What is the momentum of a 65kg ball rolling at 5 m/s?

A coin completes 18 spins in 12 seconds. The centripetal acceleration of the edge of the coin is 2.2 m/s2. The radius of the coi

stellarik [79]

Answer:

2.5 cm

Explanation:

Number of spins in 12 seconds = 18

Number of spins in 1 second = 18 / 12 = 1.5

Number of spins in one second is called frequency.

f = 1.5 rps

ac = 2.2 m/s^2

Let r be the radius of coin

Centripetal acceleration, ac = r x w^2

2.2 = r x ( 2 x 3.14 x 1.5) ^2

2.2 = r x 88.7364

r = 0.025 m = 2.5 cm

3 0

4 years ago

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For a proton in the ground state of a 1-dimensional infinite square well, what is the probability of finding the proton in the c

Butoxors [25]

Answer:

The probability of finding the proton at the central 2% of the well is almost exactly 4%

Explanation:

If we solve Schrödinger's equation for the infinite square well, we find that its eigenfunctions are sinusoidal functions, in particular, the ground state is a sinusoidal function for which only half a cycle fits inside the well.

let $L$ be the well's length, the boundary conditions for the wavefunction are:

$\psi(0) = \psi(L) =0$

And Schrödinger's equation is:

$- \frac{\hbar^2}{2m} \frac{d^2\psi}{dx^2} = E\psi$

The solution to this equation are sines and cosines, but the boundary conditions only allow for sine waves. As we pointed out, the ground state is the sine wave with the largest wavelength possible (that is, with the smallest energy).

$\psi_0(x)=\sqrt[]{\frac{2}{L} }\, \sin(\frac{\pi x}{L} )\\$

here the leading constant is just there to normalise the wavefunction.

Now, if we know the wavefunction, we can know what the probability density function is, it is:

$f_X(x) = |\psi|^2$

So in our case:

$f_X(x) = \frac{2}{L} \sin^2(\frac{\pi x}{L})$

And to find the probability of finding the particle in a strip at the centre of the well of width 2% of L we only have to integrate:

$P(X \in [0.49 L, 0.51L ])= \int\limits^{0.49L}_{0.51L } {\frac{2}{L} \sin^2(\frac{\pi x}{L})} \, dx$

If we do a substitution:

$x = u \, L$

We get the integral:

$\int\limits^{0.49}_{0.51 } 2\, \sin^2(\pi u)} \, du$

This integral can be computed analytically, and it's numerical value is .0399868, that is, almost a 4% probability.

5 0

3 years ago

What is the magnitude of velocity called?

PIT_PIT [208]

The magnitude of a velocity vector is called speed. Supposethat a wind is blowing in from the direction at a speed of 50 km/h. (This meansthat the direction from which the wind blows is west of the northerly direction.) Apilot is steering a plane in the direction at an airspeed (speed in still air) of250 km/h

3 0

4 years ago

A polo player hits a ball with a mass of 0.42 kg with a force of 7.35 Newtons.

Serga [27]

Due to the law of conservation of momentum, the force exerted on the mallet is equal and opposite to the force exerted on the ball, so the answer is C.

4 0

3 years ago

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A 50-foot flagpole is at the entrance of a building that is 300 feet tall. If the length of the flagpole's shadow is 30 feet at

natka813 [3]

First you will want to sketch out both of the situations. It should be two sketches, one for the flagpole and one for the building.

To solve this, you will want to create a proportion.

Flagpole height/flagpole shadow=building height/building shadow

Therefore, it should look like this:
50/30= 300/x

Solve for x:
50x=9,000
X= 180 feet

YOUR ANSWER IS C.

7 0

3 years ago