Chapter 11: Q. 23 (page 288)

A proton is traveling to the right at $2.0 \times 10^{7} m / s$ . It has a head on perfectly elastic collision with a carbon atom. The mass of the carbon atom is $12$ times the mass of the proton. What are the speed and direction of each after the collision?

Short Answer

Expert verified

The speed of the proton is $- 1.69 \times 10^{7} m / s .$

The speed of the carbon atom is $3.1 \times 10^{6} m / s .$

Step by step solution

Given information

We have given,

speed of the proton = $2 \times 10^{7} m / s$

$Mass of carbon atom = 2 \times Mass of proton$

We have to find the speed and direction of each one after the collision.

Simplify

From the elastic collision when one particle will be at rest, we know their final velocity will be,

$v_{if} = \frac{m_{1} - m_{2}}{m_{1} + m_{2}} v_{1} v_{2 f} = \frac{2 m_{1}}{m_{1} + m} v_{2}$

then,

After putting the value of

$m_{1} = mass of proton m_{2} = mass of carbon atom$

$v_{if} = \frac{m_{1} - m_{2}}{m_{1} + m_{2}} v_{1} v_{1 f} = \frac{m_{p} - 12 m_{p}}{m_{p} + 12 m_{p}} (v_{1}) v_{1 f} = \frac{- 11 m_{p}}{13 m_{p}} \times (2 \times 10^{7} m / s) v_{1 f} = - 1.69 \times 10^{7} m / s$

Similarly,

$v_{2 f} = \frac{2 m_{1}}{m_{1} + m_{2}} v_{1} v_{2 f} = \frac{2 m_{p}}{13 m_{p}} v_{1} v_{2 f} = \frac{2}{13} \times (2 \times 10^{7} m / s) v_{2 f} = 3.1 \times 10^{6} m / s$

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A proton is traveling to the right at $2.0 \times 10^{7} m / s$ . It has a head on perfectly elastic collision with a carbon atom. The mass of the carbon atom is $12$ times the mass of the proton. What are the speed and direction of each after the collision?

Short Answer

Step by step solution

Given information

Simplify

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A proton is traveling to the right at 2.0×107m/s. It has a head on perfectly elastic collision with a carbon atom. The mass of the carbon atom is 12 times the mass of the proton. What are the speed and direction of each after the collision?

Short Answer

Step by step solution

Given information

Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Space Physics

Electric Charge Field and Potential

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Study anywhere. Anytime. Across all devices.

A proton is traveling to the right at $2.0 \times 10^{7} m / s$ . It has a head on perfectly elastic collision with a carbon atom. The mass of the carbon atom is $12$ times the mass of the proton. What are the speed and direction of each after the collision?