Solution) The center of mass is given by
Xcm = (m1x1 + m2x2 + m3x3 + ▪▪▪+mnxn)/(m1 +m2+m3+▪▪mn)
For n particles
4. (a) Three point masses are attached to a massless rigid rod. Mass m,-1.0 kg is...
3. Two children are playing on a seesaw of negligible mass. The first child has a mass of 20.0 kg and sits 1.2 m from the pivot. (i) If the second child has a mass of 30.0 kg, how far is she from the pivot? (ii) What is the supporting force exerted by the pivot? 4. (a) Three point masses are attached to a massless rigid rod. Mass mi- 1.0 kg is located at x 1.0 cm, mass m 2.0...
m D 0.35 m Four point masses are attached together by massless rigid rods. If point mass A is 9.0 kg, point mass B is 2.0 killograms, point mass C is 4.5 kg, and D is 2.5 kg. And masses A and B have the same distance between them as B and C, distance m, 0.3 m. Finally the distance between mass C and D is, distance p, 2.5 m. Find the center of mass of the object from point,...
A 1.0 kg ball and a 4.0 kg ball are connected by a 3.0-m-long rigid, massless rod. The rod and balls are rotating clockwise about its center of gravity at 25 rpm. Part A What magnitude torque will bring the balls to a halt in 5.0 s?
A 1.0 kg ball and a 2.0 kg ball are connected by a 1.2-m-long rigid, massless rod. The rod is rotating cw about its center of mass at 17 rpm . What torque will bring the balls to a halt in 4.6 s ?
A 1.0 kg ball and a 2.0 kg ball are connected by a 1.1-m-long rigid, massless rod. The rod is rotating cw about its center of mass at 22 rpm . Part A What torque will bring the balls to a halt in 4.4 s ?
2. Two point masses m and m2 are separated by a massless rod of length L. (a) Write an expression for the moment of inertia I about an axis perpendicular to the rod and passing through it a distance x from mass mi. (b) Calculate dl/dx and show that I is at a minimum when the axis passes through the center of mass of the system.
Three small masses are positioned at the following coordinates: 3.0 kg at (3.0 m, 2.0 m); 4.0 kg at (0.0 m, -1.0 m); and 5.0 kg at (5.0 m, -7.0 m). What are the coordinates of the center of mass (or center of gravity) of this system?
Three masses are positioned at the following coordinates 3.0 kg at (4.0 m, -5.0 m); 6.0 kg at (-7.0 m, 3.0 m); and 1.0 kg (2.0 m, 2.0 m). Calculate the center of mass of the system.
1. (25 pts.) Three particles are at the vertices of a rigid, massless equilateral triangle, whose sides are L = 4.0 m. Their masses are mi = 10 kg, m2 = 20 kg and m3 = 30 kg. a. Find the x and y coordinates of the center of mass of the system, with respect to the point P halfway along the base. b. Find the moment of inertia if the system is free to rotate around an axis down...
Question 5 A pan balance is made up of a rigid, massless rod with a hanging pan attached at each end. The rod is supported at and free to rotate about a point not at its center. It is balanced by unequal masses placed in the two pans. When an unknown mass m is placed in the left pan, it is balanced by a mass of 2.10 kg placed in the right pan; when the mass m is placed in...