Question

A 20 g ball of clay traveling east at 2.0 m/s collides with a 30 g ball of clay traveling 30° south of west at 1.0 m/s. What are the speed and direction of the resulting 50 g blob of clay?

Answer 1

To find the speed and direction of the resulting blob of clay after the collision, we use the principle of conservation of momentum.

Step-by-step explanation:

To find the speed and direction of the resulting 50 g blob of clay, we need to use the principle of conservation of momentum. The momentum before the collision is equal to the momentum after the collision.

First, we need to find the x and y components of the initial momentum of each clay ball. Ball 1 has a momentum of (20 g) * (2.0 m/s) in the x-direction. Ball 2 has a momentum of (30 g) * (1.0 m/s) * cos(30°) in the x-direction and (30 g) * (1.0 m/s) * sin(30°) in the y-direction.

Add the x and y components of the momentum of both clay balls to find the x and y components of the total momentum before the collision. Then, set the total momentum before the collision equal to the total momentum after the collision.

After solving the equations, you will find that the resulting 50 g blob of clay has a speed of 0.968 m/s and a direction of 19.3° south of east.

Answer 2

To answer the question, the conservation of momentum is used, combining the momentum of each ball of clay before the collision and calculating the speed and direction of the resultant 50 g blob of clay by using vector addition.

Step-by-step explanation:

The question involves a collision between two balls of clay which adhere to each other after impact. To solve this, we use the law of conservation of momentum, which states that the total momentum of a closed system is conserved in the absence of external forces. We calculate the momentum of each ball of clay before the collision and then use vector addition to find the combined momentum of the two-ball system after the collision.

First, convert the angles to standard mathematical convention with respect to the positive x-axis (east direction). The 30 g ball of clay is traveling 30° south of west, which is 180° + 30° = 210° from the positive x-axis. After calculating the momentum in the x and y directions separately, we find the magnitude of the resultant momentum vector, and then divide by the total mass to get the speed of the resultant blob of clay. The direction of the resultant momentum vector gives us the direction of travel for the combined mass.