Need help on my Physics Homework!?

[amdt57]

Here are the diagrams for problem 5 and 6: http://physics.oregonstate.edu/~walshke/COURSES/ph211/ph211_s12_hmwk3.pdf

Okay so I'm practicing for my midterm next week but I want to really make sure I know everything, please show as many steps as you can. Thank you!! :)


1. It is not possible to see very small objects, such as viruses, using an ordinary light microscope. An electron microscope, however, can view such objects using an electron bean instead of a light beam. Electron microscopy has proved invaluable for investigations of viruses, cell membranes and sub-cellular structures, bacterial surfaces, visual receptors, chloroplasts, and the contractile properties of muscles. The “lenses” of an electron microscope consist of electric and magnetic fields that control the electron beam. As an example of the manipulation of an electron beam, consider an electron traveling away from the origin along the x axis in the xy plane with an initial velocity magnitude of 1.80 x 107 m/s. As it passes through the region x = 0 to x = d, the electron experiences a constant acceleration where ax = 8.00 x 1014 m/s2, and ay = 1.60 x 1015 m/s2. Determine at x = d = 0.0100 m
(a) the position of the electron,
(b) the velocity of the electron,
(c) the speed of the electron, and
(d) the direction of travel of the electron (i.e. the angle between its velocity and the x axis).


2. In a local bar, a customer slides an empty beer mug down the counter for a refill. The height of the counter is 1.22 m. The mug slides off the counter and strikes the floor 1.40 m from the base of the counter. (a) With what velocity did the mug leave the counter? (b) What was the mug’s velocity just before it hits the floor?


3. A cannon with a muzzle speed of 1,000 m/s is used to start an avalanche on a mountain slope. The target is 2,000 m from the cannon horizontally and 800 m above the cannon. At what angle, above the horizontal, should the cannon be fired?


4. An aging coyote cannot run fast enough to catch a roadrunner. He purchases on eBay a set of jet powered roller skates, which provide a constant horizontal acceleration of 15.0 m/s2. The coyote starts at rest 70.0 m from the edge of a cliff at the instant the roadrunner zips past in the direction of the cliff.

(a) Determine the minimum constant speed the roadrunner must have to reach the cliff before the coyote.At the edge of the cliff, the roadrunner escapes by making a sudden turn, while the coyote continues straight ahead. The coyote’s skates remain horizontal and continue to operate while he is in flight.
(b) The cliff is 100 m above the flat floor of the desert. Determine how far from the base of the cliff the coyote lands.
(c) Determine the components of the coyote’s impact velocity.
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5. A projectile is fired up an incline (incline angle ?) with an initial speed vi at an angle ?i with repect to the horizontal (?i > ?) as shown in the figure.
(a) Show that the projectile travels a distance d up the incline, where
d= [2vi^2 cos(?i) sin(?i -?)]/ g cos^2(?) <---- check out the website for a better picture!
(b) For what value of ?i is d a maximum, and what is that maximum value?


6. Centrifugal casting is used for manufacturing pipes, bearings, and many other structures. A variety of sophisticated techniques have been invented, but the basic idea is as illustrated in figure to the right. A cylindrical enclosure is rotated rapidly and steadily about a horizontal axis. Molten metal is poured into the rotating cylinder and then cooled, forming the finished product. Turning the cylinder at a high rotation rate forces the solidifying metal strongly to the outside. Any bubbles are displaced toward the axis, so unwanted voids will not be present in the casting. Sometimes it is desirable to form a composite casting, such as for a bearing. Here a strong steal outer surface is poured and then inside it a lining of special low-friction metal. In some applications, a very strong metal is given a coating of corrosion resistant metal. Centrifugal cast- ing results in strong bonding between the layers. Suppose a copper sleeve of inner radius 2.10 cm and outer radius 2.20 cm is to be cast. To eliminate bubbles and give high structural integrity, the centripetal acceleration of each bit of metal should be at least 100g. What rate of rotation is required? State the answer in revolutions per minute.

7. A ball on the end of a string is whirled around in a horizontal circle of radius 0.300 m. The plane of the circle is 1.20 m above the ground. The string breaks and the ball lands 2.00 m (horizontally) away from the point on the ground directly beneath the ball’s location when the string breaks. Find the radial acceleration of the ball during its circular motion.
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