In the figure, a 0.01-kg bullet travelling at a speed of 600 m s-1 penetrates a 10-cm woodenblock.If the bullet emerges from the block at 450 m s-1, what is the average resistance of the woodenblock? Assume the air resistance is negligible

To solve this problem, we need to use the principle of conservation of momentum and Newton's second law of motion.

Step 1: Calculate the initial momentum of the bullet before it enters the block. The initial momentum (P_initial) is given by the mass of the bullet (m) times its initial velocity (v_initial).

P_initial = m * v_initial P_initial = 0.01 kg * 600 m/s = 6 kg*m/s

Step 2: Calculate the final momentum of the bullet after it exits the block. The final momentum (P_final) is given by the mass of the bullet times its final velocity (v_final).

P_final = m * v_final P_final = 0.01 kg * 450 m/s = 4.5 kg*m/s

Step 3: Calculate the change in momentum (ΔP). The change in momentum is given by the final momentum minus the initial momentum.

ΔP = P_final - P_initial ΔP = 4.5 kgm/s - 6 kgm/s = -1.5 kg*m/s

Step 4: Calculate the time taken for the bullet to pass through the block. The time (t) is given by the distance (d) divided by the average velocity (v_avg). The average velocity is the initial velocity plus the final velocity divided by 2.

v_avg = (v_initial + v_final) / 2 v_avg = (600 m/s + 450 m/s) / 2 = 525 m/s

t = d / v_avg t = 0.1 m / 525 m/s = 0.00019 s

Step 5: Calculate the average force (F_avg) exerted by the block on the bullet. The average force is given by the change in momentum divided by the time.

F_avg = ΔP / t F_avg = -1.5 kg*m/s / 0.00019 s = -7894.74 N

The negative sign indicates that the force is acting in the opposite direction to the motion of the bullet, which is expected as it is a resistive force.

So, the average resistance of the wooden block is 7894.74 N.