### Educational Content#### Question 15**BIO** Researchers studying the possible effects of "heading" a soccer ball—hitting it with the head—use a force plate to measure the interaction force between a ball and a hard surface. Figure P8.15 shows smoothed data of the force when a 430 g soccer ball is fired horizontally at the force plate with a speed of 16 m/s. With what speed does the ball rebound from the plate?#### Figure P8.15 - Explanation The graph presents the force \( F_x \) on the vertical axis, measured in newtons (N), plotted against time \( t \) on the horizontal axis, measured in milliseconds (ms). The data points form a triangular shape. - **Force Values:** The graph starts at \( F_x = 0 \) N at \( t = 0 \) ms, rises linearly to a peak force of 3000 N at \( t = 4 \) ms, and then decreases linearly back to 0 N at \( t = 8 \) ms.This indicates that the force increases to its maximum over the first 4 milliseconds and then decreases to zero over the next 4 milliseconds.

Mass of object is Initial speed is A force vs time graph is given for the motion of object.Note:Find:The final speed of object after rebounding.The term "impulse" is used to describe how much force it takes for an object's momentum to change over time. It is given asHere represents impulse, represents change in momentum, represents force and represents time.Thus, the area enclosed by force vs time graph gives the change in momentum.The graph is given asThe area enclosed by force vs graph can be calculated asThe area of can be calculated asThe area of can be calculated asThus, the change in momentum isMomentum measures the inertia of a moving body. It is given by the product of mass of body and velocity of that body. It is a vector quantity and its direction is the same as that of body's velocity. The initial momentum of object is given asHere represents initial momentum, represents object's mass and represents initial velocity.Similarly, the final momentum of object is given asHere represents final momentum, represents object's mass and represents the final velocity.After colliding with the force plate the object rebounds which means the initial and final velocities are in opposite directions. Consider the initial velocity is negative and final velocity as positive so the momentum can be written as and The change in momentum can be written asInsert the values of change in momentum, mass and initial speed of object into the equation above.The final speed of object after rebounding is

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Researchers studying the possible effects of "heading" a soccer ball- hitting it with the head- use a force plate to mea- sure the interaction force between a ball and a hard surface. Figure P8.15 shows smoothed data of the force when a 430 g soccer ball is fired hori- Fx (N) 3000+ 2000- 1000- 0- 0 2 FIGURE P8.15 4 6 8 t (ms) zontally at the force plate with a speed of 16 m/s. With what speed does the ball rebound from the plate?

Researchers studying the possible effects of "heading" a soccer ball- hitting it with the head- use a force plate to mea- sure the interaction force between a ball and a hard surface. Figure P8.15 shows smoothed data of the force when a 430 g soccer ball is fired hori- Fx (N) 3000+ 2000- 1000- 0- 0 2 FIGURE P8.15 4 6 8 t (ms) zontally at the force plate with a speed of 16 m/s. With what speed does the ball rebound from the plate?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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