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4 years ago

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A grandfather clock keeps time using a pendulum consisting of a light rod connected to a small heavy mass. With a rod of length

L, the period of oscillation is 2.00 s. What should the length of the rod be for the period of the oscillations to be 1.00 s?

1 answer:

german4 years ago

5 0

Answer:

The length of the rod should be

$\frac{L}{4} \\$

Explanation:

Period of simple pendulum is given by

$T=2\pi\sqrt{\frac{l}{g}} \\$

We have

$\frac{T_1^2}{T_2^2}=\frac{l_1}{l_2}\\\\\frac{2^2}{1^2}=\frac{L}{l_2}\\\\l_2=\frac{L}{4} \\$

The length of the rod should be

$\frac{L}{4} \\$

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A 15 m long garden hose han an inner diameter of 2.5 cm. One end is connected to a spigot; 20 C water flows from the other end a

pogonyaev

We can solve this problem using <span>Hagen–Poiseuille equation. Derivation of this equation is a bit complicated so I will just write down the equation.
</span> $\Delta P= \frac{8\mu QL}{\pi R^4}$
This equation gives you the pressure drop <span>in an </span>incompressible<span> and </span>Newtonian<span> fluid in </span>laminar flow<span> flowing through a long cylindrical pipe of the constant cross section.
L is the length of the cylinder, Q is the volumetric flow rate, R is the radius of the pipe, and $\mu$ is dynamic viscosity.
Dynamic viscosity of water at 20 Celsius is 0.001 PaS.
Now we can calculate the pressure drop:
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3 years ago

A quantum system has three states, with energies 0, 1.6 × 10-21, and 1.6 × 10-21, in Joules. It is coupled to an environment wit

xenn [34]

To develop the problem it is necessary to apply two concepts, the first is related to the calculation of average data and the second is the Boltzmann distribution.

Boltzmann distribution is a probability distribution or probability measure that gives the probability that a system will be in a certain state as a function of that state's energy and the temperature of the system. It is given by

$z = \sum\limit_i e^{-\frac{\epsilon_i}{K_0T}}$

Where,

$\epsilon_i =$ energy of that state

k = Boltzmann's constant

T = Temperature

With our values we have that

T= 250K

$k = 1.381*10^{23} m^2 kg s^{-2} K^{-1}$

$\epsilon_1=0J$

$\epsilon_2=1.6*10^{-21}J$

$\epsilon_3=1.6*10^{-21}J$

To make the calculations easier we can assume that the temperature and Boltzmann constant can be summarized as

$\beta = \frac{1}{kT}$

$\beta = \frac{1}{(1.381*10^{23} m^2)(250)}$

$\beta = 2.9*10^{20}J$

Therefore the average energy would be,

$\bar{\epsilon} =\frac{\sum \epsilon_i e^{-\beta \epsilon_i}}{\sum e^{-\beta \epsilon_i}}$

Replacing with our values we have

$\bar{\epsilon} = \frac{0e^{-0}+1.6*10^{-21}*e^{-\Beta(1.6*10^{-21})}+1.6*10^{-2-1}*e^{-(2.9*10^{20})(1.6*10^{-21})}}{1+2e^{-2.9*10^{20}*1.6*10^{-21}}}$

$\bar{\epsilon} = 0.9*10^{-22}J$

Therefore the average internal energy is $\bar{\epsilon} = 0.9*10^{-22}J$

3 0

3 years ago

A car is moving with a constant velocity of 25 m/s. Which of the following is true?

S_A_V [24]

b) the net force on the car is zero.

Explanation:

Let's analyze each option one by one:

a) the force from the engine is greater than all the forces of friction. --> FALSE. In fact, the car is moving at constant velocity: this means that its acceleration is zero,

a = 0

and so Newton's second law becomes

$\sum F = ma = 0$

where $\sum F$ is the net force on the car and m is its mass. This means that the net force on the car is zero: so, the force from the engine cannot be greater than all the forces of friction, otherwise the net force cannot be zero.

b) the net force on the car is zero. --> TRUE, for what we said at point A)

c) the inertia is changing. --> FALSE. The inertia of an object just depend on the mass and the velocity of the object: as neither the mass nor the velocity are changing in this problem, then the inertia of the car is not changing.

d) the forces of friction are proportional to the acceleration of the car. --> FALSE. Generally, the force of friction acting on an object moving on a flat surface is

$F_f = \mu mg$

where $\mu$ is the coefficient of friction, m is the mass, and g the acceleration of gravity. Therefore, the force of friction does not depend on the acceleration of the car.

e) All of the above. --> FALSE

Learn more about net force and Newton's second law:

brainly.com/question/3820012

#LearnwithBrainly

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3 years ago

The maximum speed with which you can throw a stone is about 25 m/s. Can you hit a window 50 m away and 13 m up from the point wh

Nookie1986 [14]

Answer:

no, the maximum height = 12.3m

Explanation:

The equation for the trajectory of the ball for a given angle can be derived from:

(1) $x=cos\phi v_0t$

and

(2) $y=-\frac{1}{2}gt^2 +sin\phi v_0t$

Combining equation 1 and 2:

(3) $y=xtan\phi -\frac{gx^2}{2cos^2\phi v_0^2}$

Taking the derivative:

(4) $\frac{dy}{d\phi}=\frac{xsec^2\phi}{v_0^2}(v_0^2-gxtan\phi)$

Setting equation 4 equal to zero to calculate the maximum angle:

(5) $\phi=tan^{-1}(\frac{v_0^2}{gx})$

Plugging equation 5 back into equation2 confirms, the trajectory can't reach the target. The maximum height is 12.3m.

3 0

3 years ago

Read 2 more answers

3. What is the SI unit of force? What is this unit equivalent to in terms of fundamental units?

Serhud [2]

Answer:

force = mass * acceleration

therefore the SI unit is kg*m/s2 or newton's

it's a vector quantity because it has both direction(acceleration) and size (mass)

4 0

3 years ago