Answer:
1270 J
Explanation:
Recall that the mechanical energy of a system is the addition of the Potential energy and the Kinetic energy at any given time.
As the skier descends, potential energy is converted into kinetic energy, but the total mechanical energy should remain the same.
We see that it is not the case, so that difference is what has gone into thermal energy; 19500 J - 18230 J = 1270 J
Hooke's Law
F = k. Δx
Δx = 30 cm = 0.3 m
200 = k . 0.3
the spring stretch for 100 N:
-- The string is 1 m long. That's the radius of the circle that the mass is
traveling in. The circumference of the circle is (π) x (2R) = 2π meters .
-- The speed of the mass is (2π meters) / (0.25 sec) = 8π m/s .
-- Centripetal acceleration is V²/R = (8π m/s)² / (1 m) = 64π^2 m/s²
-- Force = (mass) x (acceleration) = (1kg) x (64π^2 m/s²) =
64π^2 kg-m/s² = 64π^2 N = about <span>631.7 N .
</span>That's it. It takes roughly a 142-pound pull on the string to keep
1 kilogram revolving at a 1-meter radius 4 times a second !<span>
</span>If you eased up on the string, the kilogram could keep revolving
in the same circle, but not as fast.
You also need to be very careful with this experiment, and use a string
that can hold up to a couple hundred pounds of tension without snapping.
If you've got that thing spinning at 4 times per second and the string breaks,
you've suddenly got a wild kilogram flying away from the circle in a straight
line, at 8π meters per second ... about 56 miles per hour ! This could definitely
be hazardous to the health of anybody who's been watching you and wondering
what you're doing.
Presumably, the ball is kicked parallel to the ground below the cliff, so its altitude <em>y</em> at time <em>t</em> is
where <em>g</em> = 9.80 m/s^2 is the acceleration due to gravity.
The ball hits the ground when <em>y</em> = 0:
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