Anonymous
Anonymous asked in Science & MathematicsPhysics · 8 months ago

# help in physics??

A proton of kinetic energy 1.6 × 10−13 J is moving toward a proton at rest. What is the

velocity of the center of mass of the system

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• Given,

Kinetic Energy (K.E) = 1.6 x 10⁻¹³JVelocity of center of mass system (vcm) = ?Mass of proton (m) = 1.67 x 10⁻²⁷kgWe know that:-Kinetic Energy (K.E) = ½mv²1.6 x 10⁻¹³J = ½ x 1.67 x 10⁻²⁷kg x v²2 x 1.6 x 10⁻¹³J = 1.67 x 10⁻²⁷kg x v²→ v = √2 x 1.6 x 10⁻¹³ / 1.67 x 10⁻²⁷ = √3.2 x 10⁻¹³ / 1.67 x 10⁻²⁷= √1.916 x 10¹⁴= 1.38 x 10⁷m/sec∴ velocity of center of mass (v) = 1.38 x 10⁷m/sec.

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• The velocity of the center of mass is ½ of the velocity of the moving proton, since the two objects have the same mass. So

Vcm = ½*v = ½*√(2*KE / m)

Vcm = ½*(2*1.6e-13J / 1.67e-27kg) = 6.9e6 m/s

This is well below the speed of light, so relativistic effects can be ignored.

Hope this helps!

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• KE 1/2 Mass of proton * velocity ^2.

v = sqrt(KE/mass of proton)

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• Seven                    .

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