Space Time & Motion A.2 Forces & Momentum (id: c8bcb9ad9)

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 jet of water with a cross sectional area of A strikejx,vm i,l th4-s perpendic+t70vjxpon, a zkg/t :b++a dwular to a wall at a speed of v After the collision, the water loses all of its horizontal speed and falls to the groun+k7g+nxb,todta+pwvj/0 a: z d. The magnitude of the force created on the wall due to the water is F Which expression give the density of the water?

A. $\frac{F}{Av^2}$
B. $\frac{F}{Av}$
C. FAv
D. $FAv^2$


参考答案:  A


本题详细解析:

$\underline{\text{xplanation}}$:

Considering the mass of water that strikes the wall in 1 second:

• $m=\rho V$

where $\rho$ is the density of the water and $V$ is the volume of the water.

Assigning the length of the column of water to be $l$

• $m=\rho Al$

But $l=vt$ and $t=1$, therefore $l=v$

Giving

• $m=\rho Av$

After the impact, the horizontal velocity of the jet is zero.

• $F=\mathrm{\Delta }p\mathrm{\Delta }t$ and  $\mathrm{\Delta }t=1$

• $F=\mathrm{\Delta }(mv)1=m\mathrm{\Delta }v$ $=(\rho Av)v=\rho A{v}^2$

Rearranging gives

• $\rho ={\displaystyle \frac{F}{A{v}^2}}$

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