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

Opposite the person’s momentum

Just before he hits the ground

Just after he hits the ground

The advantage of bending your knees when landing! a) m = 70 kg, h =3.0 m

Impulse: p = ? By definition, Ft = p = m(0-v)

First, we need to find v (just before landing). Use: K + U = 0

m(v2 -0) + mg(0 - h) = 0Gives v = 7.7 m/s

Impulse: p = -540 N s

v = 7.7 m/s

v = 0

• 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 (0.01m)!

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 (0.5m)!

v = (½ )(7.7 + 0) = 3.8 m/s

Time: t = d/v = 0.13s

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 TestA 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

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

v = - 15 m/s

v = 2.6 m/s