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which statement below is FALSE? A Gravity acts on any object with mass. B The closer objects are, the stronger the gravitational
1 answer:
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The available options are: (found the complete text on internet)
A- at a distance less than r
B- at a distance equal to r
C- at a distance greater than r
Solution:
The correct answer is C) at a distance greater than r.
In fact, the gravitational attraction between the satellite and the Earth provides the centripetal force that keeps the satellite in circular orbit, so we can write
where the term on the left is the gravitational force, while the term on the right is the centripetal force, and where
G is the gravitational constant
M is the Earth mass
m is the satellite mass
r is the distance of the satellite from the Earth's center
v is the satellite speed
Re-arranging the equation, we get
and we see from this formula that, if the second satellite has a speed less than the speed v of the first satellite, it means that the denominator of the fraction is smaller, and so r is larger for the second satellite.
A- at a distance less than r
B- at a distance equal to r
C- at a distance greater than r
Solution:
The correct answer is C) at a distance greater than r.
In fact, the gravitational attraction between the satellite and the Earth provides the centripetal force that keeps the satellite in circular orbit, so we can write
where the term on the left is the gravitational force, while the term on the right is the centripetal force, and where
G is the gravitational constant
M is the Earth mass
m is the satellite mass
r is the distance of the satellite from the Earth's center
v is the satellite speed
Re-arranging the equation, we get
and we see from this formula that, if the second satellite has a speed less than the speed v of the first satellite, it means that the denominator of the fraction is smaller, and so r is larger for the second satellite.
A concave lens is a lens that has at least one of its surfaces or both surfaces curved inwards. Due to this reason, this lens diverges the light that falls on it and hence is also called a diverging lens. The concave lens is thinner in the middle compared to its edges. These are used in flashlights, binoculars, telescopes, etc.
Please see attached image for reference.
Please see attached image for reference.
a) 5.0 m/s
This first part of the problem can be solved by using the conservation of energy. In fact, the mechanical energy of the girl just after she jumps is equal to her kinetic energy:
where m1 = 60 kg is the girl's mass and v1 = 8.0 m/s is her initial velocity.
When she reaches the height of h = 2.0 m, her mechanical energy is sum of kinetic energy and potential energy:
where v2 is the new speed of the girl (before grabbing the box), and h = 2.0m. Equalizing the two equations (because the mechanical energy is conserved), we find
b) 4.0 m/s
After the girl grab the box, the total momentum of the system must be conserved. This means that the initial momentum of the girl must be equal to the total momentum of the girl+box after the girl catches the box:
where m2 = 15 kg is the mass of the box. Solving the equation for v3, the combined velocity of the girl+box, we find
c) 2.8 m
We can use again the law of conservation of energy. The total mechanical energy of the girl after she catches the box is sum of kinetic energy and potential energy:
While at the maximum height, the speed is zero, so all the mechanical energy is just potential energy:
where h_max is the maximum height. Equalizing the two expressions (because the mechanical energy must be conserved) and solving for h_max, we find