A boxcar at a rail yard is set into motion at the top of a hump. The car rolls down quietly and without friction onto a straight
, level track where it couples with a flatcar of smaller mass, originally at rest, so that the two cars then roll together without friction. Consider the two cars as a system from the moment of release of the boxcar until both are rolling together. (a) is the mechanical energy of the system conserved? (b) is the momentum of this system conserved? Next, consider only the process of the boxcar gaining speed as it rolls down the hump. Consider the boxcar and the Earth as a system. (a) is the mechanical energy of the system conserved? (b) is the momentum of this system conserved? Finally, consider the two cars as a system as the boxcar is slowing down in the coupling process. (a) is the mechanical energy of the system conserved? (b) is the momentum of this system conserved?
1 answer:
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For this case we have that by definition, the kinetic energy is given by the following formula:
Where:
m: It is the mass
v: It is the velocity
According to the data we have to:
Substituting the values we have:
finally, the kinetic energy is
Answer:
Option A
An astronaut inside a spacecraft, which protects her from harmful radiation, is orbiting a black hole at a distance of 120 km from its center. The black hole is 5.00 times the mass of the sun and has a Schwarzschild radius of 15.0 km. The astronaut is positioned inside the spaceship such that one of her 0.030 kg ears is 6.0 cm farther from the black hole than the center of mass of the spacecraft and the other ear is 6.0 cm closer.
What is the tension between her ears?
Would the astronaut find it difficult to keep from being torn apart by the gravitational forces?
Answer:
The tension between the ears = 2.07 KN
The astronaut will find it difficult to keep and will eventually be in trouble because the tension is now greater compared to the tension in the human tissues.
Explanation:
Given that:
Orbital radius of the spacecraft (R) = 120 Km = 120 × 10³ m
Mass of the black hole (m) =
where :
Then; we have:
Schwarzchild radius of the black hole
r - 15.0 km
Mass of each ear
Farther distance between one ear and the black hole (d) = 6.0 cm
= 0.06 m
Closer distance between the other ear and the black home is (d) 6.0 cm
= 0.6 cm
NOW, If we assume that the tension force should be T; then definitely the two ears will posses the same angular velocity .
The net force on the ear closer to the black hole will be:
The net force on the ear farther to the black hole is :
Equating equation (1) and (2) & therefore making (T) the subject of the formula; we have:
The tension between the ears = 2.07 KN
The astronaut will find it difficult to keep and will eventually be in trouble because the tension is now greater compared to the tension in the human tissues.