Example 9 6 Karate blow Estimate the impulse

Example 9 -6: Karate blow Estimate the impulse p & the average force Favg, delivered by a karate blow that breaks a board a few cm thick. Assume the hand moves at roughly 10 m/s when it hits the board.

Example The advantage of bending your knees when landing! a) m = 70 kg, h =3. 0 m Just before he hits the ground Impulse: p = ? v = 7. 7 m/s By definition, F t = p = m(0 -v) First, we need to find v (just before landing). Use: K + U = 0 m(v 2 -0) + mg(0 - h) = 0 v=0 Gives v = 7. 7 m/s Impulse: p = -540 N s Opposite the person’s momentum Just after he hits the ground

• Advantage of bending knees when landing! Impulse: p = -540 N s, m = 70 kg h = 3. 0 m, F = ? b) Stiff legged: v = 7. 7 m/s to v = 0 in d = 1 cm (0. 01 m)! v = (½ )�(7. 7 + 0) = 3. 8 m/s Time: t = d/v = 2. 6 10 -3 s F = | p/ t| = 2. 1 105 N (Net force upward on the person) From the free body diagram, F = Fgrd - mg 2. 1 105 N Enough to fracture leg bone!!!

• Advantage of bending knees when landing! Impulse: p = -540 N s, m = 70 kg h = 3. 0 m, F = ? c) Knees bent: v = 7. 7 m/s to v = 0 in d = 50 cm (0. 5 m)! v = (½ )�(7. 7 + 0) = 3. 8 m/s Time: t = d/v = 0. 13 s F = | p/ t| = 4. 2 103 N (Net force upward on the person) From the free body diagram, F = Fgrd - mg 4. 9 103 N Leg bone does not break!!!

Example: Crash Test A car, m = 1500 kg, hits a wall. +x is to the right. Before the crash, v = -15 m/s. After the crash, v = 2. 6 m/s. The collision lasts Δt = 0. 15 s. Find: The impulse the car receives & the average force on the car. Assume: The force exerted by the wall is large v = - 15 m/s v = 2. 6 m/s compared to other forces on the car. Gravity & normal forces are perpendicular & don’t effect the horizontal momentum. p = mv = -2. 3 104 kg m/s, p = mv = 3. 9 103 kg m/s Impulse J = Δp = p – p = 2. 69 104 kg m/s (N s) Favg = (Δp/Δt) = 1. 76 105 N