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Scientist94
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Homework Statement
B7 State the relationships between (i) force and momentum, (ii) force and energy, (iii) force and power, (iv) power and energy. [2]
Find expressions for the momentum and kinetic energy transported per unit time in a jet of fluid having cross-sectional area A, density ρ, and speed u.[2]
In a water pistol, a trigger drives a piston at constant speed along a cylinder with cross-sectional area S forcing water out through a hole as a narrow jet with cross-sectional area A. By equating the power supplied to the piston to that transported by the jet show that the net force F needed on the piston to generate a jet with speed u is
F = 1/2 x pSu^2
where ρ is the density of water. [4]
A pistol has S = 1cm2 and A = 4mm2. A target is placed at a height h = 2.5m above the pistol and at a distance w = 5m in front of it. Find the speed of the jet needed, the direction in which the pistol must be aimed, and the force needed on the piston, to produce a jet that hits the target horizontally. [5]
Is the force of the jet sufficient to dislodge a target with a mass of 30g on a surface with a coefficient of friction of 0.5? [2] [ You may assume that the density of water is ρ = 1,000kgm−3 ]
Homework Equations
The Attempt at a Solution
Ok for the first four questions I put : i) Force x time = momentum
ii) Force x distance = Energy
iii) (Force x distance)/time = Power
iv) Energy/time = Power
For the next part I used the logic that momentum per unit time would have units kgms^(-2) and by using area= m^2 , density= kgm^(-3) and speed = ms^(-1) I arrived at the correct units using density x speed^2 x area = pAu^2
I used a similar method for kinetic energy per unit time time and arrived at ke per time = 1/2 x pAu^3
I'm not sure if these are correct.
For the next part I started with the power transported by the jet = KE/time = 1/2pAu^3
But then I don't know how to find the power supplied to the piston, I know that using the equation from iii) I can get something in terms of F but I don't know the time or distance nor how I get S involved.
Help would be much appreciated!
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