For Earth/Moon pair, find the system center of mass and the point where gravity fields cancel completely.

Consider the earth, mass M= 5.98 E 24 kg, and the moon, mass m= 7.35 E 22 kg, as a system with distance d= 3.84 E 8 m between their centers. Find the distance between the c.m. (center of mass) of the system, and the point where the gravity field of the earth cancels that of the moon to produce zero field. SEE ATTACHMENT #1 for a diagram showing parameters.

Given the x,y coordinates of three given point masses, find the center of mass, c.m., of the system.

Three point masses are located in an x,y plane as follows: M1= 7 kg, at (x1, y1)= (5, 6); M2= 8 kg, at (x2, y2)= (-4, 6); and M3= 9 kg, at (x3, y3)= (3, -2). Find the coordinates (xcm, ycm) of the c.m. of the system.

By integration, find the x coordinate of the center of mass, c.m., of a piece of sheet metal with a curved edge.

A thin, uniform piece of sheet metal in an x,y plane has one side along the x axis from (0, 0) to (3, 0), and a vertical side from (3,0) to (3, 5.4). The remaining side is curved between (0,0) and (3, 5.4) on the line y= .6 x^2. Find xcm, the x coordinate of the c.m. SEE ATTACHMENT #1 for a diagram of the object and parameters. Distances are in meters.

pulley problem

A thick rope with a length of 5m is draped over a pulley, such that the right side y=3m is dangling free and on the left side L-y=2m is dangling free. The rope has a mass of 10kg. Since the longer side is more massive than the shorter side, the rope begins falling downward, with the shorter end going up towards the pulley. Assuming the initial velocity of the rope is zero, derive an expression for the velocity of the rope when the end of the rope reaches the pulley, and calculate a numerical answer.

A bullet hits a stationary block after which the block slides to a stop. Find the velocity of the bullet before the impact.

A bullet whose mass M1= .04 kg traveling horizontallyhits a stationary block of mass M2= 2.4 kg on a horizontal surface. After the impact, the block, with embedded bullet, slides distance x= 5 meters to a stop. The coefficient of friction is f= .50 between block and surface. Find the velocity V1 of the bullet before impact.