Metamorphic rocks are formed at high temperature and medium to low pressure

Tennis balls traveling at greater than 100 mph routinely bounce off tennis rackets. At some sufficiently high speed, however, th

Kipish [7]

Answer:

Probability of tunneling is $10^{- 1.17\times 10^{32}}$

Solution:

As per the question:

Velocity of the tennis ball, v = 120 mph = 54 m/s

Mass of the tennis ball, m = 100 g = 0.1 kg

Thickness of the tennis ball, t = 2.0 mm = $2.0\times 10^{- 3}\ m$

Max velocity of the tennis ball, $v_{m} = 200\ mph$ = 89 m/s

Now,

The maximum kinetic energy of the tennis ball is given by:

$KE = \frac{1}{2}mv_{m}^{2} = \frac{1}{2}\times 0.1\times 89^{2} = 396.05\ J$

Kinetic energy of the tennis ball, KE' = $\frac{1}{2}mv^{2} = 0.5\times 0.1\times 54^{2} = 154.8\ m/s$

Now, the distance the ball can penetrate to is given by:

$\eta = \frac{\bar{h}}{\sqrt{2m(KE - KE')}}$

$\bar{h} = \frac{h}{2\pi} = \frac{6.626\times 10^{- 34}}{2\pi} = 1.0545\times 10^{- 34}\ Js$

Thus

$\eta = \frac{1.0545\times 10^{- 34}}{\sqrt{2\times 0.1(396.05 - 154.8)}}$

$\eta = 1.52\times 10^{-35}\ m$

Now,

We can calculate the tunneling probability as:

$P(t) = e^{\frac{- 2t}{\eta}}$

$P(t) = e^{\frac{- 2\times 2.0\times 10^{- 3}}{1.52\times 10^{-35}}} = e^{-2.63\times 10^{32}}$

$P(t) = e^{-2.63\times 10^{32}}$

Taking log on both the sides:

$logP(t) = -2.63\times 10^{32} loge$

$P(t) = 10^{- 1.17\times 10^{32}}$

6 0

2 years ago

How much time will it take for a bug to travel 2 meters across the floor if it is traveling at 0.5 m/s?

Lelu [443]

Answer:

it will take 4 seconds to travel 2 meters.

3 0

3 years ago

What do the three variables (f,m, a) in the equation mean?

Anna [14]

Answer:

f=force m=mass and a=acceleration

7 0

2 years ago

Malcolm and Ravi raced each other. The average of their maximum speeds was 260 km/h If doubled, Malcolm's maximum speed would be

AfilCa [17]

Answer

Given,

Average speed of Malcolm and Ravi = 260 km/h

Let speed of the Malcolm be X and speed of the Ravi Y.

From the given statement

$\dfrac{X+Y}{2}=260$

$X + Y = 520$ ....(i)

$2X - Y = 80$ ....(ii)

Adding both the equations

3 X = 600

X = 200 km/h

Putting value in equation (i)

Y = 520 - 200

Y = 320 Km/h

Speed of Malcolm = 200 Km/h

Speed of Ravi = 320 Km/h

8 0

2 years ago

When responding to sound, the human eardrum vibrates about its equilibrium position. Suppose an eardrum is vibrating with an amp

Paraphin [41]

Answer:

796.18 Hz

Explanation:

Applying,

Maximum velocity = Amplitude×Angular velocity

Therefore,

V' = A(2πf)............... Equation 1

Where V' = maximum velocity of the eardrum, A = Amplitude of vibration of the eardrum, f = frequency of the eardrum vibration, π = pie

make f the subject of the equation

f = V'/2πA................ Equation 2

From the question,

Given: V' = 3.6×10⁻³ m/s, A' = 7.2×10⁻⁷ m,

Constant: 3.14.

Substitute these values into equation 2

f = 3.6×10⁻³/( 7.2×10⁻⁷×2×3.14)

f = 796.18 Hz

6 0

2 years ago