there are two slides at the park between which you are deciding. Both start at the height of 6 meter. One is short and Steve whi
le the other is long and shallow. If both sides are frictionless, which one should you choose if you want to be moving as fast as possible at the bottom? A. short and steep. B. long and shallow. C. it doesn't matter.
It doesn't matter. If the slides are truly frictionless, then your kinetic energy at the bottom will be equal to the potential energy you had at the top, no matter what kind of route you took getting down. ___________________________
The only way I can think of that it would make a difference would be if the shallow slide were REALLY REALLY long, and you didn't have anything to eat all the way down. Then you might lose some weight while you're on the slide, and your mass might be less at the bottom than it was at the top. Then, in order to have the same kinetic energy at the bottom, you'd need to be going a little bit faster.
But if it takes less than, say, two or three days, to go down the long, shallow slide, then this effect would probably be too small to make any difference.
When standing on the bathroom scale within the moving elevator, there are two forces acting on Henry's mass: Normal force and gravity.
Gravity is always downward, and normal force is perpendicular to the surface on which the mass is located (the bathroom scale), in upward direction.
Normal force, can adopt any value needed to match the acceleration of the mass, according to Newton's 2nd Law.
Gravity (which we call weight near the Earth's surface) can be calculated as follows:
According to Newton's 2nd Law, it must be met the following condition:
As the gravity is larger than normal force, this means that the acceleration is downward, so, we choose this direction as the positive.
Solving for a, we get:
We can find the speed after the first 3.8 s (assuming a is constant), applying the definition of acceleration as the rate of change of velocity:
Now, if during the next 3.8 s, normal force is 930 N (same as the weight), this means that both forces are equal each other, so net force is 0.
According to Newton's 2nd Law, if net force is 0, the object is either or at rest, or moving at a constant speed.
As the elevator was moving, the only choice is that it is moving at a constant speed, the same that it had when the scale was read for the first time, i.e., 4 m/s downward.
