Space Time & Motion A.2 Forces & Momentum (id: 0252656a9)

本题目来源于试卷: Space Time & Motion A.2 Forces & Momentum，类别为 IB物理学

[单选题]
A mass moving with a constant speed u encounters a rough surface and comes to a stop. The mass takes a time t to stop after encountering the rough surface.




The coefficient of dynamic friction between the rough surface and the mass is 0.40. What which of the following expressions gives the initial speed u?

A. 0.2gt
B. 0.4gt
C. gt
D. 2.5gt


参考答案:  B


本题详细解析:

$\underline{\text{Explanation}}$:

When the mass is moving on the rough surface, the only horizontal force acting on it is dynamic friction. Due to Newton’s Second Law, the following relationship can be written:

• $F_f=ma$

using $F_f={\mu }_d{F}_N$ and $a=v-ut$;

• ${\mu }_d{F}_N=m{\displaystyle \frac{v-u}{t}}$

$F_N=mg$, therefore

• ${\mu }_{d}mg=m{\displaystyle \frac{v-u}{t}}$

• ${\mu }_{d}g={\displaystyle \frac{v-u}{t}}$

• ${\mu }_{d}gt=v-u$

• $u=v+{\mu }_{d}gt$

By substituting the given values

• $u=0+0.4gt$

• $u=0.4gt$

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