Problem 46PE

Confirm that the results of the example Example 8.7 do conserve momentum in both the x - and y -directions.

Example 8.7 Determining the Final Velocity of an Unseen Object from the Scattering of Another Object

Suppose the following experiment is performed. A 0.250-kg object (m1) is slid on a frictionless surface into a dark room, where it strikes an initially stationary object with mass of 0.400 kg (m2) . The 0.250-kg object emerges from the room at an angle of 45.0° with its incoming direction. The speed of the 0.250-kg object is originally 2.00 m/s and is 1.50 m/s after the collision. Calculate the magnitude and direction of the velocity (v′2 and θ2) of the 0.400-kg object after the collision.

Step 1 of 7:

Consider an unseen object collides with another object which is at rest. The masses of the objects and the initial velocities of the first objects are given. We are going to prove that the system conserves momentum in both x- and y- direction.

Before solving the problem, we need to find out the final velocity of the second object and its direction.

The mass of the first object

The mass of the second object (unseen)

The initial velocity of the first object

The initial velocity of the first object

The final velocity of the second object

The angle of the first object

Step 2 of 7:

Applying conservation of momentum in x-direction

Substituting the values

Step 3 of 7:

Applying conservation of momentum in y-direction, here the initial momentum is zero as the second object is at rest.

Substituting the known quantities

Step 4 of 7:

Dividing the equation (4) by (2)

The direction of the second object is -48.5° or 311.5° (360°-48.5°)