Starting from rest, a cart is propelled by an hydraulic cataputl(liquid jet). Th

Question

Starting from rest, a cart is propelled by an hydraulic cataputl(liquid jet). The jet strikes the curved surface and makes 180 degree turn, leaving horizontally. Air and rolling resistance may be neglected. If the mass of the cart is 100 kg and the jet of water leaves the nozzle(of area 0.001m^2 with a speed of 35m/s), Determine the speed of the cart 5 sec. after the jet is directed against the cart.

is V = 12.5 m/s. The velocity profile in section (2) is piecewise linear (as shown). Calculate: the mass flow rate in the wind tunnel and the maximum velocity at section ( 1 ), Vmax the drag of the object and its supporting vane (neglect viscous resistance) Starting from rest, the cart shown is propelled by an hydraulic catapult (liquid jet). The jet strikes the curved surface and makes a 180 digree turn, leaving horizontally. Air and rolling resistance may be neglected. If the mass of the cart is 100 Kg and the jet of water leaves the nozzle (of area 0.001 m2 with a speed of 35 m/s, determine the speed of the cart 5 s after the jet is directed against the cart.

Explanation / Answer

the jet of water exerts a force on the cart due to the change in momentum

change in momentum = mass x velocity

mass of the liquid = density x volume

volume = velocity x area of cross section x time

volume = 35 x 0.001 x 5 = 0.175 m^3

density = 1000 kg/m^3

mass = 1000 x .175 = 175 kg

change in momentum = m x v = 175 x 35 = 6125 kgm/s

force = dP/dt

force = 6125/5 = 1225 N

acceleration = force / mass = 1225 / 100

acceleration = 12.25 m/s^2

v = at

after 5 sec

velocity = 12.25 x 5

velocity = 61.25 m/s

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