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Chapter 9: Q. 2 (page 227)

Particle A has half the mass and eight times the kinetic energy of particle B. What is the speed ratio v_A/v_B?

Short Answer

Expert verified

Ratio of speed v_A/v_B= 4

Step by step solution

01

Step:1 Given Information

m_a = 1/2m_b

KE_a=8KE_b

02

Explanation

First find Kinetic energy

KE_a = 1/2 m_a v_a²...................................(1)

KE_b = 1/2 m_b v_b²...................................(2)

Divide 1 by 2 , we get

$\frac{K E_{a}}{K E_{b}} = \frac{(1 / 2 m_{a} {v_{a}}^{2})}{(1 / 2 m_{b} {v_{b}}^{2})}$

As substitute the given ratio m_a = 1/2m_{b and}KE_a=8KE_b

so

$8 = \frac{(1 / 2 m_{a} {v_{a}}^{2})}{(1 / 2 m_{b} {v_{b}}^{2})} \frac{{v_{a}}^{2}}{{v_{b}}^{2}} = 8 脳 2 \frac{v_{a}}{v_{b}} = 4$

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