A cart running on frictionless air tracks is propelled by a stream of water expe

Question

A cart running on frictionless air tracks is propelled by a stream of water expelled by a gas-powered pressure washer stationed on the cart. There is a 1.0-m3 water tank on the cart to provide the water for the pressure washer. The mass of the cart, including the operator riding it, the pressure washer with its fuel, and the empty water tank, is 450 kg. The water can be directed, by switching a valve, either backward or forward. In both directions, the pressure washer ejects 220 L of water per min with a muzzle velocity of 26.5 m/s.

Explanation / Answer

(a)
F = ma
F is the thrust, this does not change throughout the problem.
M1/M2 = M2/M3 since the mass will be less, the acceleration will be greater even though the force is the same, so to get the cart to be at rest at the end, we need to use this geometric mean (since eveything is to the first power) So the nozzle will be pointing one way longer since the cart is heavier and needs more impulse to get up to speed, and then pointing the other way for less time since the mass will be less and the cart, therefore, easier to accelerate.
one cubic meter of water is (10cm*10)^3. One liter is (10cm)^3 = 1,000ml = 1 kg, so 1 m^3 = 1,000 kg
M2 = SQRT(450*1450) = 807.774 kg this is the answer to (b)
So, how long does it take to go from 1450kg down to 807.77kg if we are shooting out 220 l per minute or, see above, 220 kg/min
distance equals rate times time
mass loss equals rates times time
t = Massloss/Rate = (1450-807.77)kg/220kg/min = 2.919 min
(a) 2.919 min
(b) solved above 807.77 kg
The velocity change during a period the jet is aimed in one direction is
deltaV = Vexhaust*ln (M1/M2).
Here's why:
Thrust = Vexhaust*dM/dt = M dV/dt
dV = Vexhaust*dM/M
V2 - V1 = Vexhaust*ln(M1/M2)
V = Vexhaust*ln(1450/877.77) = 13.301 m/s
(c) Thrust never changes T = (rate of change in mass)*v exhaust
Lets get the units to be the same 26.5 m/s is typical 220 kg/min = 220/60 kg/s
T = 26.5 m/s*220/60*kg/s = 97.166 N
(d) acceleration immediately before flipping the nozzle. We know the mass right then and we always know the Thrust which is the force, so we can easily find the acceleration.
F = ma
a = F/m
a = 97.166N/877.77kg = 0.1106m/s^2

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.