Question

Consider a system of two particles in the xy plane: m1 = 1.95 kg is at the location r with arrow1 = (1.00î + 2.00?) m and has a velocity of (3.00î + 0.500?) m/s; m2 = 3.15 kg is at r with arrow2 = (?4.00î ? 3.00?) m and has velocity (3.00î ? 2.00?) m/s.

(a) Plot these particles on a grid or graph paper. Draw their position vectors and show their velocities. (Include the center of mass of the system and its velocity found below. Submit a file with a maximum size of 1 MB.) This answer has not been graded yet.

(b) Find the position of the center of mass (in m) of the system and mark it on the grid. xCM m yCM m

(c) Determine the velocity of the center of mass (in m/s) and also show it on the diagram. vx,CM m/s vy,CM m/s

(d) What is the total linear momentum of the system (in kg · m/s)? px kg · m/s py kg · m/s

Answer 1

a)

b)

r_cm = (m₁ r₁ + m₂ r₂ )/(m₁ + m₂ )

r_cm = ((1.95) (1 i + 2 j) + (3.15) (- 4 i - 3 j) )/(1.95 + 3.15)

r_cm = ((1.95 i + 3.9 j) + (- 12.6 i - 9.45 j)) /5.1

r_cm = - 2.1 i - 1.1 j

so X_cm = - 2.1

Y_cm = - 1.1

c)

v_cm = (m₁ v₁ + m₂ v₂ )/(m₁ + m₂ )

v_cm = ((1.95) (3 i + 0.5 j) + (3.15) (3 i - 2 j) )/(1.95 + 3.15)

v_cm = 3 i - 5.325 j

V_xcm = 3

V_ycm = - 5.325 m/s

d)

total linear momentum is given as

P = (m₁ v₁ + m₂ v₂ )

P = (1.95) (3 i + 0.5 j) + (3.15) (3 i - 2 j)

P = 15.3 i - 27.2 j