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

[填空题]
For an object of massudot (g0e ;5p smd40zb3pl 6px)pq*dd7mznx1 +kl cn6 $(2.0 \pm 0.1) \mathrm{kg}$, 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 a.xxmh .o6h/ a0/u 0ljrq qa/win the kinetic energy can be calculated 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.