Question

A 3.1 kg rod of length 5.1 m has at opposite ends point masses of 4.0 kg and 6.0 kg.
a)Will the center of mass of this system be nearer to the 4.0-kg mass, nearer to the 6.0-kgmass, or at the center of the rod?   
b) Where is the center of mass of the system?

(F-net=M[Vcm/t] xCM= (summation of all mass by distance)/system of mass

Diagram please, not fully understand the system. getting 5.03m

Answer 1

a)Mass of rod=3.1 kg

Length of rod=5.1 m

Point mass at one end=4.0 kg

Point mass at the other end=6 0 kg

Since the rod is uniform, its centre of mass will be at center. However, since there are additional point masses , the center of mass of the system of rid and point masses will be nearer to place where higher mass is concentrated

Therefore, the center of mass will be near 6 kg point mass

b)let us determine the location of center of mass with respect to the 4 kg point mass

Distance of 4 kg point mass with respect to 4 kg point mass=0

Distance of center of mass of rod with respect to 4 kg point mass=5.1/2=2.55 m

Distance of 6 kg point mass with respect to 4 kg point mass=5.1 m

Distance of center of mass of system with respect to 4 kg point mass is given by summation of product of mass and corresponding distance with respect to 4 kg point mass and divide this summation by total mass

Therefore, centre of mass=((4*0)+(3.1*2.55)+(6*5.1))/(4+3.1+6)=2.94 m

Therefore, center of mass if system is at 2.94 m from 4 kg mass

Thus also validates the statement that center of mass of system is nearer to 6 kg mass compared to 4 kg mass