Answer:
v₀ = 2,562 m / s = 9.2 km/h
Explanation:
To solve this problem let's use Newton's second law
F = m a = m dv / dt = m dv / dx dx / dt = m dv / dx v
F dx = m v dv
We replace and integrate
-β ∫ x³ dx = m ∫ v dv
β x⁴/ 4 = m v² / 2
We evaluate between the lower (initial) integration limits v = v₀, x = 0 and upper limit v = 0 x = x_max
-β (0- x_max⁴) / 4 = ½ m (v₀²2 - 0)
x_max⁴ = 2 m /β v₀²
Let's look for the speed that the train can have for maximum compression
x_max = 20 cm = 0.20 m
v₀ =√(β/2m) x_max²
Let's calculate
v₀ = √(640 106/2 7.8 104) 0.20²
v₀ = 64.05 0.04
v₀ = 2,562 m / s
v₀ = 2,562 m / s (1lm / 1000m) (3600s / 1h)
v₀ = 9.2 km / h
Answer:
Explanation:
Previous concepts
Angular momentum. If we consider a particle of mass m, with velocity v, moving under the influence of a force F. The angular momentum about point O is defined as the “moment” of the particle’s linear momentum, L, about O. And the correct formula is:
Applying Newton’s second law to the right hand side of the above equation, we have that r ×ma = r ×F =
MO, where MO is the moment of the force F about point O. The equation expressing the rate of change of angular momentum is this one:
MO = H˙ O
Principle of Angular Impulse and Momentum
The equation MO = H˙ O gives us the instantaneous relation between the moment and the time rate of change of angular momentum. Imagine now that the force considered acts on a particle between time t1 and time t2. The equation MO = H˙ O can then be integrated in time to obtain this:
Solution to the problem
For this case we can use the principle of angular impulse and momentum that states "The mass moment of inertia of a gear about its mass center is 
".
If we analyze the staritning point we see that the initial velocity can be founded like this:
And if we look the figure attached we can use the point A as a reference to calculate the angular impulse and momentum equation, like this:
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And if we integrate the left part and we simplify the right part we have
And if we solve for 
we got:
Answer:
See Explaination
Explanation:
//Function
long loop (long x, long n)
{
//Declare a variable named result and initialize it to zero
long result = 0;
//Declare a variable named mask
long mask;
//For loop
for(mask = 1; mask != 0; mask = mask << (n & 0xFF))
{
//Calculate
result | = (x&mask);
}
//Return result
return result;
}
Given:
Pressure, 
= 1300 kPa
Temperature, 
= 
= 100 kPa
velocity, v = 40 m/s
A = 1
Solution:
For air propertiess at
= 1300 kPa
=
= 793kJ/K
= 
and also at
= 100 kPa
= 401 KJ/K
= 
a) Mass flow rate is given by:
Now,
= 46.51 kg/s
b) for the power produced by turbine, 
= 18.231 MW
Answer:
Apalancamiento.
Explanation:
El apalancamiento es el uso de dinero prestado (deuda) para aumentar el rendimiento esperado del capital. El apalancamiento se mide como la relación entre la deuda que devenga intereses y los activos totales. Cuanto mayor sea la deuda que devenga intereses, mayor será el apalancamiento financiero o "aceleración". Esto puede tener un efecto positivo o negativo.
Los costos por intereses de este capital de préstamo suelen ser fijos y se deducen de los ingresos. Un préstamo permite que una organización genere más ingresos sin un aumento necesario en el capital. Como no es necesario recaudar ni mantener capital social adicional, no se requieren pagos de dividendos adicionales (que no se pueden deducir de las ganancias). Sin embargo, un alto apalancamiento puede ser beneficioso durante los tiempos de auge, pero puede conducir a serios problemas de flujo de efectivo durante una recesión, ya que es posible que no haya suficientes retornos para cubrir mayores costos de intereses y obligaciones de reembolso.
