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podryga [215]
3 years ago
6

A dog sits 2.6 m from the center of a merry- go-round. a) If the dog undergoes a 1.7 m/s^2 centripetal acceleration, what is the

dog's linear speed? Answer in units of m/s. b) What is the angular speed of the merry-go- round? Answer in units of rad/s.
Physics
1 answer:
alexgriva [62]3 years ago
6 0

Answer:

a) v= 2.1 m/s

b) ω = 0.807 rad/s

Explanation

Conceptual analysis :

The dog and the merry-go- round describes a circular motion, then, the following formulas apply :

a_{c} =\frac{v^{2} }{r} Formula (1)

v = ω *r   Formula (2)

Where:

a_{c} : Centripetal acceleration(m/s²)

v: linear speed or tangential (m/s)

r :  radius of the circle (m)

ω : angular speed ( rad/s)

Data

r= 2.6 m

a_{c} =  1.7 m/s²

Problem develpment

a) We replace data in the formula 1 to calculate the dog's linear speed(v):

a_{c} =\frac{v^{2} }{r}

1.7 =\frac{v^{2} }{2.6}

v^{2} =1.7*2.6 = 4.42

v=(\sqrt{4.42})\frac{m}{s}

v= 2.1 m/s

b)We replace data in the formula 2 to calculate the angular speed of the merry-go- round (ω).

v = ω *r

2.1 = ω *2.6

ω = 2.1/2.6

ω = 0.807 rad/s

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<em><u> objects, stresses within itself, its </u></em><em><u>electric</u></em>

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Find the magnitude of the angular momentum of the second hand on a clock about an axis through the center of the clock face. Ass
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L = 4.711 *10^{-6} kg m2/s

Explanation:

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

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

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