Question

A proton of mass 1 u undergoes a headon elastic collision with a stationary atomic nucleus of mass 6 u. the speed of the proton is 192 m/s. 1 u 192 m/s 6 u find the velocity of the center of mass of the system. answer in units of m/s.

Answer 1

The velocity of the center of mass for a system where a proton (1 u) moving at 192 m/s collides with a stationary atomic nucleus (6 u) is calculated to be 27.43 m/s.

Step-by-step explanation:

The question asks for the velocity of the center of mass of a system consisting of a proton, with a mass of 1 u, colliding head-on with a stationary atomic nucleus of mass 6 u. To find the velocity of the center of mass (VCM), we use the formula:

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

Where:

• m1 = mass of the proton = 1 u
• v1 = velocity of the proton = 192 m/s
• m2 = mass of the atomic nucleus = 6 u
• v2 = velocity of the atomic nucleus = 0 m/s (since it's stationary)

Plugging these values into the formula, we get:

VCM = (1 u × 192 m/s + 6 u × 0 m/s) / (1 u + 6 u)

VCM = 192 m/s / 7 u

VCM = 27.43 m/s

Therefore, the velocity of the center of mass of the system is 27.43 m/s.