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In a rocket, the kinetic energy imparted to the consumed and ejected fuel is wasted as far as propelling the rocket is concerned. The useful power is equal to the product of the force available to propel the rocket and the speed of the rocket. If v is the speed of the rocket and u is the relative speed of the expelled fuel, show that the
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Vector Mechanics For Engineers
- (a) A 120-lb woman rides a 15-lb bicycle up a 3-percent slope at a constant speed of 5 ft/s. How much power must be developed by the woman? (b) A 180-lb man on an 18-lb bicycle starts down the same slope and maintains a constant speed of 20 ft/s by braking. How much power is dissipated by the brakes? Ignore air resistance and rolling resistance.arrow_forwardA railroad car having a mass of 15 Mg is coasting at 1.5 m/s on a horizontal track. At the same time another car having a mass of 12Mg is coasting at 0.75 m/s in the opposite direction. If the cars meet and couple together, determine the speed of both cars just after the coupling. Find the difference between the total kinetic energy before and after coupling has occurred, and explain qualitatively what happened to this energyarrow_forwardA railroad car having a mass of 15 Mg is coasting at 1.5 m/s on a horizontal track. At the same time another car having a mass of 12 Mg is coasting at 0.75 m/s in the opposite direction. If the cars meet and couple together,determine the speed of both cars just after the coupling. Find the difference between the total kinetic energy before and after coupling has occurred, and explain qualitatively what happened to this energy.arrow_forward
- To apply Newton’s second law and the theorem of conservation of energy to solve kinetic problems. A bungee jumper wants to jump off the edge of a bridge that spans a river below. The jumper has a mass m, and the surface of the bridge is a height h above the water. The bungee cord, which has lengthL when unstretched, will first straighten and then stretch as the jumper falls.Assume the following: The bungee cord behaves as an ideal spring once it begins to stretch and has spring constant k. The jumper does not actually jump but simply steps off the edge of the bridge and falls straight downward. The jumper's height is negligible compared to the length of the bungee cord. Thus, the jumper can be treated as a point particle. Use g for the magnitude of the acceleration due to gravity. How far below the bridge, d, will the jumper eventually be hanging, once the jumper stops oscillating and comes finally to rest? Assume that the jumper does not touch the water. Express your answer in…arrow_forwardEach of the two stages A and B of the rocket has a mass of 2 M-g (M=mega) when their fuel tanks are empty. They each carry 300 kg of fuel and are capable of consuming it at a rate of 50 kg/s and eject it with a constant velocity of 2500 m/s, measured with respect to the rocket. The rocket is launched vertically from rest by first igniting stage B. Then stage A is ignited immediately after all the fuel in B is consumed and A has separated from B Neglect drag resistance and the variation of the rocket’s weight with altitude. Given: Ma = Mb = 2000 Kg M Fuel = 300 Kg Fuel Consumption = 50 Kg/s V0 Ejected Fuel = 2500 m/s V0 rocket = 0 m/sarrow_forwardAn airplane has a mass of 25 Mg and its engines develop a total thrust of 40 kN during take-off. If the drag D exerted on the plane has a magnitude D= 2.25 v2, where is expressed in meters per second and D in newtons, and if the plane becomes airborne at a speed of 240 km/h, determine the length of runway required for the plane to take off.arrow_forward
- A jogger with mass m = 55 kg uses energy at a rate of P = 802 W when she jogs on horizontal ground at a constant speed of s = 3.5 m/s. The efficiency of her “human engine” however, is e = 0.27. (In other words, the power used for locomotion is e = 0.27 times the total power.) Q) Write an expression for the rate of energy expenditure whenshe jogs at the same constant speed up a slope of 4.99 degrees. Assume whatever frictional or drag forces are the same in each case. Your answer should be in terms of the symbols given in the problem statement and g(9.80 m/s^2)arrow_forwardA constant force P is applied to a piston and rod of total mass m to make them move in a cylinder filled with oil. As the piston moves, the oil is forced through orifices in the piston and exerts on the piston a force of magnitude kv in a direction opposite to the motion of the piston. Knowing that the piston starts from rest at t= 0 and x = 0, show that the equation relating x, v, and t, where x is the distance traveled by the piston and v is the speed of the piston, is linear in each of these variables.arrow_forwardA 36.0-g projectile is launched by the expansion of hot gas in an arrangement shown in figure a. The cross-sectional area of the launch tube is 1.0 cm2, and the length that the projectile travels down the tube after starting from rest is 32 cm. As the gas expands, the pressure varies as shown in figure b. The values for the initial pressure and volume are Pi = 12 ✕ 105 Pa and Vi = 8.0 cm3 while the final values are Pf = 1.1 ✕ 105 Pa and Vf = 40.0 cm3. Friction between the projectile and the launch tube is negligible. (a) If the projectile is launched into a vacuum, what is the speed of the projectile as it leaves the launch tube? In m/s. (b) If instead the projectile is launched into air at a pressure of 1.1 ✕ 105 Pa, what fraction of the work done by the expanding gas in the tube is spent by the projectile pushing air out of the way as it proceeds down the tube? w(spent)/w(env)=arrow_forward
- The missile weighs 47000 lb. The constant thrust provided by the turbojet engine isT = 18000 lb. Additional thrust is provided by two rocket boosters B. The propellant ineach booster is burned at a constant rate of 175 lb/s, with a relative exhaust velocity of 2000f t/s. If the mass of the propellant lost by the turbojet engine can be neglected, determinethe velocity of the missile after the 6 s burn time of the boosters. The initial velocity ofthe missile is 150 mi/h. Using your integration procedure from the previous labs solve thisproblem with n = 5, n = 10 and n = 100.arrow_forwardThe jet discharges water at a rate of 0.10 cu.m/s and at a speed of 18 m/s to the stationary plate. Determine the force on the plate. A. 1800 N B. 2800 N C. 2000 N D. 2500 Narrow_forwardDetermine the linear momentum of a person whose mass is 80 kg and who is running at a rate of 3 m/s. Compare it to the momentum of a car that has a mass of 2000 kg and is moving at a rate of 30 m/s in the same direction as the person.arrow_forward
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