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miv72 [106K]
3 years ago
6

Two titanium spheres approach each other head-on with the same speed and collide elastically. After the collision, one of the sp

heres, whose mass is 250 g, remains at rest. (a) What is the mass of the other sphere? (b) What is the speed of the two-sphere center of mass if the initial speed of each sphere is 1.8 m/s?
Physics
1 answer:
kotegsom [21]3 years ago
7 0

Answer:

m2  = 83.3 g

Explanation:

by conservation of momentum principle we have

m_1v_{i1} + m_2v_{i2} = m_2v_{f2}

as both sphere has same speed so v_{i2} = v_{i1}

m_2 = \frac{m_1}[\frac{v_f2}{v_{f1}}+1}

from conservation of kinetic energy principle we have

\frac{1}{2}m_1v^{2}_{i1} + \frac{1}{2}m_2v^{2}_{i2} = \frac{1}{2}m_2v^{2}_f2

v_{f1} = \sqrt {\frac{(m_1+m_2) v^2_i1}{m_2}

v_{f1} =  v_{i2}\sqrt {\frac{(m_1+m_2)}{m_2}

\frac{v_{f1}}{v_{i2}} =\sqrt {\frac{(m_1+m_2)}{m_2}

substituting this value in above equation to get m2 value

m_2 = \frac{m_1}{\sqrt {\frac{(m_1+m_2)}{m_2}+1}}

solving for m2 we  get

m2 = \frac{m_1}{3}

m_1 = 250 g

      =\frac{250}{3}

  m2  = 83.3 g

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