Presentation on theme: "Objectives Identify several forms of energy."— Presentation transcript:
1Objectives Identify several forms of energy. Calculate kinetic energy for an object.Apply the work-kinetic energy theorem to solve problems.Distinguish between kinetic and potential energy.Classify different types of potential energy.Calculate the potential energy associated with an object’s position.
2Kinetic energy Kinetic energy is a scalar quantity. Kinetic energy is the energy of motion.An object which has motion - whether it be vertical or horizontal motion - has kinetic energy.The equation for kinetic energy is:Where KE is kinetic energy, in joulesv is the speed of the object, in m/sm is the mass of the object, in kgKinetic energy is a scalar quantity.KE = ½ mv2
3Questions Which of the following has kinetic energy? a falling sky divera parked cara shark chasing a fisha calculator sitting on a deskIf a bowling ball and a volleyball are traveling at the same speed, do they have the same kinetic energy?Car A and car B are identical and are traveling at the same speed. Car A is going north while car B is going east. Which car has greater kinetic energy?
4Kinetic Energy depends on mass and speed KE = ½ m v 2The equation shows that . . .. . . the more kinetic energy it has.Speed has more effect on Kinetic energy than mass.the more mass a body hasor the faster it’s moving
5KE is directly proportional to m, so doubling the mass doubles kinetic energy, and tripling the mass makes it three times greater.KE is proportional to v 2, so doubling the speed quadruples kinetic energy, and tripling the speed makes it nine times greater.Kinetic energyKinetic energyspeedmass
6Sample Problem 5BA 7.00 kg bowling ball moves at 3.00 m/s. How much kinetic energy does the bowling ball heave? How fast must a 2.45 g table-tennis ball move in order to have the same kinetic energy as the bowling ball? Is this speed reasonable for a table-tennis ball?
7Example 1An object moving at a constant speed of 25 meters per second possesses 450 joules of kinetic energy. What is the object's mass?Known:KE = 450 Jv = 25 m/sUnknown:m = ? kgSolve:KE = ½ mv2450 J = ½ (m)(25 m/s)2m = 1.4 kg
8example 2A cart of mass m traveling at a speed v has kinetic energy KE. If the mass of the cart is doubled and its speed is halved, the kinetic energy of the cart will behalf as greattwice as greatone-fourth as greatfour times as great
9Example 3Which graph best represents the relationship between the kinetic energy, KE, and the velocity of an object accelerating in a straight line?abcd
10Class work Page 174 - #1-5 170 m/s 38.8 m/s The bullet with the greater mass; 2 to 12.4 J, 9.6 J; the bullet with the greater speed; 1 to 41600 kg
11Work-kinetic energy theorem The net work done on an object is equal to the change in the kinetic energy.
12Practice Problem #1A 1000-kg car traveling with a speed of 25 m/s skids to a stop. The car experiences an 8000 N force of friction. Determine the stopping distance of the car. Wnet = ∆KE = KEf - KEi(-8000N) • d = Jd = 39.1 m
13Practice Problem #2At the end of the Shock Wave roller coaster ride, the 6000-kg train of cars (includes passengers) is slowed from a speed of 20 m/s to a speed of 5 m/s over a distance of 20 meters. Determine the braking force required to slow the train of cars by this amount.Wnet = ∆KE = KEf - KEi
14Stopping distance is dependent upon the square of the velocity. The above problems have one thing in common: there is a force which does work over a distance in order to remove mechanical energy from an object.The force acts opposite the object's motion and thus does negative work which results in a loss of the object's total amount of mechanical energy. In each situation, the work is related to the kinetic energy change.TMEi + Wext = TMEfKEi + Wext = 0 J½ •m•vi2 + F•d•cos(180o) = 0 JF•d = ½ •m•vi2d ~ vi2 Stopping distance is dependent upon the square of the velocity.
15Stopping distance and initial velocity Wnet = ∆KEWnet = 0 - ½ •m•vi2Ff•d = - ½ •m•vi2Ff = μFnorm = μmg- μmg•d = - ½ mvi2d = vi2 / 2μgd ~ vi2
17practice (m/s) Stopping Distance (m) 0 m/s 5 m/s 4 m 10 m/s 15 m/s 5 m/s4 m10 m/s15 m/s20 m/s25 m/s4 m x 22 = 16 m4 m x 32 = 36 m4 m x 42 = 64 m4 m x 52 = 100 m
18Example 5COn a frozen pond, a person kicks a 10.0 kg sled, giving it an initial speed of 2.2 m/s. How far does the sled move if the coefficient of kinetic friction between and sled and the ice is 0.10?
19Class work Page 176 practice 5C: #1-5 7.8 m 21 m 5.1 m 300 N a.-190 J; b J; c. 750 J; d. 280 J; e. 7.6 m/s
20Potential energyAn object can store energy as the result of its position. Potential energy is the stored energy of position possessed by an object.Two form:GravitationalElastic
21Gravitational potential energy Gravitational potential energy is the energy stored in an object as the result of its vertical position (height)The energy is stored as the result of the gravitational attraction of the Earth for the object..height, in metersGravitational attraction between Earth and the object:m: mass, in kilogramsg: acceleration due to gravity = 9.81 m/s2
22GPE and gravityWhen an object falls, gravity does positive work. Object loses GPE.When an object is raised, gravity does negative work. Object gains GPE.
23Change in GPE only depends on change in height, not path As long as the object starts and ends at the same height, the object has the same change in GPE because gravity does the same amount of work regardless of which path is taken.
24exampleThe diagram shows points A, B, and C at or near Earth’s surface. As a mass is moved from A to B, 100. joules of work are done against gravity. What is the amount of work done against gravity as an identical mass is moved from A to C?100 JAs long as the object starts and ends at the same height, the object has the same change in GPE because gravity does the same amount of work regardless of which path is taken.
25Gravitational Potential Energy is relative: To determine the gravitational potential energy of an object, a zero height position must first be assigned. Typically, the ground is considered to be a position of zero height.But, it doesn’t have to be:It could be relative to the height above the lab table.It could be relative to the bottom of a mountainIt could be the lowest position on a roller coaster
26Unit of energy The unit of energy is the same as work: Joules 1 joule = 1 (kg)∙(m/s2)∙(m) = 1 Newton ∙ meter1 joule = 1 (kg)∙(m2/s2)Work and energy has the same unit
27exampleHow much potential energy is gained by an object with a mass of 2.00 kg that is lifted from the floor to the top of 0.92 m high table?Known:m = 2.00 kgh = 0.92 mg = 9.81 m/s2Solve:∆PE = mg∆h∆PE = (2.00 kg)(9.81m/s2)(0.92 m) = 18 Junknown:PE = ? J
28The graph of gravitational potential energy vs The graph of gravitational potential energy vs. vertical height for an object near Earth's surface gives the weight of the object.The weight of the object is the slope of the line.Weight = 25 J/1.0 m = 25 Nm = weight / g = 2.5 kg
29Springs are a special instance of a device that can store elastic potential energy due to either compression or stretching.A force is required to compress or stretch a spring; the more compression/stretch there is, the more force that is required to compress it further.For certain springs, the amount of force is directly proportional to the amount of stretch or compression (x); the constant of proportionality is known as the spring constant (k).
30Spring force = spring constant x displacement Hooke’s LawF = kxSpring force = spring constant x displacementF in the force needed to displace (by stretching or compressing) a spring x meters from the equilibrium (relaxed) position. The SI unit of F is Newton.k is spring constant. It is a measure of stiffness of the spring. The greater value of k means a stiffer spring because more force is needed to stretch or compress it that spring. The SI units of k are N/m.x the distance difference between the length of stretched/compressed spring and its relaxed (equilibrium) spring.
32F = kxSpring force is directly proportional to the elongation of the spring (displacement)elongationforceThe slope represents spring constant: k = F / x
33caution Sometimes, we might see a graph such as this: elongation force The slope represents the inverse of spring constant:Slope = 1/k = x / F
34exampleGiven the following data table and corresponding graph, calculate the spring constant of this spring.
35exampleA 20.-newton weight is attached to a spring, causing it to stretch, as shown in the diagram. What is the spring constant of this spring?
36exampleThe graph below shows elongation as a function of the applied force for two springs, A and B. Compared to the spring constant for spring A, the spring constant for spring B issmallerlargerthe same
37Example 12AIf a mass of 0.55 kg attached to a vertical spring stretches the spring 2.0 cm from its original equilibrium position, what is the spring constant?
38Class work Page 441, Practice 12A #1-4 a. 15 N/m; b. less stiff
39Lab 14 – Hooke’s Law (1)Purpose: To determine the spring constant of a given spring.Material: spring, masses, meter stick.Procedure: Hook different masses on the spring, record the force Fs (mg) and corresponding elongation x. Plot the graph of Force vs. elongationData section: should contain colomns: force applied, elongation.Data measured directly from the experiment. The units of measurements in a data table should be specified in column heading only.Data analysis: Graph force vs. elongation on graph paper, answer following questions:What does the slope mean in Force vs. elongation graph?Determine the spring constant
40Force (N)Elongation (m)Force vs. elongationForce (N)Elongation (m)
41Elastic potential energy Elastic potential energy is the energy stored in elastic materials as the result of their stretching or compressing.Elastic potential energy can be stored inRubber bandsBungee coresSpringstrampolines
42Elastic potential energy in a spring Elastic potential energy is the Work done on the spring.k: spring constantx: amount of compression or extension relative to equilibrium position
43Elastic potential energy is directly proportional to x2 elongation
44Example 1 PE = ½ kx2 15 J = ½ k (0.50 m)2 k = 120 N/m As shown in the diagram, a 0.50-meter-long spring is stretched from its equilibrium position to a length of 1.00 meter by a weight. If 15 joules of energy are stored in the stretched spring, what is the value of the spring constant?PE = ½ kx215 J = ½ k (0.50 m)2k = 120 N/m
45Example 2 PEs = ½ kx2 PEs = ½ k(0.20 m)2 PEs = (0.020 k) J The unstretched spring in the diagram has a length of 0.40 meter and a spring constant k. A weight is hung from the spring, causing it to stretch to a length of 0.60 meter. In terms of k, how many joules of elastic potential energy are stored in this stretched spring?PEs = ½ kx2PEs = ½ k(0.20 m)2PEs = (0.020 k) J
46Example 3Determine the potential energy stored in the spring with a spring constant of 25.0 N/m when a force of 2.50 N is applied to it.Solve:PEs = ½ k∙x2To find x, use Fs = kx,(2.50 N) = (25.0 N/m)(x)x = mPEs = ½ (25.0 N/m)(0.100 m)2PEs = JGiven:Fs = 2.50 Nk = 25.0 N/mUnknown:PEs = ? J
47Example 4A 10.-newton force is required to hold a stretched spring 0.20 meter from its rest position. What is the potential energy stored in the stretched spring?Given:F = 10. Nx = 0.20 mUnknown: PEs = ? JPEs = Favg∙xPEs = (½ F)∙xPEs = ½ (10. N)(.20 m)PEs = 1.0 J
48Sample Problem 5DA 70.0 kg stuntman is attached to a bungee cord with an unstretched length of 15.0 m. He jumps off a bridge spanning a river from a height of 50.0 m. When he finally stops, the cord has a stretched length of 44.0 m. Treat the stuntman as a point mass, and disregard the weight of the bungee cord. Assuming the spring constant of the bungee cord is 71.8 N/m, what is the total potential energy relative to the water when the man stops falling?
49Class work Page 180 – practice 5D #1-3 3.3 J 0.031 J a. 785 J; b. 105 J; c J