}{2}\times I \times \omega^2}[/tex]

[tex]\mathbf{gh = \dfrac{1}{2}(r \times \omega)^2 + \dfrac{1}{2}\times r^2 \times \omega^2}[/tex]

[tex]\mathbf{2 \times \dfrac{gh}{r^2} =\omega^2 + \omega^2}[/tex]

[tex]\mathbf{2 \omega^2=2 \times \dfrac{9.81 \times 8 m }{2.0 ^2} }[/tex]

[tex]\mathbf{\omega^2=\dfrac{39.24 }{2}}[/tex]

[tex]\mathbf{\omega=\sqrt{19.62 } \ rad/sec}[/tex]

[tex]\mathbf{\omega=4.429 \ rad/sec}[/tex]

Therefore, we can conclude that the angular velocity of the wheel at the bottom of the incline is 4.429 rad/sec

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The angular velocity of the wheel depends on the mass, radius and the

mode of rotation of the wheel (with or without slipping).

Reasons:

The given parameters are;

Radius of the wheel, r = 2.0 m

Height of the incline, h = 8.0 m

Required:

Angular velocity of the wheel at the bottom of the incline.

Solution:

The potential energy of the wheel at the top of the hill, P.E. = m·g·h

[tex]Sum \ of \ the \ kinetic \ energy \ of \ the \ wheel, \ K.E. = \mathbf{\displaystyle \frac{1}{2} \cdot m \cdot v^2 + \frac{1}{2} \cdot I \cdot \omega ^2}[/tex]

Where;

v = The translational velocity of the wheel = ω·r

I = The moment of inertia of the wheel = m·r²

Therefore'

[tex]Sum \ of \ K.E. = \displaystyle \frac{1}{2} \cdot m \cdot (\omega \cdot r)^2 + \frac{1}{2} \cdot m \cdot r^2 \cdot \omega ^2 = \mathbf{m \cdot r^2 \cdot \omega^2}[/tex]

At the bottom of the hill, the potential energy is converted to kinetic energy

Therefore;

P.E. = Sum of K.E.

m·g·h = m·r²·ω²

g·h = r²·ω²

[tex]\displaystyle \omega = \sqrt{ \frac{g \cdot h}{r^2} } = \mathbf{ \frac{\sqrt{g \cdot h} }{r}}[/tex]

Where;

g = Acceleration due to gravity ≈ 9.81 m/s²

Therefore;

[tex]\displaystyle \omega = \frac{\sqrt{9.81 \times 8} }{2} \approx \mathbf{ 4.43}[/tex]

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Answer:

English is the language

Answer: im most likely wrong but i think its A

Explanation:

Answer:

Faith, to me is almost like hope but for faith you need to believe. Some people associate the word faith with religion. But that's not it. Faith is really just a stronger term than believing someone. Like you can believe in someone but not have faith in that same person. You can have faith in someone but to do that you have to believe and trust them.

Explanation:

Answer:

Explanation:

30 m/s • 3 hr •3600 s/hr / 1000 m/km = 324 km west

Answer:

Explanation:

PE = mgh

g = PE/mh

g = 15.0 / (0.200(0.500))

g = 150 m/s²

This is one strong astronaut if he can work in an environment where gravity is more than 15 times stronger than on earth.

Answer:

n

Explanation:

TWO outcomes can be predicted the students will find:

When a constant mass of gas is cooled, its volume falls, and when the temperature is raised, its volume grows. The volume of the gas rises by 1/273 of its initial volume at 0 °C for every degree of temperature rise.

In layman's words, the volume of a fixed mass of gas is exactly proportional to temperature at constant pressure.

The teacher took two latex balloons and blew them up with helium gas to the same size. As she placed Balloon A in a -15° C freezer, its temperature decreases and that's why, the size of balloon A becomes smaller. Again she  placed Balloon B in the sun on 30° C day, its temperature increases and that's why, the size of balloon B becomes larger.

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Hi there!

We can use the following equation for angular momentum:

[tex]\large\boxed{L = mrv}[/tex]

m = mass (kg)

r = distance from reference point (m)

v = velocity (m/s)

We can simply plug-and-chug the values provided in the question.

L = (50)(30)(20) = 30000 kgm²/s

Answer:

Acceleration = (final velocity - starting velocity) / time

4 = (x-1000) / 100

<br/>x = 1400 m/s

Explanation:

The final velocity of the rocket ship which is moving with an initial velocity of 1000 m/s and acceleration of 4 m/s² after 100 seconds is 1400 m/s.

Velocity of a moving body is the rate of its speed. Mathematically velocity is the ratio of distance travelled to the time taken with a unit of m/s. Acceleration is the rate of change in velocity of  moving body. The unit of acceleration is 4 m/s² .

Thus acceleration can be determined from the change in velocity with respect to the change in time. Now, the relation between initial velocity, acceleration,  a and time,  t with the final velocity is written in the equation below:

v = u + at.

Where, v is the final velocity and u be the initial velocity.

Given here the initial velocity is 1000 m/s. Acceleration of the rocket is 4 m/s² . Thus the velocity after 100 seconds is calculated as follows:

v = 1000 m/s +  ( 4 m/s² × 100 s )

  = 1400 m/s.

Hence, the speed of the rocket after 100 seconds will be 1400 m/s.

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Answer:

Explanation:

vA / vB = √(TA/(m/L)) / √(TB/(m/L))

The lengths are the same, so the L divides out to 1

The material is identical so the mass will be directly proportional to the cross sectional area of the string

vA / vB = √(TA/(πdA²/4)) / √(TB/(πdB²/4))

π/4 is common so divides out to 1

vA / vB = √(TA/dA²) / √(TB/dB²)

vA / vB = √(410/0.489²) / √(809/1.27²)

vA / vB = 41.407 / 23.396

vA / vB = 1.8488961...

vA / vB = 1.85

Answer: the current increases with each 3 volt and 9 volt. The relationship between resistance and current in a circuit is that the greater the resistance the less the current and the greater the current the less the resistance is. yayayay I could answer this I big brain :)

Answer: The answer is A) 49 N(Newtons).

Answer:

I think some drawbacks are that since there are no solid walls meaning it is weak and if murphy's law is in place, the water will destroy the substance. Tsunami waves also happen very quickly so even if the water can travel thru the substance quickly, it probably won't be quick enough. This design could help if the wave is smaller because less destruction would occur.

Explanation:

yeah

Answer:

1.108 ×  [tex]10^{-3}[/tex]J

Explanation:

v=21.0v

Q=52.8×  [tex]10^{-6}[/tex]

E=?

V=E/Q

E=v ×Q

 =21 ×52.8 ×[tex]10^{-6}[/tex]

 =1108.8   ×[tex]10^{-6}[/tex]

E= 1.108 ×  [tex]10^{-3}[/tex]J

Answer:

[tex]\frac{a_{d}}{a_{i}} = \frac{(1 -mu)}{mu}[/tex]

= (1 - μ)/μ

Explanation:

Always draw a diagram!

Up the incline:

[tex]Fr_{max}[/tex] = maximum friction

[tex]Fr_{max}[/tex] = μk

k = R = mg.cos(45) = mg.sin(45)

Resolution of forces parallel to the slope:

F (Fp in the diagram) = force of propulsion

g = gravity

[tex]F - Fr_{max} = ma_{i}[/tex]

[tex]F -[/tex] μ.mg.cos(45) [tex]= ma_{i}[/tex]

Down the decline:

Resolution of forces:

[tex]mg.sin(45) - Fr_{max} = ma_{d}[/tex]

[tex]mg.sin(45) -[/tex] μ.mg.cos(45) [tex]= ma_{d}[/tex]

Then, find the ratio:

[tex]\frac{ma_{d}}{ma_{i}} = \frac{mg.sin(45) - mu.mg.cos(45)}{-F + mu.mg.cos(45)} \\\\ \frac{a_{d}}{a_{i}} = \frac{k - k.mu}{-F + k.mu} \\\\ = \frac{k(1 -mu)}{-F + k.mu}[/tex]

Potentially, there is no need to consider F in this situation, in which case:

[tex]\frac{a_{d}}{a_{i}} = \frac{k(1 -mu)}{k.mu} \\\\ = \frac{(1 -mu)}{mu}[/tex]

= (1 - μ)/μ

Answer: push force gravity tension and reverse force

Explanation: sense they are pushing the box there is a push force gravity because this is likely on earth tension because it is the reverse of gravity and the reverse force because you have to have the reverse of push

Answer:

lithosphere

Explanation:

hope this helps you!!

Answer:

Heat flow

Explanation:

Answer:

Explanation:

For an ideal spring over a frictionless horizontal surface, stored energy is only a function of the spring constant k and the distance of compression. The mass of the block doing the compressing is irrelevant

Energy stored in the first example is

Em = ½kd²

Energy stored in the second example is

E₂m = ½k(2d)² = 4(½kd²) = 4Em

So the second situation has four times as much stored spring potential energy as the first situation

4 Em is correct

Good job!

Answer:

fifth harmonic

Explanation:

Answer:

Explanation:

F = ma

a = F/m

a = 75/25

a = 3 m/s²

Answer:

Explanation:

70.0(5.00)(9.81) = 3,433.5 = 3430 N

To solve this we must be knowing each and every concept related to  centripetal force and its calculations. Therefore, the centripetal force acting on her is 3430 N.

The term centripetal relates to a propensity to gravitate toward the center. Centripetal refers to moving in the direction of the center. The force that maintains an item moving in a circular direction and helps it stay on the path is referred to as centripetal force.

Furthermore, centrifugal force is indeed the tendency of things to deviate from a circular route and fly in a straight line. People frequently confuse centripetal force with centrifugal force.

Mathematically,

F = m a

  = 70 acceleration

  = 70 × 5 × 9.81

 = 3430 N

Therefore, the centripetal force acting on her is 3430 N.

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Answer:

The first one is the only one that is true all the time

Explanation:

The second one may be true if friction is high enough.

The other three are false all the time

Answer:

inertia   .

because yes

Hi there!

a.

We can use the initial conditions to solve for w₀.

It is given that:

[tex]\frac{d\theta}{dt} = w_0e^{-\sigma t}[/tex]

We are given that at t = 0, ω =  3.7 rad/sec. We can plug this into the equation:

[tex]\omega(0)= \omega_0e^{-\sigma (0)}\\\\3.7 = \omega_0 (1)\\\\\omega_0 = \boxed{3.7 rad/sec}[/tex]

Now, we can solve for sigma using the other given condition:

[tex]2 = 3.7e^{-\sigma (8.6)}\\\\.541 = e^{-\sigma (8.6)}\\\\ln(.541) = -\sigma (8.6)\\\\\sigma = \frac{ln(.541)}{-8.6} = \boxed{0.0714s^{-1}}[/tex]

b.

The angular acceleration is the DERIVATIVE of the angular velocity function, so:

[tex]\alpha(t) = \frac{d\omega}{dt} = -\sigma\omega_0e^{-\sigma t}\\\\\alpha(t) = -(0.0714)(3.7)e^{-(0.0714) (3)}\\\\\alpha(t) = \boxed{-0.213 rad\sec^2}[/tex]

c.

The angular displacement is the INTEGRAL of the angular velocity function.

[tex]\theta (t) = \int\limits^{t_2}_{t_1} {\omega(t)} \, dt\\\\\theta(t) = \int\limits^{2.5}_{0} {\omega_0e^{-\sigma t}dt\\\\[/tex]

[tex]\theta(t) = -\frac{\omega_0}{\sigma}e^{-\sigma t}\left \| {{t_2=2.5} \atop {t_1=0}} \right.[/tex]

[tex]\theta = -\frac{3.7}{0.0714}e^{-0.0714 t}\left \| {{t_2=2.5} \atop {t_1=0}} \right. \\\\\theta= -\frac{3.7}{0.0714}e^{-0.0714 (2.5)} + \frac{3.7}{0.0714}e^{-0.0714 (0)}[/tex]

[tex]\theta = 8.471 rad[/tex]

Convert this to rev:

[tex]8.471 rad * \frac{1 rev}{2\pi rad} = \boxed{1.348 rev}[/tex]

d.

We can begin by solving for the time necessary for the angular speed to reach 0 rad/sec.

[tex]0 = 3.7e^{-0.0714t}\\\\t = \infty[/tex]

Evaluate the improper integral:

[tex]\theta = \int\limits^{\infty}_{0} {\omega_0e^{-\sigma t}dt\\\\[/tex]

[tex]\lim_{a \to \infty} \theta = -\frac{\omega_0}{\sigma}e^{-\sigma t}\left \| {{t_2=a} \atop {t_1=0}} \right.[/tex]

[tex]\lim_{a \to \infty} \theta = -\frac{3.7}{0.0714}e^{-0.0714a} + \frac{3.7}{0.0714}e^{-0.0714(0)}\\\\ \lim_{a \to \infty} \theta = \frac{3.7}{0.0714}(1) = 51.82 rad[/tex]

Convert to rev:

[tex]51.82 rad * \frac{1rev}{2\pi rad} = \boxed{8.25 rev}[/tex]

Answer:

Explanation:

conservation of momentum

m(u) + M(0) = (m + M)v

u = (m + M)v/m

u = (0.250 + 1.35)(11.9) / 0.250

u = 76.16

u = 76.2 m/s

That's a fairly massive, and slow, bullet.

Crazy Wally Ok Ok ok hhahahaha

Answer:

Explanation:

F = mv²/R

F = 11.0(3.50²)/0.600 = 225 N

Answer:

*1) 100 Joule energy

*2) 101.2 m/s

Explanation:

*1) 1J = 1w

100J = 100w

*2) A 70-kg person will have to run at a speed of 101.2 m/s to have that amount of kinetic energy.