جامعة الفيزياء: العمل المبذول بواسطة الربيع PDF

Work Done by a Spring force constant or the spring constant Fx = - kx This force law for springs is known as Hooke’s law. The value of k is a measure of the stiffness of the spring. Stiff springs have large k values, and soft springs have small k values. As can be see...

Work Done by a Spring force constant or the spring constant Fx = - kx This force law for springs is known as Hooke’s law. The value of k is a measure of the stiffness of the spring. Stiff springs have large k values, and soft springs have small k values. As can be seen from Equation, the units of k are N/m The negative sign in Equation signifies that the force exerted by the spring is always directed opposite to the displacement from equilibrium 1 Because the spring force always acts toward the equilibrium position (x = 0), it is sometimes called a restoring force. Suppose the block has been pushed to the left to a position -xmax and is then released. Let us identify the block as our system and calculate the work Ws done by the spring force on the block as the block moves from xi =-xmax to xf = 0. 2 The work done by the spring force is positive because the force is in the same direction as the displacement of the block (both are to the right) Because the block arrives at x = 0 with some speed, it will continue moving, until it reaches a position xmax. xi = 0 to xf = xmax, Ws =-0.5kx2max Therefore, the net work done by the spring force as the block moves from xi =-xmax to xf = xmax is zero. 3  ‫يتم تحميل السهام في لعبة مسدس السهام المحملة بنابض عن طريق دفع الزنبرك على مسافة ‪d‬‬ ‫للتحميل التالي‪ ،‬يتم ضغط الزنبرك مسافة ‪.2d‬ما قيمة الشغل الالزم لتحميل السهم الثاني من البندقية‬ ‫مقارنة باألول؟ (أ) أربعة مرات (مرتين (ج) نفس الشيء (د) نصف (هـ) ربع‪.‬‬ ‫‪4‬‬ Example: A 6.0-kg block initially at rest is pulled to the right along a horizontal, frictionless surface by a constant horizontal force of 12 N. Find the speed of the block after it has moved 3.0 m. Using the work–kinetic energy theorem and noting that the initial kinetic energy is zero, we obtain 5 7.8 Power average power = instantaneous power where dE/dt is the rate at which energy is crossing the boundary of the system by a given transfer mechanism. 6 Note that a kilowatt-hour is a unit of energy, not power 7 Quick Quiz 7.12 An older model car accelerates from rest to speed v in 10seconds. A newer, more powerful sports car accelerates from rest to 2v in the same time period. What is the ratio of the power of the newer car to that of the older car? (a) 0.25 (b) 0.5 (c) 1 (d) 2 (e) 4 Example 7.12 Power Delivered by an Elevator Motor An elevator car has a mass of 1600kg and is carrying passengers having a combined mass of 200kg. A constant friction force of 4000 N retards its motion upward, as shown in Figure (A)What power delivered by the motor is required to lift the elevator car at a constant speed of 3m/s? 8 Solution: The motor must supply the force of magnitude T that pulls the elevator car upward. The problem states that the speed is constant, which provides the hint that a=0. Therefore we know from Newton’s second law that From Newton’s second law we obtain where Mis the total mass of the system (car plus passengers), equal to 1 800kg. Therefore, 9 (B)What power must the motor deliver at the instant the speed of the elevator is v if the motor is designed to provide the elevator car with an upward acceleration of 1 m/s2? 10 11 Larger than A