LECTURE 15 WORK & KINETIC ENERGY. Instructor: Kazumi Tolich

Transcription

1 LECTURE 15 WORK & KINETIC ENERGY Instructor: Kazumi Tolich

2 Lecture 15 2 Reading chapter 7-1 to 7-2 Work done by a constant force Energy Kinetic Energy Work-Energy Theorem

3 Systems and environments 3 A system is a small portion of the universe. A valid system may be a single object or particle. be a collection of objects or particles. be a region of space. vary with time in size and shape. A system boundary is an imaginary surface that divides the universe into the system and the environment surrounding the system.

4 Work 4 Work, W, is the amount of energy transferred by a force acting through a distance. In order to accomplish work on an object there must be a force exerted on the object, and the point of application of the force must move in the direction of the force. If the object does not move, no work is done on it. The SI unit of work, J (joule), is N m, the unit of force times the unit of distance.

5 Work done by a constant force 5 Suppose a constant force displaces a box by d. If the force is in the same direction as d, the work done by the force on the box is W = Fd Work done by a constant force The work done by this force on the box given above does not change even if there are other forces acting on the box.

6 Work done by a constant force: 2 6 Suppose a constant force displaces a box by d, and the angle between F and d is θ. The work done by the force on the box is W = Fd cosθ Work done by a constant force Work is the component of force in the direction of displacement times the magnitude of the displacement.! d

7 Work as an energy transfer 7 If a force, external to a system, displaces the system in the same direction as that of the force, work done on a system is positive, and energy is transferred to the system. If a force, external to a system, displaces the system in the opposite direction from that of the force, work done on the system is negative, and energy is transferred from the system.

8 Work done by a constant force, graphically 8 Work is the area under the curve.

9 Clicker question: 1

10 Example: 1 10 Water skiers often ride to one side of the center line of a boat as shown. In this case, the ski boat is traveling at v = 15 m/s and the tension in the rope is T = 75 N. If the tension does W = 3500 J of work on the skier in d = 50.0 m, what is the angle θ between the tow rope and the center line of the boat?

11 Net work 11 When more than one force acts on an object, the total work is given by the sum of the work done by each force. W total = W 1 + W 2 + W = Equivalently, the total work can be also calculated by W total = ( F total cosθ)d i where θ is the angle between the net force, F total, and the displacement, d. W i

12 12 Clicker question: 2

13 Example: 2 13 Three forces are applied to a greased trunk that moves leftward by 3.00 m over a frictionless floor. The forces magnitudes are F 1 = 5.00 N, F 2 = 9.00 N, and F 3 = 3.00 N. During the displacement, what is the net work done on the trunk by the three forces? F 2 θ = 60.0 F 1 F 3

14 Energy 14 Energy of a system is a measure of its ability to do work. Different types of energies based on different conditions or states Kinetic Energy: associated with motion Potential Energy: associated with configuration Thermal Energy: is associated with random motion of particles etc Energy is a scalar quantity. The SI unit for energy is joule (J).

15 Kinetic energy 15 Kinetic energy (K) is associated with the state of motion of an object and is given by K = 1 2 mv2 The faster the object moves, the more kinetic energy it has. Kinetic energy is zero when the object is stationary, and never negative.

16 Work-energy theorem 16 Work-energy theorem states that the change in the kinetic energy of an object is equal to the total work done on the object, or W total on = ΔK = K f K i = 1 mv 2 2 f 1 mv 2 i2 For example, to stop a moving block, some force needs to be applied over some distance. When W total on is positive the kinetic energy increases. When W total on is negative the kinetic energy decreases.

17 17 Clicker question: 3 & 4

18 Example: 3 18 A pine cone with a mass m = 0.21 kg falls h = 14 m to the ground, where it lands with a speed of v f = 13 m/s. a) What was the kinetic energy of the pine cone just before it landed? b) With what speed would the pine cone have landed if there had been no air resistance? c) Did the air resistance do positive work, negative work, or zero work on the pine cone?

19 Example: 4 19 A car with a mass of m = 1300 kg, coasts on a horizontal road with a speed of v i = 18 m/s. After crossing an unpaved, sandy stretch of road, d = 30.0 m long, its speed decreases to v f = 15 m/s. a) What is the net work done on the car? b) Find the magnitude of the average net force on the car in the sandy section. c) If the sandy portion of the road had been only d = 15.0 m long, what is the final speed in this case? Assume the average net force acts on the car.

20 Example: 5 20 The U.S. National Highway Traffic Safety Administration lists the minimum braking distance for a car traveling at 40.0 mi/h to be 101 ft. If the braking force is the same at all speeds, what is the minimum braking distance for a car traveling at 65.0 mi/h?