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It is assumed that each of the two automobiles involved in the collision described in Prob. 14.35 had been designed to safely withstand a test in which it crashed into a solid, immovable wall at the speed v0. The severity of the collision of Prob. 14.35 may then be measured for each vehicle by the ratio of the energy it absorbed in the collision to the energy it absorbed in the test. On that basis, show that the collision described in Prob. 14.35 is
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Vector Mechanics For Engineers
- 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.arrow_forwardTwo small balls A and B with masses 2m and m , respectively, are released from rest at a height h above the ground. Neglecting air resistance, which of the following statements is true when the two balls hit the ground? a. The kinetic energy of is the same as the kinetic energy of B.b. The kinetic energy of A is half the kinetic energy of B.c. The kinetic energy of A is twice the kinetic energy of B.d. The kinetic energy of A is four times the kinetic energy of B.arrow_forwardCar B is towing car A at a constant speed of 10 m/s on an uphill grade when the brakes of car A are fully applied causing all four wheels to skid. The driver of car B does not change the throttle setting or change gears. The masses of the cars A and B are 1400 kg and 1200 kg, respectively, and the coefficient of kinetic friction is 0.8. Neglecting air resistance and rolling resistance, determine (a) the distance traveled by the cars before they come to a stop, (b) the tension in the cable.arrow_forward
- . In an elevator shaft, a ball is thrown vertically upward with an initial velocity of 18 m/s from a height of 12 m above ground. At the same instant, an open-platform elevator passes the 5-m level, moving upward with a constant velocity of 2 m/s. Determine (a) when and where the ball hits the elevator, (b) the relative velocity of the ball with respect to the elevator when the ball hits the elevator.arrow_forwardA 16-Mg jet airplane maintains a constant speed of 774 km/h while climbing at an angle a = 18°. The airplane scoops in air at a rate of 300 kg/s and discharges it with a velocity of 665 m/s relative to the airplane. If the pilot changes to a horizontal flight while maintaining the same engine setting, determine (a) the initial acceleration of the plane, (b) the maximum horizontal speed that will be attained. Assume that the drag due to air friction is proportional to the square of the speed.arrow_forwardTwo blocks A and b , of mass 4 kg and 5 kg, respectively, are connected by a cord that passes over pulleys as shown. A 3-kg collar A is placed on block A and the system is released from rest. After the blocks have moved 0.9 m, collar C is removed and blocks A and B continue to move. Determine the speed of block A just before it strikes the ground.arrow_forward
- In a game of pool, ball A is moving with the velocity v0 = v0i when it strikes balls B and C , which are at rest side by side. Assuming frictionless surfaces and perfectly elastic impact (i.e., conservation of energy), determine the final velocity of each ball, assuming that the path of A is (a) perfectly centered and that A strikes B and C simultaneously, (b) not perfectly centered and that A strikes B slightly before it strikes C.arrow_forwardA block a of 5000g is released from rest if the masses of the pulleys and ropes are disregarded determine the speed of block b of 1 Kg in 5 secondsarrow_forwardIMPULSE AND MOMENTUM A 4kg ball and 3kg ball move on a smooth plane along a straight path withspeeds equivalent to 6m/s going to the right and 8 m/s going to the left, respectively.1. Determine the speed of the 3kg ball after impact if the impact is elastic.2. Determine the speed of the 3kg ball after impact if the coefficient of restitutionis 0.50.arrow_forward
- A ball is thrown with a speed of 12 m / s directed vertically upwards from a window located 16 m above the ground. If it is assumed that friction with the air does not affect the movement of the ball and that its acceleration is that of gravity g = 9.8 m / s2 downwards. Determine:a) the velocity V and the height y of the ball above the ground as a function of time t b) the highest position the ball reaches on the ground and the corresponding value of time t c) the time in which the ball hits the ground and the corresponding velocity. d) draw the curves (v - t) and (y - t)arrow_forwardThe Skier starts from rest at point A. Determine the horizontal distance X traveled after he leaves the ramp and the landing speed. Neglect friction. The Skier starts from rest at point A. Determine the horizontal distance traveled after he leaves the ramp and the landing speed. Neglect friction. X=10.2 m, vc=24.2 ms X=7.81 m, vc=18.1 ms X=13.1 m, vc=24.9 ms X=8.96 m, vc=−21.2 msarrow_forwardRockfalls 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 a = 40°. Knowing that the coefficient of restitution between rock A and the incline is 0.2, determine the velocity of the rock after the impact.arrow_forward
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