[Problem 4: 20 points] A water jet strikes the vertical surface of a cart moving

Question

[Problem 4: 20 points] A water jet strikes the vertical surface of a cart moving horizontally at a constant velocity of 10 m/s in the flow direction. The water exits the nozzle at 35 m/s and the mass flow rate through the nozzle is 30 kg/s. Determine the following: a) b) c) What is the force that needs to be applied by the brakes of the cart to prevent it from accelerating? If this force were used to generate power instead of being converted to heat (via the brakes), how much power could be generated? If the mass of the cart is 400 kg and the brakes fail, what will be the acceleration of the cart when the water jet first strikes it. Ignore mass of water that wets the back of the cart.

Explanation / Answer

(A) force provided by water jet,

F= rate of change of momentum of water jet

F = (30 kg /s) (35 - 10) m/s

F = 750 kg m / s^2 OR 750 N

so force needed to moving with constant velocity.

F = 750 N

(B) P = Fv = 750 x 10 = 7500 Watt

(C) initial acc, a = F/m

a = 750 / 400 = 1.875 m/s^2

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