Question

A proton with mass 1.673.10⁻²⁷ kg is moving with a speed of 3.715-106 m/s toward an alpha particle with mass 6.645-10-27 kg. What is the speed of the center of mass of the proton + alpha particle system?

Answer 1

The speed of the center of mass of the proton and alpha particle system is found by using the center of mass velocity formula, which, assuming the alpha particle starts at rest, simplifies to considering only the mass and velocity of the proton.

Step-by-step explanation:

To find the speed of the center of mass of the proton and alpha particle system, we can use the formula for the velocity of the center of mass (Vcm):

Vcm = (m1v1 + m2v2) / (m1 + m2)

Where m1 and m2 are the masses of the proton and alpha particle, respectively, and v1 and v2 are their velocities. Assuming the alpha particle is initially at rest (v2 = 0 m/s), the formula simplifies to:

Vcm = (m1v1) / (m1 + m2)

By plugging in the given values (m1 = 1.673 × 10−27 kg, v1 = 3.715 × 106 m/s, m2 = 6.645 × 10−27 kg), we get:

Vcm = (1.673 × 10−27 kg × 3.715 × 106 m/s) / (1.673 × 10−27 kg + 6.645 × 10−27 kg)

Calculating that gives us the speed of the center of mass of the system.