Question

Answer the following questions:

1. A uniform meter stick has a mass m1 = 10.0 kg placed at 100.0 cm mark and another mass m2 = 

20.0 kg placed at 20.0 cm mark. Determine the center of mass of the stick and the two masses 

together. (Show solution)

2. Three masses are placed on a plane such that the coordinates of the masses are, m1 = 1.0 kg at (1, 

0), m2 = 2.0 kg at (2, 0), and m3 = 3.0 kg at (0, 3). Determine the coordinates of the center of the 

mass of the three masses.

3. Two pop cans are at rest on a stand. A firecracker is placed between the cans and lit. The 

firecracker explodes and exerts equal and opposite forces on the two cans. Assuming the system 

of two cans to be isolated, the post-explosion momentum of the system ____.

Answer 1

1

$$m*l=M*L$$

$$20*l=10*(100-20-l)$$

$$l=26.7 cm$$

$$L=100-20-26.7=53.3 cm$$

 The center of mass is (53.3-50=3.3 cm) from the centre of the stick.

2

$$Xc=(m1X1+m2X2+m3X3)/(m1+m2+m3)$$

$$Xc=(1*1+2*2+3*0.3)/(1+2+3)=0.98$$

3

$$p=\Sigma pi$$

$$p=p1+p2=m1v1+m2v2$$

$$m1=m2$$

$$v1=v2$$

As cans move in different directions, they have opposite impulses

$$p=mv+ (-mv)=0$$