Answer:
a) 
b)
c) 
d) Treat the humans as though they were points or uniform-density spheres.
Explanation:
Given:
- mass of Mars,
- radius of the Mars,
- mass of human,
a)
Gravitation force exerted by the Mars on the human body:
where:
= gravitational constant
b)
The magnitude of the gravitational force exerted by the human on Mars is equal to the force by the Mars on human.
c)
When a similar person of the same mass is standing at a distance of 4 meters:
d)
The gravitational constant is a universal value and it remains constant in the Universe and does not depends on the size of the mass.
- Yes, we have to treat Mars as spherically symmetric so that its center of mass is at its geometric center.
- Yes, we also have to ignore the effect of sun, but as asked in the question we have to calculate the gravitational force only due to one body on another specific body which does not brings sun into picture of the consideration.
If the force were constant or increasing, we could guess that the speed of the sardines is increasing. Since the force is decreasing but staying in contact with the can, we know that the can is slowing down, so there must be friction involved.
Work is the integral of (force x distance) over the distance, which is just the area under the distance/force graph.
The integral of exp(-8x) dx that we need is (-1/8)exp(-8x) evaluated from 0.47 to 1.20 .
I get 0.00291 of a Joule ... seems like a very suspicious solution, but for an exponential integral at a cost of 5 measly points, what can you expect.
On the other hand, it's not really too unreasonable. The force is only 0.023 Newton at the beginning, and 0.000067 newton at the end, and the distance is only about 0.7 meter, so there certainly isn't a lot of work going on.
The main question we're left with after all of this is: Why sardines ? ?
Answer:
f = 12 cm
Explanation:
<u>Center of Curvature</u>:
The center of that hollow sphere, whose part is the spherical mirror, is known as the ‘Center of Curvature’ of mirror.
<u>The Radius of Curvature</u>:
The radius of that hollow sphere, whose part is the spherical mirror, is known as the ‘Radius of Curvature’ of mirror. It is the distance from pole to the center of curvature.
<u>Focal Length</u>:
The distance between principal focus and pole is called ‘Focal Length’. It is denoted by ‘F’.
The focal length of the spherical (concave) mirror is approximately equal to half of the radius of curvature:
where,
f = focal length = ?
R = Radius of curvature = 24 cm
Therefore,
<u>f = 12 cm</u>
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