Concept explainers
A rocket sled bums fuel at the constant rate of 120 lb/s. The initial weight of the sled is 1800 lb. including 360 lb of fuel. Assume that the track is lubricated and the sled is aerodynamically designed so that air resistance and friction are negligible. (a) Derive a formula for the acceleration a of the sled as a function of time t and the exhaust velocity
Want to see the full answer?
Check out a sample textbook solutionChapter 14 Solutions
Vector Mechanics For Engineers
- The rocket shown is designed to test the operation of a new guidance system. When it has reached a certain altitude beyond the effective influence of the earth's atmosphere, its mass has decreased to 2.49 Mg, and its trajectory is 0= 34° from the vertical. Rocket fuel is being consumed at the rate of 130 kg/s with an exhaust velocity of 625 m/s relative to the nozzle. Gravitational acceleration is 9.54 m/s² at its altitude. Calculate the n- and t-components of the acceleration of the rocket. Answers: an= Vert. 18 at = M 1 Da - Horiz- m/s² m/s²arrow_forwardmass m, which starts from rest at x =0 and t =0, subject to the following force functions: 1- Find the velocity i and the position x as functions of the time t for a particle of (a) F = F.+ ct (b) Fx = F, sin ct (c) F, = F, e Where F, andc are positive constants.arrow_forwardA football is thrown upward at 30.0° above the horizontal. The ball travels a horizontal distance of 40.0 m. Find: (b) the maximum altitude attained, and(c) the velocity of the ball at t = 2.00 s.arrow_forward
- A ball is thrown vertically up with a velocity of 50 m /s at the edge of a 100-m cliff. Calculate the height h to which the ball rises and the total time t after release for the ball to reach the bottom of the cliff. Neglect air resistance and take the downward acceleration to be 9.81 m /s^2 .arrow_forwardThere are two bodies which moving towards each other. They collide and stay connected. The presses the spring afterwards. Calculate the spring compression x. Result write in meters. Bodies are assumed as mass points and there is no friction. Bodies remains connected (into one body) after the collision. • m,u4kg • V,=16m/s • m3=Bkg • vz-34m/s • k-3,2kN/m • x+?m; Result needs to be with 3 digits precision k m, m, x=? Answer: 5.657arrow_forwardA crate, initially traveling horizontally with a speed of 18 ft/s, is made to slide down a 14 ft chute inclined at 35◦. The surface of the chute has a coefficient of kinetic friction μk, and at its lower end, it smoothly lets the crate on to a horizontal trajectory. The horizontal surface at the end of the chute has a coefficient of kinetic friction μk2. Model the crate as a particle, and assume that gravity and the contact forces between the crate and the sliding surface are the only relevant forces. Using conservation law methods, if μk= 0.35, what is the speed with which the crate reaches the bottom of the chute (immediately before the crate’s trajectory becomes horizontal)?arrow_forward
- A lightweight drone (1.00 kg) is launched at 800 m high and moves upward at a constant velocity (whileignoring the effects of gravity only on the drone). The balloon, when measured at a horizontal distance fromyou, is about 1600 m away from you. At the moment when the drone moves, you shoot a bullet (weight =180g) with an initial velocity of 1009 m/s at a fixed angle α, where sin α=3/5 and cos α= 4/5. (g = 9.8 m/s2) d. Provided that the collision is inelastic, calculate the speed after the collision.e. Calculate the height the two objects taken from the impact up to the maximum height before it startsfalling to the ground.arrow_forwardA crate with a mass of 155 kg starting from rest, slides down a ramp making an angle of 32 degrees with respect to horizontal. The ramp is 6 meters long. A constant frictional force of 200 N acts throughout the motion and a force F is being applied by a rope as shown to prevent the block from sliding too fast. Suppose that while traveling at v=0.1 m/s down the ramp, at d=4meters from the end of the ramp, the rope breaks, Use the work-kinetic energy theorem to calculate the speed, in m/s, of the crate when it touches the bottom of the ramp.arrow_forward8. An application to mecanics A particule r(t) of mass 1kg is moving along an horizontal straight line (positively oriented on the right). The particle is under the effect of a positive constant force F(t) = g. Knowing that the particle what initially at the origin, with negative speed -vo, find the expression of x(t) time t in terms of g and vo and find the position further on the left where the particule will be. Finally, find the expression of the time T when the particle will be back at the origin.arrow_forward
- A ball is thrown vertically up with a velocity of 29 m/s at the edge of a 77-m cliff. Calculate the height h to which the ball rises and the total time t after release for the ball to reach the bottom of the cliff. Neglect air resistance and take the downward acceleration to be 9.81 m/s². Answers: h= t = i i 77 m m Sarrow_forwardA crate, initially traveling horizontally with a speed of 18 ft/s, is made to slide down a 14 ft chute inclined at 35◦. The surface of the chute has a coefficient of kinetic frictionμk, and at its lower end, it smoothly lets the crate ontoa horizontal trajectory. The horizontal surface at the end of the chute has a coefficient of kinetic frictionμk2. Model thecrate as a particle, and assume that gravity and the contact forces between the crate and the sliding surface are the onlyrelevant forces.Using conservation law methods, ifμk= 0.35, what is the speed with which the crate reaches thebottom of the chute (immediately before the crate’s trajectory becomes horizontal)?arrow_forwardPROBLEM NO. 3 A 5-kg collar slides from A to B along a frictionless vertical rod as shown. The spring attached to the collar has an undeformed (initial) length of 4 m and a spring constant of 30 N/m. What is the collar's velocity at point B? 8.0 m A B 1.5 marrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY