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Vector Mechanics for Engineers: Statics and Dynamics
- A 1.62-oz golf ball is hit with a golf club and leaves it with a velocity of 100 mi/h. We assume that for 0 ≤ t≤t0 , where t0 is the duration of the impact, the magnitude F of the force exerted on the ball can be expressed as F=Fmsin (πt/t0). Knowing that t0 = 0.5 ms, determine the maximum value Fm of the force exerted on the ball.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_forwardThe coefficient of restitution e, between car A and car B is:a. e = 0. 8 b. e = 0. 6 c. e = 0. 4 d. e = 0arrow_forward
- At engine burnout on a mission, a shuttle had reached point A at an altitude of 40 mi above the surface of the earth and had a horizontal velocity v0. Knowing that its first orbit was elliptic and that the shuttle was transferred to a circular orbit as it passed through point B at an altitude of 170 mi, determine (a) the time needed for the shuttle to travel from A to B on its original elliptic orbit, (b) the periodic time of the shuttle on its final circular orbit.arrow_forwardProve that a force F(x,y,z) is conservative if, and only if, the following relations are satisfied:arrow_forwardThe coefficient of restitution is 0.9 between the two 60-mm-diameter billiard balls A and B . Ball A is moving in the direction shown with a velocity of 1 m/s when it strikes ball B , which is at rest. Knowing that after impact B is moving in the x direction, determine (a) the angle 0, (b) the velocity of B after impact.arrow_forward
- Rock falls can cause major damage to roads and infrastructure. To design mitigation bridges and barriers, engineers use the coefficient of restitution to model the behavior of the rocks. Rock A falls a distance of 20 m before striking an incline with a slope of α = 40o. Knowing that the coefficient of restitution between rock A and the incline is 0.2, determine the velocity of the rock right after the impact, both magnitude and angle with respect to the horizontal.arrow_forwardFor the system of particles of Prob. 14.13, determine (a) the position vector r of the mass center G of the system, (b) the linear momentum mv of the system, (c) the angular momentum HG of the system about G . Also verify that the answers to this problem and to Problem 14.13 satisfy the equation given in Prob. 14.27.Reference to Problem 14.13:A system consists of three particles A, B, and C. We know that mA =3kg, mB =2kg, and mC = 4 kg and that the velocities of the particles expressed in m/s are, respectively, vA = 4i +2j +2k, vB = 4i + 3j, and vC = -2i + 4j +2k. Determine the angular momentum HO of the system about O.arrow_forwardA 900-lb space vehicle traveling with a velocity v0 = (1500 ft/s)k passes through the origin O. Explosive charges then separate the vehicle into three parts A, B, and C , with masses of 150 lb, 300 lb, and 450 lb, respectively. Knowing that shortly thereafter the positions of the three parts are, respectively, A (250, 250, 2250), B (600, 1300, 3200), and C (-475, -950, 1900), where the coordinates are expressed in feet, that the velocity of B is vB = (500 ft/s)i+ (1100 ft/s)j+ (2100 ft/s)k, and that the x component of the velocity of C is -400 ft/s, determine the velocity of part A.arrow_forward
- Three identical small spheres, each weighting 2 lb, can slide freely on a horizontal frictionless surface. Spheres B and C are connected by a light rod and are at rest in the position shown when sphere B is struck squarely by sphere A, which is moving to the right with a velocity v0 = (8 ft/s)i . Knowing that θ = 30° and that the velocities of spheres A and B immediately after the impact are vA = (0.5 ft/s)i and vB = (3.75 ft/s)i + (vB)yj, determine (vB)y and the velocity of C immediately after impact.arrow_forwardDuring a high-speed chase, a 2400-lb sports car traveling at a speed of 100 mi/h just loses contact with the road as it reaches the crest A of a hill. (a) Determine the radius of curvature P of the vertical profile of the road at A. (b) Using the value of P found in part a , determine the force exerted on a 160-lb driver by the seat of his 3100-lb car as the car, traveling at a constant speed of 50 mi/h, passes through A.arrow_forwardCar A was traveling west at a speed of 15 m/s and car B was traveling north at an unknown speed when they slammed into each other at an intersection. Upon investigation it was found that after the crash the two cars got stuck and skidded off at an angle of 50° north of east. Knowing the masses of A and B are m mA and mB, respectively, draw the impulse-momentum diagram that can be used to determine the velocity of B before impact.arrow_forward
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