Two masses, m1 = 2.0 kg and m2 = 3.3 kg, are moving in the xy-plane. The velocity of their center of mass and the velocity of mass 1 relative to mass 2 are given by the vectors vcm = (−1,+2.2) m/s and vrel = (+4.5, +1.0) m/s.
(a) Determine the total momentum of the system.
?? kg m/s
(b) Determine the momentum of mass 1.
?? kg m/s
(c) Determine the momentum of mass 2.
?? kg m/s
To determine the total momentum of the system, we can use the equation:
Total momentum = momentum of mass 1 + momentum of mass 2
The momentum of an object is given by the equation:
Momentum = mass * velocity
(a) To find the total momentum of the system, we need to calculate the momentum of both masses. We're given the masses and velocities, so we can use the equation mentioned earlier.
Total momentum = (mass 1 * velocity 1) + (mass 2 * velocity 2)
To find the total momentum, we substitute the given values:
Total momentum = (2.0 kg * (-1, +2.2) m/s) + (3.3 kg * (+4.5, +1.0) m/s)
Using the distributive property, we can calculate:
Total momentum = (2.0 kg * -1 m/s, + 2.0 kg * 2.2 m/s) + (3.3 kg * 4.5 m/s, + 3.3 kg * 1.0 m/s)
Calculating each component separately:
Total momentum = (-2.0 kg m/s, + 4.4 kg m/s) + (14.85 kg m/s, + 3.3 kg m/s)
Combining the components:
Total momentum = (-2.0 kg m/s + 14.85 kg m/s, + 4.4 kg m/s + 3.3 kg m/s)
Simplifying:
Total momentum = (12.85 kg m/s, + 7.7 kg m/s)
Therefore, the total momentum of the system is 12.85 kg m/s in the x-direction and 7.7 kg m/s in the y-direction.
(b) The momentum of mass 1 is given by:
Momentum of mass 1 = mass 1 * velocity 1
Substituting the given values:
Momentum of mass 1 = 2.0 kg * (-1, +2.2) m/s
Calculating each component:
Momentum of mass 1 = -2.0 kg m/s, + 4.4 kg m/s
Therefore, the momentum of mass 1 is -2.0 kg m/s in the x-direction and 4.4 kg m/s in the y-direction.
(c) The momentum of mass 2 is given by:
Momentum of mass 2 = mass 2 * velocity 2
Substituting the given values:
Momentum of mass 2 = 3.3 kg * (+4.5, +1.0) m/s
Calculating each component:
Momentum of mass 2 = 14.85 kg m/s, + 3.3 kg m/s
Therefore, the momentum of mass 2 is 14.85 kg m/s in the x-direction and 3.3 kg m/s in the y-direction.