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Zorluk: KolayPhysical Quantities, Units and Dimensions

The physical quantity impulse is defined as the product of force and time. Which of the following physical quantities has the same dimensions as impulse?

  1. Linear momentumCevap
  2. B
    Work done
  3. C
    Power
  4. D
    Force

Cevap

Linear momentum
Linear momentum is calculated as mass times velocity, which yields the base dimensions [MLT−1][M L T^{-1}]. This is identical to impulse, which is force times time ([MLT−2]×[T]=[MLT−1][M L T^{-2}] \times [T] = [M L T^{-1}]).

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1
Determine the dimensions of impulse.
Impulse=Force×Time=[MLT−2][T]=[MLT−1]\text{Impulse} = \text{Force} \times \text{Time} = [M L T^{-2}][T] = [M L T^{-1}]
Force has base dimensions [MLT−2][M L T^{-2}] and time has dimension [T][T].
2
Determine the dimensions of linear momentum.
Linear Momentum=Mass×Velocity=[M][LT−1]=[MLT−1]\text{Linear Momentum} = \text{Mass} \times \text{Velocity} = [M][L T^{-1}] = [M L T^{-1}]
Mass has base dimension [M][M] and velocity has dimensions [LT−1][L T^{-1}].
3
Compare the dimensions of impulse and linear momentum.
Both quantities have identical dimensions of [MLT−1][M L T^{-1}].
By the impulse-momentum theorem, impulse equals change in momentum.

Anahtar Kavram

Dimensional analysis of physical quantities
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Physical Quantities, Units and Dimensions

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