course mth174
A few questions.
Show that LEFT(2n) = .5 [ LEFT(n) + MID(n) ], and also that TRAP(n) = LEFT(n) + RIGHT(n).for this, what would be the best way to show it? Can I just make up an integral and show that the left of 2 subdivisions, equals 1/2 * the sum of left(2n)+ Mid(2n)
Also, that one problem I completely missed on test 2- the one that involved trap(10)=87.85 then trap(30)= 86.45 whats your best estimate of this integral? Honestly, I am still not completely sure what you really want as the answer, or how I quantitatively answer this...
trap(30) is about 9 times closer to the correct result than trap(10).
So what number is 86.45 nine times closer to than is 87.85?
Physics:
How would we find at speed at which a Ferris wheel can give you the feeling of weightlessness v? I know we are going to use the relationship
fnet= mv^2/R . In my mind I'm thinking that we need to find a speed at which G will equal zero, but the problem in that lies in the fact that then the left hand of my equation will equal zero (so that doesn't make much sense).
You’ve just about got it.
If at the top of the wheel gravity provides all your centripetal acceleration, but no more, then you feel weightless at the top.
Note that g is case-sensitive. G is the universal gravitational constant, not the acceleration of gravity.
I'm pretty sure I figured out determining the coefficient of friction between the grinding wheel and the force applied.
How do we determine, for instance, the coefficient of (static or kinetic?) friction for a truck traveling and stopping from a certain speed, in a certain time interval, at which the load in the truck stays put. If you exceed that speed, the load in the truck does not remain stationary (so its static) when coming to a stop.
When the truck accelerates, so does the load. If the load stays put in the truck, that means it is accelerating at the same rate as the truck, so the net force on the load is equal to m * a, where a is the acceleration of the truck. This net force is the result of friction between the load and the truck bed, so mu * m g must not be less than m * a. This case you and inequality you can solve for the condition on a.
This is a problem from a practice test that I'm a little confused on.
Basically, a mass on a light string is being swung in a vertical circle with radius R, with the mass just barely going slack in the top. The string is released when the mass is at the top of its arc.
Here are the questions that you ask:
* If t = 0 at the top of the arc, and if range(t) is the function that gives the horizontal range of the released mass as a function of the clock time t of the release, then what is d/dt (range(t))?
The mass is released and proceeds to fall as a projectile to the floor. If t = 0 its velocity at the instant of release, which is tangent to the circular path, is in the horizontal direction and the vertical displacement between release and the floor is from the top of the arc to the floor. For any other value of t the projectile’s initial position is not at the top of the arc so its velocity (which is again perpendicular to the path) is not horizontal, and its displacement of the floor is less than the displacement from the top of the arc to the floor. So as a function of t, what is the initial position of the mass on the circle, and what therefore is its position and the direction of its motion as a function of t? What is its speed? What therefore is its initial velocity vector, the vertical displacement, and the time and horizontal range of the fall (all as functions of t)? The horizontal range is the function range(t). You may assume that t is small enough to keep you near, but not at, the top of the arc.
* What is the significance of this quantity for the error in estimating the velocity of the mass at release, based on the assumption of zero initial vertical velocity?
* On a circle of radius 45 cm, what would be the error expected if the actual time of release was .04 seconds before the top of the arc?
I've got decent understanding of circular motion, but I haven't encountered any problems dealing with the range(t) function, though it is covered in chapter three (which I have yet to get started on due to time constraints). But your help on these would be greatly appreciated.
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