Answer:
R=3818Km
Explanation:
Take a look at the picture. Point A is when you start the stopwatch. Then you stand, the planet rotates an angle α and you are standing at point B.
Since you travel 2π radians in 24H, the angle can be calculated as:
t being expressed in hours.
From the triangle formed by A,B and the center of the planet, we know that:
Solving for r, we get:
(1) The potential energy at the top of the ball’s motion is 18 J.
(3) The kinetic energy increases as the potential energy decreases.
(4) The kinetic energy decreases as the potential energy increases.
(5) The total mechanical energy of the ball stays constant.
Explanation:
The total mechanical energy of the ball is equal to the sum of its kinetic energy (K, energy due to the motion) and its potential energy (U, energy due to the height of the ball). Mathematically:
In absence of friction, the mechanical energy of the ball is conserved, so in this case, it is always equal to 18 J. Let's now use this information to analyze each of the given statements:
(1) The potential energy at the top of the ball’s motion is 18 J. --> TRUE. In fact, at the top, the ball's speed becomes zero, so its kinetic energy is zero: K = 0. This means that all the mechanical energy of the ball is potential energy, therefore
E = U = 18 J
(2) The kinetic energy is less when the ball is thrown than when it is caught. --> FALSE. As we said, in absence of friction, the mechanical energy is conserved, therefore it always remains equal to 18 J.
(3) The kinetic energy increases as the potential energy decreases. --> TRUE. As we said, the sum of potential+kinetic energy remains constant:
E = K + U = 18 J
therefore, when the potential energy decreases, the kinetic energy increases.
(4)The kinetic energy decreases as the potential energy increases. --> TRUE. For the same reason described in (3).
(5)The total mechanical energy of the ball stays constant. --> TRUE. As we said at the beginning, the total mechanical energy is constant.
(6) The mechanical energy decreases as the ball moves up and increases as the ball comes down. --> FALSE. As we said, the mechanical energy remains constant, so it cannot change.
Learn more about kinetic and potential energy:
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