Show that for a completely inelastic collision with m. initially at rest that: I

Question

Show that for a completely inelastic collision with m. initially at rest that: It is true generally that the kinetic energy can always be written in terms of momentum m the form. For example, consider any object with mass m moving with velocity v. The magnitude of the momentum of this object is: p - mv. If we square this and dived it by twice the mass of the object we get p^2/2m=(mtv)/2m=1/2 which is easily recognized to be the formula for the kinetic energy, A' Thus it is true that the kinetic energy of an object can be written as in Eq. (20). In your proof of Eq. (19). write K_i and K_f in the form shown in Eq. (20). You will need to think about what the relevant masses are for K_t and K_f. Do not substitute any numerical values for any of the quantities shown in Eq.

Explanation / Answer

Completely or perfactly inelastic collision is one in which bodies stick to each other after collision and move witha common velocity V .

u1 = initial velocity of mass m1

u2 = 0m/s = initial velocity of mass m2 ,at rest

V = final velocity after collision

from copnservation of momentum:

pi = pf

m1*u1 + m2*u2 = (m1+ m2)*V

m1*u1 + 0 = ( m1+m2) *V

V = m1*u1 / m1 + m2

K.E_f / K.E_i = ( 1/2)*( m1+m2)*V2 / [ (1/2)*m1*u12]

put value of V

K.E_f / K.E_i = ( m1+m2)* (m1*u1 / m1 + m2)2 / m1*u12

= m1 / m1 + m2

[K.E_i - K.E_f] / K.E_i = 1 - ( K.E_f / K.E_i)

= 1 - (m1 / m1 + m2)

= m2 / m1+m2

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