Group Problem #14 Center of Mass Physics 111-4 Spring 2012 Page 1 of 4

Group Problem #14 Center of Mass Physics 111-4 Spring 2012 Page 1 of 4

Group problem #14: Center of mass

During a summer internship at a manufacturing company, your supervisor asks you to calculate the center of mass of a uniform density semi-circular loop of radius R that will be attached to your product at the center of mass. She provides you with a coordinate axes so that the origin is at the center of the base of the semi-circle, with the y-axis bisecting the semi-circle in the middle. You decide that for your calculations, using polar coordinates and radians (instead of Cartesian and degrees) will be easiest.

You and a friend decide to go for a ride in a rowboat on Lake Calhoun one fine fall afternoon. The day you pick is a lovely day and the lake is calm. Your friend is near the bow of the boat rowing and you are in the stern, 2.0m from your friend. Your friend gets tired of rowing, so you graciously offer to trade places and row instead. Your friend stops rowing and, after the boat stops moving, you trade places. You know that the switch in locations will cause the boat to move as you are noticeably more massive than your friend. Since you took physics, you decide to calculate how much the boat moved as you traded places. You estimate that your friend has a mass of 80 kg and you have a mass of 120kg.

You have been hired on a summer project in the University Chemistry lab. Your work includes looking at potassium bromide atom. A potassium bromide atom consists of a potassium atom and a bromine atom in a configuration of a straight line with a distance of 2.82 Å apart. The mass of the bromine atom is 79.9 u and the mass of the potassium atom is 39.1 u. Since you took physics, your supervisor asks you to calculate the location of the center of mass of the atom.

You have decided to tackle cleaning up your storage space one weekend, which includes a large number of tools that you wish to put into an organized storage scheme. In your collection of tools you have a symmetrically T-shaped mallet with an iron head of mass of 4.0kg with a wooden handle 1.2 m long and a mass of 1.8 kg. For designing your tool storage, you need to calculate the mallet’s center of mass. (Hint: Find the center of mass of the handle alone first.)