Could someone please help me with solving these problems, thank you! In the foll

Question

Could someone please help me with solving these problems, thank you!

In the following apparatus, the moving first cart is allowed to collide with the stationary second cart: The first cart has a mass m_1 and an initial velocity v_o. The second cart has a mass m_2 and is initially at rest. After the collision, the carts stick together (i.e. this is a perfectly inelastic collision) Using the conservation of momentum equation, find an expression for the final velocity of the system assuming the two carts have the same final velocity v_F. Using your answer to Part (a) above, show that the ratio of final kinetic energy to initial kinetic energy is given by the expression: K_F/K_O = m_1/m_1 + m_2 You will use this result in the Analysis section of the lab

Explanation / Answer

Given

   two carts of masses m1,m2, are moving with initial velocity for m1 ,v0, and m2 is at rest

after the collision( perfectly inelastic collision) , they stick togeter and move with common speed Vf
a)

by conservation of momentum

   m1*V0+ m2*0 = (m1+m2)VF

   m1V0 = (m1+m2)VF

   VF = m1V0 / (m1+m2) ---------------->>(1)

b)

   kinetic energy initial k.e = m1V0^2 + 0

           final k.e = (m1+m2) VF^2

   ratio is KF/K0 = (m1+m2) VF^2 /m1V0^2

using eq (1)

       KF/K0 = (m1+m2)(m1V0 / (m1+m2))^2/m1V0^2

  
       KF/K0 = m1 / (m1+m2)

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