Kognity IB Physics A.0 Measurements & Uncertainty (id: 5c29bb6d6)

[填空题]
For an object of masmt kej)by f:bx/xka, *eq/7n, s l, bmt9 /ays0e*: ,.xcjtc* jx6p. jucggrj4f$(2.0 \pm 0.1) \mathrm{kg}$, what percentage uncertainty in the velocity will give a $7.0 \%$ uncertainty in the kinetic energy ($KE = \frac{1}{2}mv^2$) ?   % (do not include the percent sign in your final result)

参考答案: 1.0


本题详细解析:
The percentage error in the kinetic energy can be ca yu)fj.ng4k( zlculated as: $$ \frac{\Delta E_K}{E_K}=\frac{\Delta m}{m}+2 \frac{\Delta v}{v} $$ Hence: $$ \begin{aligned} &0.07=\frac{0.1}{2.0}+2 \frac{\Delta v}{v} \\ &0.07=0.05+2 \frac{\Delta v}{v} \end{aligned} $$ and: $$ \frac{\Delta v}{v}=0.01 $$ So it is 1 percent.