Imagine a monkey is sitting inside a barrel turned on its side. A cruel elephant pushes the barrel down a hill and the monkey starts to roll inside the barrel. This particular monkey gets motion sickness, and an outside observer has noticed that if the monkey spins more than once per second, the monkey will likely vomit. The barrel rolls perfectly down the slope (without slipping) and the outside observer calculates the angular acceleration of the barrel to be 1.2rad/s2. The barrel has a diameter of 1.5 m.
(a) How long will it take for the monkey to spin fast enough to vomit? (b) How far will the monkey have rolled before vomiting?
(c) How many times will the monkey have made a complete circle before vom- iting?

Answer:

Choice C: Approximately [tex]1.64[/tex].

(Assuming that light entered into this glass block from air.)  

Explanation:

Let [tex]n_{1}[/tex] denote the refractive index of the first medium (in this example, air.) Let [tex]\theta_{1}[/tex] denote the angle of incidence.

Let [tex]n_{2}[/tex] denote the refractive index of the second medium (in this example, the glass block.) Let [tex]\theta_{2}[/tex] denote the angle of refraction.

By Snell's Law:

[tex]n_{1} \, \sin(\theta_{1}) = n_{2}\, \sin(\theta_{2})[/tex].

Rearrange the equation to find an expression for [tex]n_{2}[/tex], the refractive index of the second medium (the glass block.)

[tex]\begin{aligned}n_{2} = \left(\frac{\sin(\theta_{1})}{\sin(\theta_{2})}\right)\, n_{1}\end{aligned}[/tex].

The refractive index of air is approximately [tex]1.00[/tex]. Substitute in the values and solve for [tex]n_{2}[/tex], the refractive index of the glass block:

[tex]\begin{aligned}n_{2} &= \left(\frac{\sin(\theta_{1})}{\sin(\theta_{2})}\right)\, n_{1} \\ &= \left(\frac{\sin(46^{\circ})}{\sin(26^{\circ})}\right)\times 1.00 \\ &\approx 1.64\end{aligned}[/tex].

Answer:

C

Explanation:

Fusion and fission are similar in that they both release large amounts of energy. Nuclear fusion is a process in which two nuclei join to form a larger nucleus. Nuclear fission is a process in which a nucleus splits into two smaller nuclei.

Answer:

c. lubricant..........

Answer:

it is 1 / square root of the change in distance

Explanation:

since the equation of the gravitational force is

[tex]F=G{\frac{m_1m_2}{r^2}}[/tex]

then F and r are inversely related, by the equation

[tex]F \alpha \frac{1}{r^2}[/tex]

this means when F is multiplied by 2 then r^2 is multiplied by half

so when r is multiples by half we first square the number (0.5) ^ 2 = 0.25

so

[tex]F \alpha \frac{1}{(0.25)r^2}[/tex]

which means F is multiples by 1/0.25 or 4 when the radius is halfed

What is the weight of a car with the mass of 1000 kg?

Answer: it is 9800 N.

Answer:

SONGS CLICKS AND WHISTLE

Explanation:

Answer:

v=30m/s

Explanation:

m = 1500kg

v = 30m/s

t = 25s

The velocity time graph is parallel to the time axis,

that means The Velocity is constant. ('constant' means remains same).

Therefore, after 25s, v=30m/s

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The neutron has no charge, and a mass of slightly over 1 amu. Some scientists propose the neutron is made up of a proton and electron-like particle. The electron is a very small particle located outside the nucleus.

Electron: -1

Neutron: 0

Proton: +1

Answer: 100 pascals times 0.2 m^2= 20 N force is applied.

Explanation:

Answer:

the electric energy travels through the plug or wire or whatever is connecting the energy source to the lightbulb, which conducts electricity, and to the light bulb. the electric energy is transfered into light energy and thermal energy

Explanation:

i hope i understood this question and answered it correctly XD

The conservation of the momentum allows to find the velocity of the second body after the elastic collision is:

           [tex]v_f = \frac{2u_o}{1- \frac{m_2}{m_1} }[/tex]  

the momentum is defined by the product of the mass and the velocity of the body.

        p = mv

The bold letters indicate vectors, p is the moment, m the mass and v the velocity of the body.

If the system is isolated, the forces during the collision are internal and the it  is conserved. Let's find the momentum is two instants.

Initial instant. Before crash.

      p₀ = m₁ u₀ + 0

Final moment. After crash.

      [tex]p_f = m_1 u_f + m_2 v_f[/tex]  

The momentum is preserved.

      p₀ = [tex]p_f[/tex]  

      [tex]m_1 u_o = m_1 u_f + m_2 v_f[/tex]  

Since the collision is elastic, the kinetic energy is conserved.

      K₀ = [tex]K_f[/tex]

      ½ m₁ u₀² = ½ m₁ [tex]u_f^2[/tex]  + ½ m₂  [tex]v_f^2[/tex]  

Let's write our system of equations.

       [tex]m_1 u_o = m_1 u_f + m_2 v_f \\m_1 u_o^2 = m_1 u_f^2 + m_2 v_f^2[/tex]

Let's solve

       [tex]u_f = u_o - \frac{m_2}{m_2} \ v_f \\u_f^2 = u_o^2 - \frac{m_2}{m_1} \ v_f^2[/tex]

       [tex]( u_o - \frac{m_2}{m_1} v_f)^2 = u_o - \frac{m_2}{m_1} \ v_f^2 \\u_o^2 - 2 \frac{m_2}{m_1} \ u_o v_f + (\frac{m_2}{m_1} )^2 v_f^2 = u_o^2 - \frac{m_2 }{m_1} \ v_f^2[/tex]  

        [tex]2 \frac{m_2}{m_1} \ u_o = \frac{m_2}{m_1} v_f \ ( 1 - \frac{m_2}{m_1}) \\v_f = \frac{2u_o}{1-\frac{m_2}{m_1} }[/tex]

In conclusion, using the conservation of momentum, we can find the velocity of the second body after the elastic collision is:

           [tex]v_f = \frac{2u_o}{1-\frac{m_2}{m_1} }[/tex]  

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Answer:

Mechanical energy is the energy a substance or system has because of its motion. For example machines use mechanical energy to do work.

Answer:

(D)

E = V Q      energy of charge Q  thus V = E / Q

Formulas change from F to degree C : C = (F – 32) / 1.8

so we have (176-32) /1.8= 80 oC

Formulas change from F to degree K : K = 5 / 9 x (F – 32) + 273.15

so we have 5/9 x (176-32) + 273.15 = 353 oK

ok done. Thank to me :>

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The velocity for the entire trip is 0.4 m/s as It takes her 500 seconds to make the round trip and 60 kg • m/s2 = (45 kg • v) + (20 kg • 3 m/s).

Path 1 = 400 m В B. A Path 2 = 200 m Path 3 = 300 m. Thus, option C is correct.

A particle's settling velocity known as the rate at which is travels through a still fluid. The specific gravity of the particles, their size, and their shape all have an impact on settling velocity.

A particle in still air will gravitationally settle and reach its terminal velocity fairly quickly. A particle's terminal velocity in a still fluid is referred to as the settling velocity (also known as the "sedimentation velocity").

Understanding variations in the hydraulic regime and interactions between sediment and fluid in the surf zone depends heavily on the particle settling velocity at the foreshore region. In contrast to sedimentation, which is the end product of the settling process, settling is the movement of suspended particles through the liquid.

Therefore, Thus, option C is correct.

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Answer:

it is correct

Explanation:

Though no rounded numbers can be defined as accurate, if we were going by people's discovery, and research, we can define that the number, g = 9.8m/s^2, is accurate

Answer:

18.66m

Explanation:

This was actually fun! Let set up the problem first: As you drop the sphere, it will accelerate till it hits the water with a given speed [tex]\dot z[/tex]. Once sinking the ball is subjected to two forces: its own weight [tex]m_sg = \rho_sVg[/tex] directed towards the bottom of the lake, and buoyancy (Archimedes law), ie a force upward equal to the volume of displaced water, [tex]m_wg=\rho_wVg[/tex]. At this point it's the classical "how high can I toss a ball before it falls down" with a water twist. Please note that I'm using z as the height of the sphere, and [tex]\dot z; \ddot z[/tex] represent the velocity (with one dot) and the acceleration (with two dots) in the z direction .Let's assume the sign of all quantities being positive if directed upwards, and negative if towards the bottom of the lake.

Let's first determine how fast the ball hit the water. For me the easiest way is saying "at 8m it has a given potential energy, and 0 kinetic energy. When it hits the water it loses all potential energy and has only kinetic energy". In numbers:

[tex]m_sgz=\frac12m_s\dot z_0^2[/tex] Let's divide by the masses, g is a known value ([tex]9.81 ms^{-2}[/tex]), z is 8 meters, and we get that [tex]\dot z_0 = 4\sqrt g =12.52 m/s[/tex]

At this point, let's determine the force acting on the sphere, courtesy of Newton second law and the debate we had earlier:

[tex]m_s \ddot z = -m_sg + m_wg\\\rho_sV \ddot z = -\rho_sVg + \rho_wV g[/tex]

At this point we can divide by the volume of the sphere, and make use of the fact that [tex]\rho_s = 0.7 \rho_w[/tex]

[tex]0.7\rho_w \ddot z = -.7\rho_w g+ \rho_wg \rightarrow 0.7 \ddot z = 0.3 g\\\ddot z = \frac {0.3}{0.7} g= \frac 37g = 4.2 ms^-2[/tex]

We're almost there. At this point we can write the law of motion for the sphere.

[tex]\dot z = \dot z_0 + \ddot z t[/tex] that we will use to find the time for the ball to stop sinking - ie reaches 0 velocity.

[tex]0 = -12.52 +4.2t \rightarrow t= 12.52/4.2 \approx 3s[/tex]

At this point we can use the other law of motion to find out the distance traveled

[tex]z= z_0 + \dot z_ot + \frac12 \ddot z t^2\\z= 0 -12.52 (3) + \frac12 (4.2)(3)^2 = -37.56+18.90 = -18.66 m[/tex]

as usual, please double and triple check all the calculations, it's almost 1.30 am here and I am not the most confident number cruncher even when fully awake.

Answer:

please check the image

Explanation:

I hope this image helps you please follow the steps. Thank you

Answer:

1kg/```````2

Explanation:

solution

The amount of work done to stop the car is equal to 322,099.85 Joules.

Given the following data:

Conversion:

Velocity = 95 km/h = [tex]\frac{95 \times 1000}{60 \times 60} = 26.39 \;m/s^2[/tex]

To determine the amount of work done to stop the car, we would apply the work-energy theorem:

Note: The amount of work done must balance the kinetic energy possessed by the car due to its motion.

From the work-energy theorem, we have:

[tex]Work\done = \Delta K.E\\\\Work\done = \frac{1}{2} MV^2[/tex]

Substituting the given parameters into the formula, we have;

[tex]Work\;done = \frac{1}{2} \times 925 \times (26.39)^2\\\\Work\;done =462.5 \times 696.4321[/tex]

Work done = 322,099.85 Joules

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For the 100 kg roller coaster that comes over the first hill of height 20 meters at 2 m/s, we have:

1) The total energy for the roller coaster at the initial point is 19820 J

2) The potential energy at point A is 19620 J

3) The kinetic energy at point B is 10010 J

4) The potential energy at point C is zero

5) The kinetic energy at point C is 19820 J

6) The velocity of the roller coaster at point C is 19.91 m/s

1) The total energy for the roller coaster at the initial point can be found as follows:

[tex] E_{t} = KE_{i} + PE_{i} [/tex]

Where:

KE: is the kinetic energy = (1/2)mv₀²

m: is the mass of the roller coaster = 100 kg

v₀: is the initial velocity = 2 m/s

PE: is the potential energy = mgh

g: is the acceleration due to gravity = 9.81 m/s²

h: is the height = 20 m

The total energy is:

[tex] E_{t} = KE_{i} + PE_{i} = \frac{1}{2}mv_{0}^{2} + mgh = \frac{1}{2}*100 kg*(2 m/s)^{2} + 100 kg*9.81 m/s^{2}*20 m = 19820 J [/tex]

Hence, the total energy for the roller coaster at the initial point is 19820 J.

2) The potential energy at point A is:

[tex] PE_{A} = mgh_{A} = 100 kg*9.81 m/s^{2}*20 m = 19620 J [/tex]

Then, the potential energy at point A is 19620 J.

3) The kinetic energy at point B is the following:

[tex] KE_{A} + PE_{A} = KE_{B} + PE_{B} [/tex]

[tex] KE_{B} = KE_{A} + PE_{A} - PE_{B} [/tex]

Since

[tex] KE_{A} + PE_{A} = KE_{i} + PE_{i} [/tex]

we have:

[tex] KE_{B} = KE_{i} + PE_{i} - PE_{B} =  19820 J - mgh_{B} = 19820 J - 100kg*9.81m/s^{2}*10 m = 10010 J [/tex]

Hence, the kinetic energy at point B is 10010 J.

4) The potential energy at point C is zero because h = 0 meters.

[tex] PE_{C} = mgh = 100 kg*9.81 m/s^{2}*0 m = 0 J [/tex]

5) The kinetic energy of the roller coaster at point C is:

[tex] KE_{i} + PE_{i} = KE_{C} + PE_{C} [/tex]            

[tex] KE_{C} = KE_{i} + PE_{i} = 19820 J [/tex]      

Therefore, the kinetic energy at point C is 19820 J.

6) The velocity of the roller coaster at point C is given by:

[tex] KE_{C} = \frac{1}{2}mv_{C}^{2} [/tex]

[tex] v_{C} = \sqrt{\frac{2KE_{C}}{m}} = \sqrt{\frac{2*19820 J}{100 kg}} = 19.91 m/s [/tex]

Hence, the velocity of the roller coaster at point C is 19.91 m/s.

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Answer:

They will go backwards?

Explanation:

If positive they go forward but is negative they go backwards.

Answer:

The formula for potential energy depends on the force acting on the two objects. For the gravitational force the formula is P.E. = mgh, where m is the mass in kilograms, g is the acceleration due to gravity (9.8 m / s2 at the surface of the earth) and h is the height in meters.

Answe16000/3500(-1.5-2-)225000= 1.1

Explanation:

The mass of the mixture will be 2.19 ×10⁻³ kg. The unit of mass is kg and it is a scalar quantity.

Mass is a numerical measure of inertia, which is a basic feature of all matter. It is, in effect, a body of matter's resistance to a change in speed or position caused by the application of a force.

In the International System of Units (SI), the kilogram is the unit of mass.

The given data in the problem is;

The initial temperature of the mixture was, [tex]\rm T_i = 20 ^0 \ C[/tex]

The mixture froze at the temperature of, [tex]\rm T_F = -1.5 ^0 \ C[/tex]

The internal energy is,[tex]\rm E = \rm 165 \ kJ[/tex]

The specific heat capacity of the mixture is,[tex]\rm C = 3500 J/kg ^0C[/tex]

The specific latent heat of fusion of the mixture is,[tex]\rm l = 255 000 J/kg[/tex]

m is the mass of the mixture,

The latent heat is equal to the heat transfer. Because the net work done is zero.

The formula for the heat transfer is found as;

[tex]\rm Q = mCdt \\\\ m = \frac{Q}{Cdt} \\\\ m = \frac{165 }{3500(20-(-1.5)} \\\\ m = 2.19 \times 10^{-3} \ kg[/tex]

Hence the mass of the mixture will be 2.19 ×10⁻³ kg.

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Answer:

No

Explanation:

The rate of diffusion defines the gas that passes through some area over the course of time.

Answer:

2hr 21 min

Explanation:

0 days 2 hours 20 minutes 0 seconds

+ 0 days 0 hours 0 minutes 60 seconds

= 0 days 2 hours 21 minutes 0 seconds

P= 10m = 10 x 115 = 1150 N

work done while lifting a 115 kg sofa 1.5 m off the ground :

A= Ph = 1150 x 1.5 = 1725 J

P/s: I think the weight first is 115kg

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