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Question
A heavy truck and bike are moving with the same kinetic energy. If the mass of the truck is four times that of the bike, then calculate the ratio of their momenta. (Ratio of momenta = 2:1)
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Solution
Given: Let m1, m2 are the masses of truck and bike.
m1 = 4m2
Here kinetic energies of both truck and bike are the same
`"m"_1"v"_1^2` = `"m"_2"v"_2^2`
`4"m"_2"v"_1^2` = `"m"_2"v"_2^2`
`"v"_1/"v"_2` = `1/2`
V2 = 2v1
Ratio of momenta: `"P"_1/"P"_2` = `("m"_1"v"_1)/("m"_2"v"_2)` = `(4"m"_2)/"m"_2`. `"v"_1/(2"v"_1)` = 2
P1 : P2 = 2 : 1.
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