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Question
Solve the following problem.
A marble of mass 2m travelling at 6 cm/s is directly followed by another marble of mass m with double speed. After a collision, the heavier one travels with the average initial speed of the two. Calculate the coefficient of restitution.
Solution
Given: m1 = 2m, m2 = m, u1 = 6 cm/s,
u2 = 2u1 = 12 cm/s,
v1 = `("u"_1 + "u"_2)/2 = 9` cm/s
To find: Coefficient of restitution (e)
Formulae:
i. m1u1 + m2u2 = m1v1 + m2v2
ii. e = `("v"_2 - "v"_1)/("u"_1 - "u"_2)`
Calculation:
From formula (i),
[(2m) × 6] + (m × 12) = (2m × 9) + mv2
∴ 12 + 12 = 18 + v2
∴ v2 = 6 cm/s
From formula (ii),
e = `(6 - 9)/(6 - 12) = (- 3)/(-6) = 0.5`
The coefficient of restitution is 0.5.
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