Question

a rifle with a barrel length of 60 cm fires a 12 g bullet with a horizontal speed of 400 m/s. the bullet strikes a block of wood and penetrates to a depth of 13 cm. you may need to review (page). for general problem - solving tips and strategies for this topic, you may want to view a video tutor solution of ready for takeoff. part a what resistive force (assumed to be constant) does the wood exert on the bullet? express your answer with the appropriate units. part b how long does it take the bullet to come to rest after entering the wood? express your answer with the appropriate units.

Explanation:

Step1: Find the acceleration of the bullet

Use the kinematic equation \(v^{2}=v_{0}^{2}+2ax\). The final velocity \(v = 0\), initial velocity \(v_{0}=400\ m/s\), and displacement \(x = 0.13\ m\).

$$0=(400)^{2}+2a(0.13)$$

$$2a(0.13)=-(400)^{2}$$

$$a=\frac{-(400)^{2}}{2\times0.13}$$

$$a=\frac{-160000}{0.26}\approx - 615384.62\ m/s^{2}$$

Step2: Calculate the resistive force

Use Newton's second law \(F = ma\). The mass of the bullet \(m=12\ g=0.012\ kg\)

$$F=(0.012\ kg)\times(- 615384.62\ m/s^{2})$$

$$F=-7384.62\ N$$

The magnitude of the resistive force is \(F = 7384.62\ N\)

Step3: Find the time taken for the bullet to stop

Use the kinematic equation \(v = v_{0}+at\)

$$0 = 400+( - 615384.62)t$$

$$t=\frac{-400}{- 615384.62}$$

$$t\approx6.5\times10^{-4}\ s$$

Answer:

Part A: \(f_{k}=7384.62\ N\)
Part B: \(t = 6.5\times10^{-4}\ s\)