know Force, know mass of a cart propelled by air.. how to calculate the air speed used to propel the cart?

You need to use conservation of momentum in fluid mechanics.

The equation for each direction is as follows:

∑F = dB/dt + ∑(m_dot_exit*v_exit) - ∑(m_dot_in*v_in)

where m_dot means mass flow rate, v means velocity in the direction of interest, and dB/dt means the rate of change in the control volume's momentum (if stationary or at constant velocity, this equals zero). ∑F is the sum of all forces including body forces (such as gravity), solid constraint forces, and pressure forces.

Below I post a diagram:

http://img163.imageshack.us/img163/5393/jetenginef...

F is the horizontal restraint shear force (transmitted to the aircraft when in flight, but provided by the ropes in this case). T is the vertical tension in the restraint.

At station 1, the air is drawn in at the speed of the aircraft. For a stationary jet engine, v1 is nearly zero.

At station 2, the fuel is added. This doesn't provide thrust, but instead just increases the tension slightly in the attachment of the engine to the wing. Although the engine weight has more of an effect.

At station 3, the exhaust gasses are let out at high velocity. This is the velocity whose value is known.

Do we need to know the mass of the air? Well not the mass, but instead the mass flow rate. If you measure the cross sectional area of exhaust nozzle A, you instead just need the density of air, which is about 1 kg/m^3, although highly depends on the exhaust temperature of the engine.

To relate speed to mass flow rate:

m_dot = rho*v*A

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