Transcript Physics 121
Physics 121 6. Work and Energy 6.1 Work 6.3 Kinetic Energy 6.4 Potential Energy 6.5 Conservative and Non-conservative forces 6.6 Mechanical Energy / Problem Solving 6.8 Conservation of Energy 6.9 Dissipative Forces / Problem Solving 6.10 Power Work Work = Force x Distance W=F.d Example 6.1 . . . Work for Slackers! You push a car with a force of 200 N over a distance of 3 m. How much work did you do? 200 N Solution 6.1 . . . Work for Slackers! W = F.d W = 200x3 W = 600 Nm W = 600 J Note: A Joule (J) is just another term for newton . meter (N m) Energy Energy is the capacity to do work Kinetic Energy Potential Energy (motion) (position) Kinetic Energy K.E. = 1/2 mv2 Example 6.2 . . . Kinetic Energy The K.E. of a car is 600 J and its mass is 1000 kg. What is its speed? Solution 6.2 . . . Kinetic Energy K.E. = 1/2 m v2 600 = 1/2(1000)(v2) v = 1.1 m/s Example 6.3 . . . Save your work! You lift a 2 kg book and put it on a shelf 3 meters high. (a) How much work did you do? (b) Was the work “lost”? Solution 6.3 . . . Save your work! (a) W = F.d W = mgh W = 2x10x3 W = 60 J (b) Work was stored as Potential Energy (hidden). So gravitational P.E. = mgh Example 6.4 . . . Downhill A 65 kg bobsled slides down a smooth (no friction) snow-laden hill. What is its speed at the bottom? 15 m 30 m Solution 6.4 . . . Downhill P.E. = K.E. mgh = 1/2 mv2 9,555 = (1/2)(65) v2 v = 17.1 m/s 15 m 30 m Example 6.5 . . . Sticky bobsled Suppose the speed of the bobsled was actually measured to be 14.8 m/s instead of 17.1 m/s (a) What could have caused that? (b) What was the work done by the bobsled against friction? Solution 6.5 . . . Sticky bobsled (a) Not all the P.E. was converted to K.E. because some work was lost (heat energy) in doing work against friction: P.E. = K.E. + Wf (b) mgh = 1/2 mv2 + Wf 9,555 = 1/2(65) (14.8)2 + Wf Wf = 2,436 J Stretching Springs Hooke’s Law: The amount of stretch is directly proportional to the force applied. F=kx Lab Experiment Slope = “k” F x Example 6.6 . . . Springy Spring The spring constant (k) of a spring is 20 N/m. If you hang a 50 g mass, how much will it stretch? Solution 6.6 . . . Springy Spring F=kx mg = kx (50 /1000)(9.8) = (20)(x) x = 2.5 cm Lab Experiment Example 6.7 . . . Body building How much work would you have to do to stretch a stiff spring 30 cm (k = 120 N/m)? “Solution” 6.7 . . . Body building W=F.d W = (kx)(x) W = kx2 W = (120)(0.3)2 W = 10.8 J X Correct Solution 6.7 . . . Body building W=F.d We must use the AVERAGE Force! W = (1/2)(kx)(x) W =1/2 kx2 W = (1/2)(120)(0.3)2 W = 5 .4 J P.E. of a Spring = 1/2 kx2 Example 6.8 . . . Lugging the Luggage What is the speed when the distance is 3 m? 40 N 10 kg Hawaii or Bust! 600 Solution 6.8 . . . Lugging the Luggage What is the speed when the distance is 3 m? F.d = 1/2 m v2 (40 cos 600)(3) = (1/2)(10)(v2) v = 3.5 m/s 40 N 10 kg Hawaii or Bust! Moral of the story W = (F)(d)(cos) 600 Conservative Forces If the work done against a force does not depend on the path taken then that force is called a conservative force. Examples are gravity and spring force. The total mechanical energy (P.E. + K.E.) will remain constant in this case. If the work done against a force depends on the path taken then that force is called a non-conservative force. Example is friction. The total mechanical energy (P.E. + K.E.) will not remain constant in this case. Vote Democrat . . . Just kidding! Example 6.9 . . . Playing with Power Power is the rate of doing work P=W/t A pump can lift at most 5 kg of water to a height of 4 m every minute. What is the power rating of this pump? Solution 6.9 . . . Playing with Power W = mgh W = (5)(10)(4) W = 200 J P=W/t P = 200 J / 60 s P = 3.3 J / s P = 3.3 W Note: Watt (W) is just another term for Joules / second (J / s) That’s all folks!