VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)
12th Edition
ISBN: 9781260916942
Author: BEER
Publisher: MCG
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Chapter 12.3, Problem 12.96P
A particle with a mass m describes the path defined by the equation r = r0/(6 cos θ − 5) under a central force F directed away from the center of force O. Using Eq. (12.35), show that F is inversely proportional to the square of the distance r from the particle to O.
Fig. P12.96
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A particle of mass m is projected from point A with an initial velocity v0 perpendicular to OA and moves under a central force F along an elliptic path defined by the equation r=r0 /(2 - cos 0) Using Eq. (12.35), show that F is inversely proportional to the square of the distance r from the particle to the center of force 0.
applied mechanics 2
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.
Chapter 12 Solutions
VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)
Ch. 12.1 - A 1000-lb boulder B is resting on a 200-lb...Ch. 12.1 - Marble A is placed in a hollow tube, and the tube...Ch. 12.1 - The two systems shown start from rest. On the...Ch. 12.1 - Blocks A and B are released from rest in the...Ch. 12.1 - People sit on a Ferris wheel at points A, B, C,...Ch. 12.1 - Crate A is gently placed with zero initial...Ch. 12.1 - Two blocks weighing WA and WB are at rest on a...Ch. 12.1 - Objects A, B, and C have masses mA, mB, and mC,...Ch. 12.1 - Prob. 12.4FBPCh. 12.1 - Blocks A and B have masses mA and mB,...
Ch. 12.1 - A pilot of mass m flies a jet in a half-vertical...Ch. 12.1 - Wires AC and BC are attached to a sphere that...Ch. 12.1 - A collar of mass m is attached to a spring and...Ch. 12.1 - Prob. 12.9FBPCh. 12.1 - At the instant shown, the length of the boom AB is...Ch. 12.1 - Disk A rotates in a horizontal plane about a...Ch. 12.1 - Pin B has a mass m and slides along the slot in...Ch. 12.1 - The acceleration due to gravity on Mars is 3.75...Ch. 12.1 - The value of g at any latitude may be obtained...Ch. 12.1 - A Global Positioning System (GPS) satellite is in...Ch. 12.1 - Prob. 12.4PCh. 12.1 - A loading car is at rest on a track forming an...Ch. 12.1 - A 0.5-oz model rocket is launched vertically from...Ch. 12.1 - Determine the maximum theoretical speed that may...Ch. 12.1 - A tugboat pulls a small barge through a harbor....Ch. 12.1 - Prob. 12.9PCh. 12.1 - A 4-kg package is released from rest at point A...Ch. 12.1 - The coefficients of friction between the load and...Ch. 12.1 - A light train made up of two cars is traveling at...Ch. 12.1 - The two blocks shown are originally at rest....Ch. 12.1 - The two blocks shown are originally at rest....Ch. 12.1 - Prob. 12.15PCh. 12.1 - Prob. 12.16PCh. 12.1 - A 5000-lb truck is being used to lift a 1000-lb...Ch. 12.1 - Block A has a mass of 40 kg, and block B has a...Ch. 12.1 - Block A has a mass of 40 kg, and block B has a...Ch. 12.1 - The flat-bed trailer carries two 1500-kg beams...Ch. 12.1 - Prob. 12.21PCh. 12.1 - To unload a bound stack of plywood from a truck,...Ch. 12.1 - To transport a series of bundles of shingles A to...Ch. 12.1 - An airplane has a mass of 25 Mg and its engines...Ch. 12.1 - Determine the maximum theoretical speed that a...Ch. 12.1 - A constant force P is applied to a piston and rod...Ch. 12.1 - A spring AB of constant k is attached to a support...Ch. 12.1 - Block A has a mass of 10 kg, and blocks B and C...Ch. 12.1 - Prob. 12.29PCh. 12.1 - Prob. 12.30PCh. 12.1 - A 10-lb block B rests as shown on a 20-lb bracket...Ch. 12.1 - Knowing that k = 0.30, determine the acceleration...Ch. 12.1 - Knowing that k = 0.30, determine the acceleration...Ch. 12.1 - The 30-lb block B is supported by the 55-lb block...Ch. 12.1 - Block B of mass 10 kg rests as shown on the upper...Ch. 12.1 - Knowing that the swings of an amusement park ride...Ch. 12.1 - During a hammer throwers practice swings, the...Ch. 12.1 - Human centrifuges are often used to simulate...Ch. 12.1 - A single wire ACB passes through a ring at C...Ch. 12.1 - Prob. 12.41PCh. 12.1 - The 0.5-kg flyballs of a centrifugal governor...Ch. 12.1 - As part of an outdoor display, a 5-kg model C of...Ch. 12.1 - Prob. 12.44PCh. 12.1 - During a high-speed chase, a 2400-lb sports car...Ch. 12.1 - An airline pilot climbs to a new flight level...Ch. 12.1 - The roller-coaster track shown is contained in a...Ch. 12.1 - A spherical-cap governor is fixed to a vertical...Ch. 12.1 - A series of small packages, each with a mass of...Ch. 12.1 - A 55-kg pilot flies a jet trainer in a half...Ch. 12.1 - Prob. 12.51PCh. 12.1 - A curve in a speed track has a radius of 1000 ft...Ch. 12.1 - Tilting trains, such as the Acela Express that...Ch. 12.1 - Prob. 12.54PCh. 12.1 - A 3-kg block is at rest relative to a parabolic...Ch. 12.1 - Prob. 12.56PCh. 12.1 - A turntable A is built into a stage for use in a...Ch. 12.1 - The carnival ride from Prob. 12.51 is modified so...Ch. 12.1 - Prob. 12.59PCh. 12.1 - A small 8-oz collar D can slide on portion AB of a...Ch. 12.1 - A small block B fits inside a slot cut in arm OA...Ch. 12.1 - The parallel-link mechanism ABCD is used to...Ch. 12.1 - Prob. 12.63PCh. 12.1 - A small 250-g collar C can slide on a semicircular...Ch. 12.1 - A small 250-g collar C can slide on a semicircular...Ch. 12.1 - An advanced spatial disorientation trainer is...Ch. 12.1 - The 3-kg collar B slides on the frictionless arm...Ch. 12.1 - A 0.5-kg block B slides without friction inside a...Ch. 12.1 - Pin B weighs 4 oz and is free to slide in a...Ch. 12.1 - The parasailing system shown uses a winch to let...Ch. 12.1 - A 700-kg horse A lifts a 50-kg hay bale B as...Ch. 12.2 - A particle of mass m is projected from point A...Ch. 12.2 - A particle of mass m is projected from point A...Ch. 12.2 - Determine the mass of the earth knowing that the...Ch. 12.2 - Show that the radius r of the moons orbit can be...Ch. 12.2 - Communication satellites are placed in a...Ch. 12.2 - Prob. 12.81PCh. 12.2 - The orbit of the planet Venus is nearly circular...Ch. 12.2 - A satellite is placed into a circular orbit about...Ch. 12.2 - The periodic time (see Prob. 12.83) of an earth...Ch. 12.2 - A 500-kg spacecraft first is placed into a...Ch. 12.2 - A space vehicle is in a circular orbit of 2200-km...Ch. 12.2 - Prob. 12.87PCh. 12.2 - Prob. 12.88PCh. 12.2 - Prob. 12.89PCh. 12.2 - A 1-kg collar can slide on a horizontal rod that...Ch. 12.2 - Two 2.6-lb collars A and B can slide without...Ch. 12.2 - A small ball swings in a horizontal circle at the...Ch. 12.3 - A uniform crate C with mass mC is being...Ch. 12.3 - A uniform crate C with mass m is being transported...Ch. 12.3 - Prob. 12.94PCh. 12.3 - Prob. 12.95PCh. 12.3 - A particle with a mass m describes the path...Ch. 12.3 - A particle of mass m describes the parabola y =...Ch. 12.3 - Prob. 12.98PCh. 12.3 - Prob. 12.99PCh. 12.3 - Prob. 12.100PCh. 12.3 - Prob. 12.101PCh. 12.3 - A satellite describes an elliptic orbit about a...Ch. 12.3 - Prob. 12.103PCh. 12.3 - Prob. 12.104PCh. 12.3 - Prob. 12.105PCh. 12.3 - Halleys comet travels in an elongated elliptic...Ch. 12.3 - Prob. 12.109PCh. 12.3 - A space probe is to be placed in a circular orbit...Ch. 12.3 - The Clementine spacecraft described an elliptic...Ch. 12.3 - A space probe is describing a circular orbit of...Ch. 12.3 - Prob. 12.115PCh. 12.3 - A space shuttle is describing a circular orbit at...Ch. 12.3 - Prob. 12.117PCh. 12.3 - A satellite describes an elliptic orbit about a...Ch. 12.3 - Prob. 12.119PCh. 12.3 - Prob. 12.120PCh. 12.3 - Show that the angular momentum per unit mass h of...Ch. 12 - In the braking test of a sports car, its velocity...Ch. 12 - A bucket is attached to a rope of length L = 1.2 m...Ch. 12 - A 500-lb crate B is suspended from a cable...Ch. 12 - The parasailing system shown uses a winch to pull...Ch. 12 - A robot arm moves in the vertical plane so that...Ch. 12 - Telemetry technology is used to quantify kinematic...Ch. 12 - The radius of the orbit of a moon of a given...Ch. 12 - Prob. 12.131RPCh. 12 - Prob. 12.132RPCh. 12 - Disk A rotates in a horizontal plane about a...
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- 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. 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_forward5. A particle of mass m is projected from Point A with an initial velocity v0 perpendicular to line OA and moves under a central force F directed away from the center of force O. Knowing that the particle follows a path defined by the equation rr=- show (a) that the V cos20 velocity of the particle and the central force F are proportional to the distance r from the particle to the center of force O, (b) that the radius of curvature of the path is proportional to A hparrow_forwardA 1.5-lb ball that can slide on a horizontal frictionless surface is attached to a fixed point O by means of an elastic cord of constant k= 1 lb/in. and undeformed length 2 ft. The ball is placed at point A, 3 ft from O , and given an initial velocity v0 perpendicular to OA ., allowing the ball to come within a distance d = 9 in. of point O after the cord has become slack. Determine (a) the initial speed v0 of the ball, (b) its maximum speed.arrow_forward
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