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Lesson 2: Impulse Graphs! ! Impulse = Change in Momentum! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! The area under a force as a function of time graph equals impulse! ! ! ! ! ! ! You will be expected to find the area of:! ! Squares ! But never curved graphs! ! ! ! Triangles Negative Areas Trapezoids Example: ! ! Force as a function of time for a 1500 kg car! ! ! ! ! ! ! What is the impulse?! ! ! ! ! ! ! ! What is the change in speed?! ! ! ! ! ! ! ! ! Example: What is the change in momentum in the graph below?! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! Practice Problems ! Impulse (Graphing) ! ! 1. A child hits a ball with a force of 350 N. If the ball and bat are in contact for 0.12 s, what impulse does the ball receive? What is its change in momentum? (42 N⋅s, 42 kg m/s) 2. Given the below force-time graph for a 0.75 kg object that was accelerated from rest, calculate the velocity at 4.0 s. (16 m/s) ! ! ! ! ! ! ! ! ! ! ! ! 3. Given the below force-time graph for a 0.50 kg object that was initially travelling 10 m/s, calculate the velocity after 5.0 s. (5.0 x 101 m/s) ! ! ! 4. What is the mass and the weight of an object that has a velocity of 10.0 m/s and momentum of 2.0 x 102 kg·m/s? (2.0 x 102 N) 5. A 0.45 kg ball is moving east at a velocity of 11.0 m/s when it hits a wall. If the ball rebounds with a velocity of 10.0 m/s west, what was the impulse of the wall on the ball? (9.5 kg·m/s) 6. A 0.146 kg baseball pitched at 40 m/s is hit back toward the pitcher at a speed of 45 m/s. a) What is the impulse provided to the ball? (12 N s) b) The bat is in contact with the ball for 8.0 ms (0.008 s). What is the average net force that the bat exerts on the ball? (1.6 x 103 N) ! ! 7. From the graph below, (notice the x axis is in ms) a) What is the magnitude of the impulse provided to a 48 g tennis ball that is served due south? (2.3 Ns) b) What is the velocity of the ball when the racquet and ball separate? (47 m/s) 8. An object of mass m = 2.0kg experiences a force in Newtons according to the Force vs. time graph shown here. For the time interval shown below, what is the total change in momentum of the object? (35 kg m/s) 9. In the graph below, what value of Fmax gives an impulse of 7.1 Ns? (1.8 N) ! ! ! ! ! !
