What is the speed ratio (vA/vB) if particle A has 7 times the kinetic energy and half the mass of particle B? 0.267 1.87 3.74 2.65
Question
What is the speed ratio (vA/vB) if particle A has 7 times the kinetic energy and half the mass of particle B?
- 0.267
- 1.87
- 3.74
- 2.65
Solution
The kinetic energy (KE) of a particle is given by the equation KE = 1/2 * m * v^2, where m is the mass and v is the velocity of the particle.
Given that particle A has 7 times the kinetic energy of particle B, we can write:
7 * (1/2 * mB * vB^2) = 1/2 * mA * vA^2
Given that particle A has half the mass of particle B, we can substitute mA = 1/2 * mB into the equation:
7 * (1/2 * mB * vB^2) = 1/2 * (1/2 * mB) * vA^2
Solving for vA/vB gives:
vA/vB = sqrt(14) = 3.74
So, the speed ratio (vA/vB) is 3.74.
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