Linear Impulse − Momentum Applications Chapter 9 KINE 3301 Biomechanics of Human Movement

The force shown below is applied to a 3 kg bowling ball with an initial horizontal velocity of −2 m/s. Compute the final velocity of the ball.

What was the impulse?

Integration of the force with respect to time (area under the force – time curve) can be used to obtain the velocity – time curve.

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 performer’s center of mass in the direction of the reaction force.

Relationship between Force & Acceleration The shape of an acceleration curve is the exactly the same as the force curve, only the units are different.

Vertical Impulse-Momentum Horizontal Impulse-Momentum Impulse-Momentum

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 ∆Vx = +.46 m/s Braking ≈ Propulsion ∆Vx = +.01 m/s Braking > Propulsion ∆Vx = −.24 m/s

Free Body Diagram for Vertical Impulse - Momentum

Use the average force F Ave = N to compute the vertical impulse and Vy at toe-off (t =.234 s).

Use the average force to compute braking impulse, propulsion impulse and Vx at t = 0.04, t = 0.4, and t = 0.7 s. Walking Forces

Use the average force F Ave = 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 (Vy i ) of −0.26 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. ∆t = 0.2 s, F Ave = 1449 N