The valve of a cylinder containing 15 kg of compressed gas is opened and the cylinder empties in 1min 20s. If the force exerted on the cylinder 4.0 N,   show that the force required to accelerate the gas out of the cylinder is equal to (the change in momentum  )  divided by  ( the time taken)   Find   (i)  the average velocity at which the gas issues from the exit nozzle of the cylinder             (ii) the change in momentum of the gas

Principle of Linear Impulse and Momentum for a System of Particles To apply the principle of linear impulse and momentum to a system of particles. Integrating the equation of motion, as applied to all particles in a system, yields ∑mi(vi)1+∑∫t2t1Fidt=∑mi(vi)2 where mi is the ith particle's mass, vi is the ith particle's velocity, and Fi is the external force that acts on the ith particle. This relationship states that the sum of the initial linear momenta, at time t1, and the impulses of all the external forces acting between times t1 and t2 is equal to the sum of the linear momenta of the system, at time t2. If the system has a mass center, G, the expression becomes m(vG)1+∑∫t2t1Fidt=m(vG)2 This expression allows the principle of linear impulse and momentum to be applied to a system of particles that is represented as a single particle.   Two blocks, each of mass m = 6.90 kg , are connected by a massless rope and start sliding down a slope of incline θ = 36.0 ∘ at t=0.000 s. The…

The second stage of a two-stage rocket weighs 2000 lb (empty) and is launched from the first stage with a velocity of 3000 mi/h. The fuel in the second stage weighs 1000 lb. If it is consumed at the rate of 50lb/s and ejected with a relative velocity of 8000 ft/s, determine the acceleration of the second stage just after the engine is fired. What is the rocket’s acceleration just before all the fuel is consumed? Neglect the effect of gravitation.

A rocket lifts off from Earth initially at a mass of 50,000 kg. If it burns 40,000 kg of fuel during 40 seconds, it increases its speed by 5 km/s. 1. What is the exhaust velocity of the rocket? 2. What is the mass loss rate of the rocket? 3. What is the thrust of the rocket?