String Swing Wall
March 26th, 2010 | 
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physics questions... plz...?
1. A weight on the end of a string starts at a height h and an initial velocity 0, and when released swings as a pendulum. The ratio of velocity at half the original height to its maximum velocity is?
2. Ben Stupid and Al Bonehead decided to celebrate the holidays by drinking and test crashing their cars into a concrete wall. Car A (A.Bonehaed) is traveling 2 times as fast as car B (B. Stupid). The ratio of energies of Car A to Car B is???
3.A pendulum, which has a period T on Earth, is transported to a planet where the gravitational acceleration is 4.9 m/s^2 what is the pendulum's new period?
4. Force F stretches a spring by a distance x. Force 2F will stretch this spring to a distance of what?
5. A marble rolling down a ramp would have a (((((greater/same/lesser)))) velocity at the bottom of the ramp than if it were to slide down the ramp?
1. v^2 = 2gd (d = depth from the highest point), so
v(1/2 d) / v(d) = sqrt(1/2).
That relationship is ALWAYS true, and includes when d = h (downwards from the start), of course.
2. E(A) / E(B) = 4 M(A) / M(B), as E = 1/2 M v^2.
(You didn't tell us that the masses of the cars were equal.)
3. P = (sqrt 2) T, as p = 2 pi sqrt (L / g).
4. 2f ==> 2x (Hooke's Law, ut tensio sic vis).
5. This is a tricky one, and I must criticize how it's been set. In order to "roll," there must be friction. (It's needed to rotate the marble.) That rotation means that some of the P.E. released in rolling down the ramp has gone into K.E. of rotation, and therefore the K.E. of linear motion is LESS (and the speed down the ramp less) than if it were to "slide down the ramp" (presumably without rolling).
But how would that latter be achieved? Only if the coefficient of friction were zero. So the problem is in fact comparing a "real-world" situation with friction to an "idealized" situation with zero friction whatsoever.
I suppose that one point of setting the question without clarifying this difference between the two situations, was to stimulate you to MAKE and EXPLAIN this distinction yourself.
Perhaps a more interesting situation is to compare the rolling and linear speeds of "real-world" rolling objects with different mass distributions such as solid or hollow marbles and solid or hollow cylinders. Each of these has different moments of inertia, and so for a given rotational speed, have differing rotational K.E.'s. Therefore, they will all have DIFFERENT linear speeds at any given depth down from the point where they are released from rest on a ramp. Those differences will result in certain ratios of distance rolled down the ramp at any given time, and careful comparisons could experimentally test (and, one hopes, verify) the theoretical predictions.
Live long and prosper.
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