A 3.1-kg block is traveling to the right (the + x direction) at 5.2 m/s, and a s

Question

A 3.1-kg block is traveling to the right (the +x direction) at 5.2 m/s, and a second 3.1-kg block is traveling to the left at 2.2 m/s.

(a) Find the total kinetic energy of the two blocks. ______J

(b) Find the velocity of the center of mass of the two block system. ________ m/s

(c) Find the velocity of each block relative to the center of mass.

(d) Find the kinetic energy of the blocks relative to the center of mass. ______ J

Explanation / Answer

a) Total Kinetic energy = 0.5*m1*u1^2 + 0.5*m2*u2^2

= 0.5*3.1*5.2^2 + 0.5*3.1*2.2^2

= 49.4 J

b)

Vcm = (m1*u1 + m2*u2)/(m1+m2)

= (3.1*5.2 + 3.1*(-2.2))/(3.1+3.1)

= 1.5 m/s

c)

3.1-kg block (traveling to the right)relative to the center of mass = 5.2 - Vcm

= 5.2 - 1.5

= 3.7 m/s

3.1-kg block (traveling to the left)relative to the center of mass = -2.2 - 1.5

= -3.7 m/s

D) Total kinetic enrgy = 0.5*3.1*3.7^2 + 0.5*3.1*(-3.7)^2

= 42.4 J

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