[填空题]
For an object of mass1/ts.(kk otrnrfd4y(qock3tf 3f74qw da.z 0j1 eo1f $(2.0 \pm 0.1) \mathrm{kg}$, 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 e 3otou;( 3 xsn4dtl5vhzjzy 10nergy 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.
