11. Consider two objects whose position vectors are given by r1 and r2 and whose momenta are given by p1 = m1v1 and p2 = m2v2 respectively. Show that in the special case that the center of mass of the two bodies is at rest at the origin (that is P = p1 + p2 = 0, and the position of the center of mass is R = 0), the sum of the angular momenta of the two objects about the center of mass equals the angular momentum of a single object of mass mu = m1m2/(m1+m2), rotating in circular motion about the origin at a distance r = r2-r1. The quantity mu is called the reduced mass.

24. A Pulley system is used to lift a heavy mass. How much force must be applied to lift the object in the attached document aat a steady speed? Neglect friction at the axle.

5. A man of mass 95kg is dancing with his wife, who has a mass of 68kg. Assume that each person's mass is concentrated at their respective centers of mass, which are separated by 48cm.
a. What is the gravitational attraction between them?
b. Which person has the greater gravitational attraction toward the other?

Task 3
For the pulley shown below, the tension T in the cable is 100N. First express each tension in Cartesian form and add these together to find the resultand force on the pulley shaft of diameter 12mm. Then express the resultant force in Polar form. Hence determine the shear stress in the pulley shaft. given that it is in do

A 3.00-kg mass and a 5.00-kg mass hang vertically at the ends of a rope that goes over an ideal pulley. If the masses are released, what is the resulting acceleration of the masses?
0 m/
3.68 m/
2.45 m/
6.13 m/

In a pulley system, the time of descent of a 100 gram mass is found to be 35 seconds. The vertical distance is given as 120 cms. The radius of the pulley (in the form of a disc) is 5 cms. Mass of the pulley is unknown. Determine (a) angular acceleration of the pulley (b) number of revolutions it makes during this time (c) To

If an object with a mass of X kg sits on a frictionless table and another object with a mass of Y kg is connected to it by a wire over a frictionless pulley, how do you calculate the acceleration of the system and how do you calculate the tension of the wire?

Please answer eight (8) calculus problems. Please show as much works as possible for every problem. The problems are posted in the following website:
http://www.netprofitspro.com/math.html

The medial triangle of a triangle ABC is the triangle whose vertices are located at the midpoints of the sides AB, AC, and BC of triangle ABC. From an arbitrary point O that is not a vertex of triangle ABC, you may take it as a given fact that the location of the centroid of triangle ABC is the vector (vector OA + vector OB + ve

Please help with the following problem.
By means of a rope whose mass is negligible, two blocks are suspended over a pulley, as the drawing shows. The pulley can be treated as a uniform solid cylindrical disk. The downward acceleration of the 44.0-kg block is observed to be exactly one-half the acceleration due to gravity. N

The system consists of 60-lb and 20-lb blocks A and B, respectively, and 5-lb pulleys C and D that can be treated as thin disks (see the attachment). Determine the speed of block A after block B has risen 5 ft, starting from rest. Assume that the cord does not slip on the pulleys, and neglect the mass of the cord.