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 1.00-m^3 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 355 kg, the water can be directed, by switching a valve, either backward or forward. In both directions, the pressure washer ejects 179 L of water per min with a muzzle velocity of 24.5 m/s
a) If the cart starts from res, after what time should the valve be switched from backward (forward thrust) to forward (backward thrust) for the cart to end up at res?
b) What is the mass of the cart at that time, and what is its velocity? (Hint: it is safe to neglect the decrease in mass due to the gas consumption of the gas-powered pressure washer!)
c) What is the thrust of this “rocket”?
d) What is the acceleration of the cart immediately before the valve is switched?
My answers are:
a) 112 s
b)m= 694 kg v= 16.4 m/s
c) 145 N
d) 0.209m/s^2
I know that c is supposed to be 81.6 N but I don't know how to get that answer... and that will make my answer for d wrong too... can someone please tell me how to do this?
To find the thrust of the rocket (c), we need to calculate the force produced by the expelling water. The formula for force is given by Newton's second law: F = ma, where F is the force, m is the mass, and a is the acceleration.
In this case, the force is given by the rate of change of momentum, which is the mass flow rate (dm/dt) multiplied by the muzzle velocity (v).
The mass flow rate can be calculated by converting the volume flow rate of 179 L/min to kg/s. We know that 1 L of water has a mass of 1 kg, so the mass flow rate is 179 kg/min. To convert this to kg/s, divide by 60: (179 kg/min) / 60 = 2.9833 kg/s.
Now we can calculate the force:
F = (dm/dt) * v
F = (2.9833 kg/s) * (24.5 m/s)
F ≈ 72.9 N
So the thrust of the rocket is approximately 72.9 N.
Regarding part (d) - the acceleration of the cart immediately before the valve is switched - the calculation is based on Newton's second law. We know the mass of the cart (355 kg), and we can assume that the only force acting on it is the thrust force produced by the expulsion of water.
F = ma
a = F / m
a = 72.9 N / 355 kg
a ≈ 0.205 m/s^2
Therefore, the acceleration of the cart immediately before the valve is switched is approximately 0.205 m/s^2.
Please note that there may be slight differences in the final answer due to rounding errors during calculations.