Answer: Add an incline or grade to the road track.
Explanation:
Refer to the figure shown below.
When a vehicle travels on a level road in a circular path of radius r, a centrifugal force, F, tends to make the vehicle skid away from the center of the circular path.
The magnitude of the force is
F = mv²/r
where
m = mass of the vehicle
v = linear (tangential) velocity to the circular path.
The force that resists the skidding of the vehicle is provided by tractional frictional force at the tires, of magnitude
μN = μW = μmg
where
μ = dynamic coefficient of friction.
At high speeds, the frictional force will not overcome the centrifugal force, and the vehicle will skid.
When an incline of θ degrees is added to the road track, the frictional force is augmented by the component of the weight of the vehicle along the incline.
Therefore the force that opposes the centrifugal force becomes
μN + Wsinθ = W(sinθ + μ cosθ).
The inner planets are not colder or larger than the outer ones,
and they're not comprised of gas.
The inner planets are the ones that are made of rock. ( D ).
The Pacific is loosely shaped like a triangle, opening widely to the south but barely at all to the north, while the Atlantic is shaped like an hourglass with the choke point located very loosely at the equator (somewhat south of it in the west).
Answer:
a)
, b) ![v \approx 659.568\,\frac{m}{s}](https://tex.z-dn.net/?f=v%20%5Capprox%20659.568%5C%2C%5Cfrac%7Bm%7D%7Bs%7D)
Explanation:
a) According to the First Law of Thermodinamics, the system is not reporting any work, mass or heat interactions. Besides, let consider that such box is rigid and, therefore, heat contained inside is the consequence of internal energy.
![Q = U](https://tex.z-dn.net/?f=Q%20%3D%20U)
The internal energy for a monoatomic ideal gas is:
![U = \frac{3}{2} \cdot n \cdot R_{u} \cdot T](https://tex.z-dn.net/?f=U%20%3D%20%5Cfrac%7B3%7D%7B2%7D%20%5Ccdot%20n%20%5Ccdot%20R_%7Bu%7D%20%5Ccdot%20T)
Let assume that cubical box contains just one kilomole of monoatomic gas. Then, the temperature is determined from the Equation of State for Ideal Gases:
![T = \frac{P\cdot V}{n\cdot R_{u}}](https://tex.z-dn.net/?f=T%20%3D%20%5Cfrac%7BP%5Ccdot%20V%7D%7Bn%5Ccdot%20R_%7Bu%7D%7D)
![T = \frac{(202.65\,kPa)\cdot(1.29\,m)^{3}}{(1\,kmole)\cdot(8.314\,\frac{kPa\cdot m^{3}}{kmole\cdot K} )}](https://tex.z-dn.net/?f=T%20%3D%20%5Cfrac%7B%28202.65%5C%2CkPa%29%5Ccdot%281.29%5C%2Cm%29%5E%7B3%7D%7D%7B%281%5C%2Ckmole%29%5Ccdot%288.314%5C%2C%5Cfrac%7BkPa%5Ccdot%20m%5E%7B3%7D%7D%7Bkmole%5Ccdot%20K%7D%20%29%7D)
![T = 52.325\,K](https://tex.z-dn.net/?f=T%20%3D%2052.325%5C%2CK)
The thermal energy contained by the gas is:
![U = \frac{3}{2}\cdot (1\,kmole)\cdot (8.314\,\frac{kPa\cdot m^{3}}{kmole\cdot K})\cdot (52.325\,K)](https://tex.z-dn.net/?f=U%20%3D%20%5Cfrac%7B3%7D%7B2%7D%5Ccdot%20%281%5C%2Ckmole%29%5Ccdot%20%288.314%5C%2C%5Cfrac%7BkPa%5Ccdot%20m%5E%7B3%7D%7D%7Bkmole%5Ccdot%20K%7D%29%5Ccdot%20%2852.325%5C%2CK%29)
![U = 652.545\,kJ](https://tex.z-dn.net/?f=U%20%3D%20652.545%5C%2CkJ)
b) The physical model for the cat is constructed from Work-Energy Theorem:
![U = \frac{1}{2}\cdot m_{cat} \cdot v^{2}](https://tex.z-dn.net/?f=U%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20m_%7Bcat%7D%20%5Ccdot%20v%5E%7B2%7D)
The speed of the cat is obtained by isolating the respective variable and the replacement of every known variable by numerical values:
![v = \sqrt{\frac{2 \cdot U}{m_{cat}}}](https://tex.z-dn.net/?f=v%20%3D%20%5Csqrt%7B%5Cfrac%7B2%20%5Ccdot%20U%7D%7Bm_%7Bcat%7D%7D%7D)
![v = \sqrt{\frac{2\cdot (652.545 \times 10^{3}\,J)}{3\,kg} }](https://tex.z-dn.net/?f=v%20%3D%20%5Csqrt%7B%5Cfrac%7B2%5Ccdot%20%28652.545%20%5Ctimes%2010%5E%7B3%7D%5C%2CJ%29%7D%7B3%5C%2Ckg%7D%20%7D)
![v \approx 659.568\,\frac{m}{s}](https://tex.z-dn.net/?f=v%20%5Capprox%20659.568%5C%2C%5Cfrac%7Bm%7D%7Bs%7D)
Bc the equator is constantly facing the sun while the earth rotates