13. How many feet high do you think you could jump on the moon?
1 answer:
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Answer: 1010.92 m/s
Explanation:
According to Newton's law of universal gravitation:
(1)
Where:
is the gravitational force between Earth and Moon
is the Gravitational Constant
is the mass of the Earth
is the mass of the Moon
is the distance between the Earth and Moon
Asuming the orbit of the Moon around the Earth is a circular orbit, the Earth exerts a centripetal force on the moon, which is equal to :
(2)
Where is the centripetal acceleration given by:
(3)
Being the orbital velocity of the moon
Making (1)=(2):
(4)
Simplifying:
(5)
Making (5)=(3):
(6)
Finding :
(7)
(8)
Finally:
Answer:
<em>P=33.6 \ W</em>
Explanation:
<u>Mechanical Work and Power</u>
Work is the amount of energy transferred by a force. It's a scalar quantity, with SI units of joules.
Being the force vector and
the displacement vector, the work is calculated as:
If both the force and displacement are parallel, then we can use the equivalent scalar formula:
Mechanical Power is the amount of energy transferred or converted per unit of time. The SI unit of power is the watt, equal to one joule per second.
The power can be calculated as:
Where W is the work and t is the time.
If an object of mass m has an acceleration a, the net force is:
F=m.a
The go-kart and rider have a mass of m=14 kg and accelerate at , thus the net force applied is:
The work done by the cart when traveling d= 40 m is:
Finally, the power for t= 100 seconds is:
P=33.6 \ W