Q5.4 Kinetic energy and linear momentum (S)
How fast must you walk or run to have
- the same kinetic energy
- the same momentum
as a 1600 kg car moving at 1 kmh-1.
Hint
Reveal
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Hint
Straightforward if you remember the definitions of linear momentum (Key Point 4.5)and kinetic energy (Key Point 3.8)Solution
Reveal
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Solution
Let’s denote my mass and (magnitude of) velocity by m and v respectively, and that of the car by mc and vc.Equal kinetic energy:
Therefore![\[ \frac{1}{2} m v^2 = \frac{1}{2} m_c v_c^2 \]](mastermathpng-0.png)
![\[ v = \sqrt{\frac{m_c}{m}} v_c \]](mastermathpng-1.png)
If we assume your mass to be 75 kg, then you would have to run at 4.61 kmh-1
- Equal momenta:
mv=mvctherefore v=vcmc/m. Again taking m=75 kg, I have to run at 21.33 kmh-1, which is about equivalent to a five minute mile pace.