Exercise 9.34 A block of mass m undergoes a one-dimensional elastic collision wi

Question

Exercise 9.34 A block of mass m undergoes a one-dimensional elastic collision with a block of mass M initially at rest. Part A If both blocks have the same speed after the collision, how are their masses related? Express M in terms of m. oT-Mobile LTE 9:52 PM 10% session.masteringphysics.com Exercise 9.34 MasteringPhysics Exercise 9.34 A block of mass m undergoes a one-dimensional elastic collision with a block of mass M initially at rest Part A If both blocks have the same speed after the collision, how are their masses related? Express M in terms of m. M= Submit Give Up Continue >

Explanation / Answer

The energy and momentum are conserved so we can write:

Ekm0 + EkM0 = Ekm1 + EkM1
pm0 + pM0 = pm1 + pM1

We know that the block of mass M is initially at rest, so both EkM0 and pM0 are equal to 0:

Ekm0 = Ekm1 + EkM1
pm0 = pm1 + pM1

We also know that the speeds after collision are the same. We have to assume that the block of mass m bounces off the block of mass M for the collision to be elastic and therefore the momentum of the block of mass m should be negative:

1/2 m v2 = 1/2 m u2 + 1/2 M u2
m v = -m u + M u

Now we have to multiply the first equation by 2/m and the second equation by 1/m.

v2 = (1+M/m) u2
v = (M/m-1) u

After substituting the second equation into the first equation:

(M/m-1)2 u2 = (1+M/m) u2

After dividing by u2 :

(M/m-1)2 = (1+M/m)
(M/m)2 - 2 (M/m) +1 = 1 + M/m
(M/m)2 - 2 (M/m) - M/m = 0
(M/m)2 - 3 (M/m) = 0

Divide by M/m:

M/m - 3 = 0
M/m = 3

M = 3m

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