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Type: Double Date: ____________ Objective: Work and Energy Conservation I Work and Energy Conservation II Homework: Assignment (1-27) Do PROBS # (38, 55) Ch. 6 + PROBS # (8) Ch. 10 AP Physics “B” Mr. Mirro Date: Work and Energy Conservation I ________ Ex 1: A 755 N diver drops from a platform 10.0 m above the water surface, as shown. [Serway5.4] a. Use conservation of mechanical energy to find his speed 5.0 m above the surface of the water. h = 5m b. Find the speed of the diver just before he strikes the water. Ex 2: The spring constant for a spring in a dart gun is 1400 N/m. When the gun is cocked, the spring is compressed by 0.075 m. If the gun is shot vertically upward, neglecting air resistance [Cutnell4EP50mod] a. What is the speed of a 2.4 x 10-2 kg dart when it leaves the gun ? b. Determine the maximum height of the dart. Ex 3: A sled and its rider together weigh 800 N. They (the sled-rider system) move down a frictionless hill through a vertical distance of 10 m as shown. Use conservation of mechanical energy to find the speed of the sled-rider system at the bottom of the hill, assuming the rider pushes off with an initial speed of 5.0 m/s. [Serway5.5] vi = 5 m/s 10 m θ 0m Ex 4: A 1 kg sphere (M), suspended by a string from point (P), is lifted to a height (h). The sphere is released and passes through the lowest point in its swing at a speed (v) of 10 m/s. [General] a. Determine the height from which the sphere was released. P M h M Δx b. If the constant of elasticity for the spring is 1600 N/m, how much will the spring compress upon impact ? AP Physics “B” Mr. Mirro Date: ________ Work and Energy Conservation II Ex 1: A horizontal spring having a spring constant k = 360 N/m is lying on a frictionless surface. One end of the spring is attached to a wall, and the other end is connected to a mass of m = 2.8 kg. The spring is then compressed by 0.065 m and released from rest. [Cutnell4EP48] a. Using conservation of energy, determine the expression for the speed at any position in terms of k, x and m only. xf = .048 m stretch xi = .065 m Eq compress b. What is the speed of the object at the instant when the spring is stretched by 0.048 m relative to its unstrained length ? c. Compute the maximum speed, veq, of the mass at the instant it crosses the equilibrium point. Ex 2: A rifle fires a 2.2 x 10-2 kg pellet straight upward, because the pellet rests on a compressed spring that is released when the trigger is pulled. The spring has a negligible mass and is compressed by 9.5 x 10-2 m from its unstrained length. The pellet rises to a maximum height of 7.0 m above its position on the compressed spring. Ignoring air resistance, determine the spring constant. [Cutnell4EP52] Ex 3: Assuming the height of the first hill in a roller coaster is h1 = 50 m. A roller coaster proceeds to gain speed as it goes through several dips. At the end of the last dip there is an elastic protection device (EPD) that has an elastic constant of 20000 N/m. If the roller coaster car has mass m = 10 kg and the car essentially starts from rest at the top of the first hill, determine the following information about the motion of the roller coaster car: [Cutnell6.7sim] A B 50 m C 60 m E 20 m D vf (comp) =0 a. Find the potential energy due to gravity, translational kinetic energy, elastic potential energy and total mechanical energy for the situation depicted above. NO WORK necessary for this section ! Position PEg [J] KE [J] PES [J] Total “ME” [J] A B C D E b. What is the velocity of the car at position D ? c. How much does the “EPD” compress as the car is brought momentarily to rest ?