Estimate the force with which a karate master strikes a board if the hand's speed at time of impact is 4.78m/s, decreasing to 1.55m/s during a constant time of 0.00239 s with the board. The mass of coordinated hand and arm is 0.701 kg. Answer in units of N.

Estimate the shear stress if this force is exerted on a 1.31 cm thick pine board that is 6.35 cm wide. Answer in units of N/m^2

I figured this question out:

F = (mass of the arm x change in velocity)/time
So, ((0.701kg.)(4.78m/s-1.55m/s))/(0.00239s) = 947.376569
And shear stress is
F/Area = (947.376569N)/((0.0635m)(0.0131m))

To estimate the force with which the karate master strikes the board, we can use Newton's second law of motion. The formula is given by:

Force (F) = mass (m) x acceleration (a)

In this case, we are given the mass of the coordinated hand and arm as 0.701 kg.

Now let's find the acceleration. Since we have the initial and final speeds, we can calculate the acceleration using the formula:

Acceleration (a) = (final speed - initial speed) / time

Given:
Initial speed (v1) = 4.78 m/s
Final speed (v2) = 1.55 m/s
Time (t) = 0.00239 s

Substituting the values into the formula, we have:

Acceleration (a) = (1.55 m/s - 4.78 m/s) / 0.00239 s

Now we can calculate the acceleration.

Acceleration (a) = (-3.23 m/s) / 0.00239 s

Acceleration (a) ≈ -1352.3 m/s^2

Note: The negative sign indicates that the acceleration is in the opposite direction of the initial velocity.

Finally, substituting the values of mass and acceleration into the formula for force:

Force (F) = 0.701 kg x (-1352.3 m/s^2)

Calculating this, we get:

Force (F) ≈ -947.16 kg⋅m/s^2 or (-947.16 N)

Since force cannot be negative in this context, we take the absolute value of the force:

Force (F) ≈ 947.16 N

Therefore, the estimated force with which the karate master strikes the board is approximately 947.16 Newtons.

Now let's move on to estimating the shear stress exerted on the pine board.

Shear stress is calculated by dividing the force applied (F) by the area over which the force is distributed (A). The formula is given by:

Shear stress (σ) = Force (F) / Area (A)

Given:
Thickness of the pine board (t) = 1.31 cm
Width of the pine board (w) = 6.35 cm
Length of the pine board (l) is not provided.

To calculate the area (A) of the board, we multiply the thickness (t) by the width (w):

Area (A) = thickness (t) x width (w)

Converting the thickness and width to meters:

Thickness (t) = 1.31 cm = 0.0131 m
Width (w) = 6.35 cm = 0.0635 m

Area (A) = 0.0131 m x 0.0635 m

Now, substituting the value of force and area into the formula for shear stress:

Shear stress (σ) = 947.16 N / (0.0131 m x 0.0635 m)

Calculating this, we get:

Shear stress (σ) ≈ 1137641.11 N/m^2

Therefore, the estimated shear stress exerted on the pine board is approximately 1,137,641.11 Newtons per square meter (N/m^2).