Concept explainers
Show that the values vA and vP of the speed of an earth satellite at the apogee A and the perigee P of an elliptic orbit are defined by the relations
where M is the mass of the earth, and rA and rP represent, respectively, the maximum and minimum distances of the orbit to the center of the earth.
Fig. P13.112 and P13.113
Want to see the full answer?
Check out a sample textbook solutionChapter 13 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
- 2B Show that in a field of attractive forces F(r) a body of mass m can always perform circular motion of radius r0 with constant angular velocity w. Also show that the velocity u of the circular orbit is given by the relation u² == ToF (1) marrow_forwardCollision at an Angle To apply conservation of linear momentum in an inelastic collision. Two cars, both of mass m, collide and stick together. Prior to the collision, one car had been traveling north at a speed 2v, while the second was traveling in a southeastern direction at an angle ϕ with respect to the east-west direction and at a speed v. After the collision, the two-car system travels in a northeastern direction at an angle θ with respect to the north-south direction and at a speed v final. What is the angle θ (with respect to north) made by the velocity vector of the two cars after the collision? Express your answer in terms of ϕ. Your answer should contain an inverse trigonometric function.arrow_forwardA 2-kg small block B fits inside a smooth slot cut in arm OA. The arm rotates counterclockwise in a vertical plane at a constant rate of 5 rad/s and r= 0.5 – 0.3 cos 0 in meters. At the instant that 0= 30°, determine (a) the force exerted by the spring on block B, (b) the normal force exerted by the arm OA on block B. Use radial and transverse components. spring Aarrow_forward
- Collision at an Angle To apply conservation of linear momentum in an inelastic collision. Two cars, both of mass m, collide and stick together. Prior to the collision, one car had been traveling north at a speed 2v, while the second was traveling in a southeastern direction at an angle ϕ with respect to the east-west direction and at a speed v. After the collision, the two-car system travels in a northeastern direction at an angle θ with respect to the north-south direction and at a speed v final. Find v final, the speed of the joined cars after the collision. Express your answer in terms of v and ϕ.arrow_forward5. A 2-kg sphere is attached to a massless rigid rod attached to a fixed pivot point O. The rigid rod and mass rotate in the horizontal plane. A moment is applied to the rod of magnitude M = 0.5t² N. m, where t is in seconds. The length of the rod is 0.5 m. Determine the speed of the sphere after the moment is applied for 5 seconds. M(t)arrow_forwardr = 1 A A 1-kg collar has a velocity of 9 m/s when to the right when it is at A. It then travels along the circular smooth guide of radius r+l B 199-cm from A, to B, a quarter of circle right-down to A. The collar is also connected to a spring, attached on its right-hand side to the collar and its left- hand side to a point, the same height as Barrow_forward
- A Dynamics experiment consists of collar B (mg = 10 kg) traveling to the left at VB = 1.5 m/s on a frictionless rail when a constant FB = 45 N force is applied to it. The collar is connected through a frictionless pulley system to weight A (mà = 3 kg). In the position shown the collar is x₁ = 1.25 m from the support at C. Determine: (a) The speed of collar B as it strikes the support at C if force FB acts on it throughout. (b) After what distance d should the FB force be removed if the collar is to reach support C with zero velocity? FBarrow_forward1) A cable is attached to a 0.5 kg block that slides over the smooth rigid horizontal rod AB. The diagram shown depicts the vertical plane. The cable tension is constant value T. At point C the speed of the block is 6 m/s to the left and at point D the speed is 1 m/s to the left. Determine the value of T. Note: take gravitational acceleration g=9,806 3 m D C A 4 m-arrow_forwardASAParrow_forward
- Q.1. A block of mass m = 0.5 kg is pushed against a horizontal spring of spring constant k = 450 N/m and negligible mass. The spring is compressed a distance x from equilibrium, and then released from rest. The block travels along a frictionless horizontal surface and reaches point B with a speed vg = 12 m/s. Take g = 10 m/s2. The compression of the spring is: a. x = 0.16 m b. x = 0.467 m c. x = 0.533 m B. d. x = 0.4 marrow_forwardSlider C has a mass of 0.5 kg and may move in a slot cut in arm AB, which rotates at constant speed in a horizontal plane. The slider is attached to a spring of constant k = 150 N/m, which is unstretched when r = 0. When arm AB rotates about the vertical axis, the slider moves without friction outward along the smooth slot cut. Determine for the position r = 80 mm: a) The constant speed (V) of the slider. b) The normal force (N) exerted on the slider by arm AB. A r=80mm Barrow_forwardRod OA rotates counterclockwise at a constant angular rate θ˙ = 4 rad/s. The double collar B is pin-connected together such that one collar slides over the rotating rod and the other collar slides over the circular rod described by the equation r=(1.6cosθ)m. Both collars have a mass of 0.7 kg . Motion is in the horizontal plane. (Figure 1)arrow_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