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Rotational Mechanics Problems

by barnsworth
Tags: mechanics, rotational
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Nov30-04, 10:00 PM
P: 5
Alright here's a problem that seemed pretty easy, but i'm really worried i over-simplified (which i often have a problem of doing) since the question was rated one of the harder ones...

1) A 2000-kg block is lifted at constant speed (v = .08 m/s) by a steel cable pasing over a massless pulley to a motor-driven winch with radius (r = .3 m).

(a) What force must be exerted by the cable?
(b) What torque does the cable exert on the winch drum?
(c) What is the angular velocity of the winch drum?
(d) What power must be developed by the motor to drive the winch drum?

For (a) i did T = mg.
(b) Torque = rF = 6,000 N
(c) w = v / r = .266
(d) P = torque * w = 1600

Can anyone check me on this?? Did i forget to factor in anything?? i always get killed on these things...

The next two questions i pretty much had no idea...

2) An Atwoods machine has two objects of m1 = .5 kg and m2 = .51 kg. The pulley is a uniform disk with mass Mp = .05 kg and radius of .04 m. The string does not slip.

(a) Acceleration of the objects?
(b) Tension of the string supporting m1? Tension of string supporting m2?
(c) What would your answers be if you neglected the mass of the pulley?

uhhh i got for (a) acceleration = 10 / 1100, but i'm pretty sure that's wrong. i'm thinking i do something like T2 - T1 - Ia.

3) A uniform rod of mass M and length L is pivoted at one end and hangs freely. It is struck by a horizontal force "F" for a short time "t" at a distance "x" below the pivot.

(a) Show that the speed of the center of mass just after being struck is given by "v = 3Fxt/2ML.

(b) Find the force delivered by the pivot, and show that this force is zero if x = 2L / 3 (called the center of percussion).

Damn i hate rotational mechanics... Thanks for any help in advance...
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