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KINE 3301 Biomechanics of Human Movement Linear Impulse β Momentum Applications Chapter 9 The force shown below is applied to a 3 kg bowling ball with an initial horizontal velocity of β2 m/s. Compute the final velocity of the ball. πΉ βπ‘ = πππ β πππ (31.65 N) .315π = (3 ππ)ππ β ππ = +1.33 π/π What was the impulse? π½ = πΉβπ‘ π½ = 31.65 π (.315π ) π½ = 9.97 π β π ππ β π (3 ππ)(β2 ) π Integration of the force with respect to time (area under the force β time curve) can be used to obtain the velocity β time curve. π‘1 πΉ ππ‘ = πππ β πππ π‘0 The two force curves shown below are applied to a 0.5 kg ball with an initial horizontal velocity of 0 m/s. Compute the final velocity of the ball after each force is applied. Draw an estimated velocity-time curve that each force-time curve would produce. Reaction Force Accelerates the CM The force applied accelerates the ground in the direction of the force. The reaction force accelerates the performerβs center of mass in the direction of the reaction force. Relationship between Force & Acceleration πΉ = ππ The shape of an acceleration curve is the exactly the same as the force curve, only the units are different. πΉ π= π Impulse-Momentum πΉ βπ‘ = πππ β πππ π‘1 πΉ ππ‘ = πππ β πππ π‘0 Horizontal Impulse-Momentum πΉπ₯ βπ‘ = πππ₯π β πππ₯π π‘1 πΉπ₯ ππ‘ = πππ₯π β πππ₯π π‘0 Vertical Impulse-Momentum πΉπ¦ βπ‘ + ππ βπ‘ = πππ¦π β πππ¦π π‘1 (πΉπ¦ + ππ) ππ‘ = πππ¦π β πππ¦π π‘0 Use the average force to compute braking impulse, propulsion impulse and Vx at midstance (t = .112 s) and toe-off (t = .234 s). Braking and Propulsion Braking < Propulsion βVx = +.46 m/s Braking β Propulsion βVx = +.01 m/s Braking > Propulsion βVx = β.24 m/s Free Body Diagram for Vertical Impulse - Momentum πΉπ¦ βπ‘ + ππ βπ‘ = πππ¦π β πππ¦π π‘1 (πΉπ¦ + ππ) ππ‘ = πππ¦π β πππ¦π π‘0 Use the average force F Ave = 1007.075 N to compute the vertical impulse and Vy at toe-off (t = .234 s). Walking Forces Use the average force to compute braking impulse, propulsion impulse and Vx at t = 0.04, t = 0.4, and t = 0.7 s. Use the average force F Ave = 621.88 N to compute the vertical impulse and Vy at toe-off (t = 0.76 s). Vertical Force & Acceleration for a Vertical Jump Use the average force at each time point to compute the vertical velocity. t = 0.2 s, F Ave = 440 N t = 0.4 s, F Ave = 632 N t = 0.6 s, F Ave = 904 N Use the average force at each time point to compute the vertical velocity. t = 0.2 s, F Ave = 440 N Use the average force at each time point to compute the vertical velocity. t = 0.4 s, F Ave = 632 N Use the average force at each time point to compute the vertical velocity. t = 0.6 s, F Ave = 904 N At t = 0.4 sec the jumper has a vertical velocity (Vyi) of β0.26 m/s. Use the average force from t = .4 to t = .6 to compute the impulse and the final vertical velocity at t = 0.6 sec. βt = 0.2 s, F Ave = 1449 N