In the figure below, block 1 of mass m slides along an x axis on a frictionless

Question

In the figure below, block 1 of mass m slides along an x axis on a frictionless floor with a speed of V 2.60 m/s. Then it undergoes a one-dimensional elastic collision with stationary block 2 of mass m2 - 0.290m. Next, block 2 undergoes a one-dimensional elastic collision with stationary block 3 of mass ms 0.290m2. (a) What then is the speed of block 3 (b) Is the speed of block 3 greater than, less than, or the same as the initial value for block 1? O greater than O less thar O the same as (c) Is the kinetic energy of block 3 greater than, less than, or the same as the initial value for block 1? O greater than O less than O the same as (d) Is the momentum of block 3 greater than, less than, or the same as the initial value for block 17 O greater than O less thar O the same as

Explanation / Answer

given block m1

frictionless floor

v1i = 2.6 m/s

one dimensional elastic collsiion with m2 = 0.29 m1

speed of block A and B after this collision = v1m, v2m

one dimensional elastic collision of B and C, m3 = 0.29m2

speed of block B and C after this collsion = v2f, v3f

hence

fomr conservation of momentum for first collision

m1v1i = m1v1m + m2v2m

2.6 = v1m + 0.29v2m

form definition of coefficient of restitution for elastic collsions

v1i/(v2m - v1m) = 1

2.6 = v2m - v1m

v1m = v2m - 2.6

2.6 = v2m - 2.6 + 0.29v2m

v2m = 4.031 m/s

v1m = 1.431 m/s

from conservation of moemntum for second collision

m2v2m = m2v2f + m3v3f

4.031 = v2f + 0.29v3f

also from COR

v2m/(v3f - v2f) = 1

4.031 = v3f - v2f

v2f = v3f - 4.031

4.031 = v3f - 4.031 + 0.29v3f

v3f = 6.249 m/s

v2f = 2.2186 m/s

a. speed of block 3 = v3f = 6.249 m/s

b. speed of block 3 v3f > speed of block 1 initially v1i

c. KE of block 3 cannot be greater than that of block one from conservation of energy as block 1 and 2 are still moving and have some energy

hence KE of block 3 < KE of block 1 initially

d. as momentum now stands distributed amongst the three blocks moving in the same direction

momentum of block 3 < momentum of block 1 initially

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