Calculating Total Momentum of Objects Moving in Different Directions

[ckaiser813]

Homework Statement

A 4.00 kg ball is moving at 3.00 m/s to the NORTH and a 5.00 kg ball is moving at 2.00 m/s to the NORTHWEST. The total momentum of the system is:


I have a very bad book that doesn't discuss how to deal with total momentum with relationship to different directions other than head on, would just like for someone to explain the way to set up my formula to find this one.

 

[dx]

Hi ckaiser813,

Momentum is a vector, and it has one component for each of the three perpendicular directions. For example, here's how you find the momentum in the north direction. If ball one has a velocity v in the north direction and has mass m, and if ball two has velocity w in the north direction and mass M, then the momentum in the north direction is mv + Mw.

 

[nlightner]

The total momentum of a system can be calculated by adding together the individual momentums of each object. In this case, the momentums of the 4.00 kg ball and the 5.00 kg ball must be added together. However, since the balls are moving in different directions, it is important to take into account the direction of the momentum.

To do this, we can use vector addition. This involves breaking down the individual momentums into their components in the NORTH and WEST directions.

For the 4.00 kg ball, the momentum in the NORTH direction is 4.00 kg * 3.00 m/s = 12 kg*m/s. There is no momentum in the WEST direction.

For the 5.00 kg ball, the momentum in the NORTH direction is 5.00 kg * 2.00 m/s = 10 kg*m/s. The momentum in the WEST direction is 5.00 kg * 2.00 m/s * cos(45) = 7.07 kg*m/s.

To find the total momentum, we can add the components in each direction separately. In the NORTH direction, the total momentum is 12 kg*m/s + 10 kg*m/s = 22 kg*m/s. In the WEST direction, the total momentum is 7.07 kg*m/s.

Using the Pythagorean theorem, we can find the magnitude of the total momentum:

Total momentum = √(22^2 + 7.07^2) = 23.32 kg*m/s

To find the direction of the total momentum, we can use trigonometry. The angle can be found by taking the inverse tangent of the ratio of the WEST and NORTH momentums:

Angle = tan^-1(7.07/22) = 18.88 degrees WEST of NORTH.

Therefore, the total momentum of the system is 23.32 kg*m/s at an angle of 18.88 degrees WEST of NORTH.