What are (a) the x coordinate and (b) the y coordinate of the center of mass for the uniform plate shown in the figure if L = 5.0 cm? 3L 4L 2L (a) Number i -.4545 Units m^-1 (b) Number i 2.05 Units m 2L 4L 2L ☑

P A person’s arm is held with the upper arm vertical, the lower arm and hand horizontal. (a) Find the center of massof the arm in this configuration, given the following data: The upper arm has a mass of 2.5 kg and a center of mass 0.18 mabove the elbow; the lower arm has a mass of 1.6 kg and a center of mass 0.12 m to the right of the elbow; the hand has amass of 0.64 kg and a center of mass 0.40 m to the right of the elbow. (b) A 0.14-kg baseball is placed on the palm of thehand. If the radius of the ball is 3.7 cm, find the center of mass of the arm–ball system.

The center of mass for a human body can be determined by a segmental method. Using cadavers, it is possible to determine the mass of individual body segments (as a proportion of total body mass) and the center of mass for each segment (often expressed as a distance from one end of the segment). Finding the overall body center of mass can be a complex calculation, involving more than 10 body segments. Below, we will look at a simplified model that uses just six segments: head, trunk, two arms, and two legs. y X X X

Fred Flintstone’s club–ax is made up of two parts:  an uniform 2.5 kg stick and a symmetrical 8 kg stone attached to the end of the stick.  The dimensions of the club-ax are shown in the figure.  How far is the center of mass from the handle end of the club-ax? Express your answer in cm.

9-4. Find the center of mass of a uniform wire that subtends an arc 8 if the radius of the circular arc is a, as shown in Figure 9-A. 2. FIGURE 9-A Problem 94.

A meter stick balances horizontally on a knife-edge at the 50.0 cm mark. With two 5.04 g coins stacked over the 18.2 cm mark, the stick is found to balance at the 41.8 cm mark. What is the mass of the meter stick? Number i Units

What are (a) the x coordinate and (b) the y coordinate of the center of mass for the uniform plate shown in the figure if L = 5.0 cm? 3L 4L (a) Number i (b) Number i 2L 2L 4L ! 2L | IL -X Units Units E m

Objects with a uniform mass distribution and a symmetric shape have a center of mass at the center of the object. For non-uniform objects, the center of mass needs to be determined experimentally. To measure the center of mass of such an object, a pivot is placed in the middle of a board and the top of the non-uniform object is placed to the right of the pivot. When a uniform 10.0 kg mass has its center placed 60.0 cm to the left of the pivot the system balances perfectly (as shown below). The mass of the non-uniform object is measured with an electronic scale in the lab and found to beM = 39.8 kg . Top of non-uniform object 10.0 kg M 60.0 cm Part A Where is the center of mass of the non-uniform object? (report the location from the top of the object, and in cm) ΑΣΦ ? dCM = ст

400 4 The amount of mass shown on the triple beam riders is – F 401.4 g G 404.5 g H 414.5 g J 444.5 g cm 0 2 3 4 6. 7 8 9 10 11 12 13 14 15 What is the length of the metal rod? A 7.0 cm B 7.5 cm C 8.0 cm D 8.5 cm

The 600-kg uniform I-beam supports the load shown. Determine the reactions at the supports. Answers: Ax Ay = = By = p -7.5 m- +4.5 m 285 kg N N N B