yg yg Choose dm as the study object: dm When it reaches the ground its speed is: v=v2 Using impulse-momentum theorem: (dmg -T' )dt=-dyv2gy Since dmg <<T, we can neglect it, 2 Use Newton's third law T=T, so T=.. 2gy Then we have the magnitude of the normal force of the ground on the chain is N=.yg +2gy 2. A fire hose fixed to a support delivers a horizontal stream of water at a speed vo and a mass flow rate B kilograms per (a) The water stream is directed against a wall along a perpendicular to the wall Fig 6 st.(see Figure 6(a)What the magnitude of the force of the water on the wall? b)What is the momentum per unit length of the stream?(c)The stream now is directed into a hole in the back of a tank car(see Figure 2(b)) that is free to roll from rest(with no frictional work done) The tank car has an initial mass mo. Let the total mass of the tank car be m (tank car plus accumulated water). Find the x-component of the velocity of the tank car at time t Solution (a) Assume the time interval during the water act on the wall is At, and the mass of the water which act on the wall is Am= BAt. We choose Am as the study object, which get the average force from the wall is f. Using impulse-momentum theorem. ( the direction of right is i)yg T l m yg T N N l m + − = 0 ⇒ = + Choose dmas the study object: y l m dm = d When it reaches the ground its speed is: v = 2gy Using impulse-momentum theorem: y gy l m (dmg −T')dt = − d 2 Since dmg << T' , we can neglect it, gy l m v gy l m gy t y l m T 2 2 2 d d '= = = Use Newton’s third law T = T' , so gy l m T = ⋅ 2 Then we have the magnitude of the normal force of the ground on the chain is l mgy gy l m yg l m N 3 = + 2 = 2. A fire hose fixed to a support delivers a horizontal stream of water at a speed v0 and a mass flow rate β kilograms per second. (a) The water stream is directed against a wall along a perpendicular to the wall and is brought to rest. (see Figure 6(a))What the magnitude of the force of the water on the wall? (b) What is the momentum per unit length of the stream? (c) The stream now is directed into a hole in the back of a tank car (see Figure 2(b)) that is free to roll from rest (with no frictional work done). The tank car has an initial mass m0. Let the total mass of the tank car be m (tank car plus accumulated water). Find the x-component of the velocity of the tank car at time t. Solution: (a) Assume the time interval during the water act on the wall is ∆t , and the mass of the water which act on the wall is ∆m = β∆t . We choose ∆m as the study object, which get the average force from the wall is f. Using impulse-momentum theorem. (the direction of right is i ˆ ） 0 v r (a) 0 v r v m r (b) Fig.6