Question

A 9.9 g bullet is accelerated in a rifle barrel 101 cm long to a speeen of 933 m/s. Use the work-energy theorem to find the average force exerted on the bullet while it is being accelerated. Answer in units of N

Answer 1

Task:

A 9.9 g bullet is accelerated in a rifle barrel 101 cm long to a speed of 933 m/s. Use the work-energy theorem to find the average force exerted on the bullet while it is being accelerated. Answer in units of N

Solution:

$$m = 0.0099 \, kg, \quad v_1 = 933 \, \frac{m}{s}, \quad v_0 = 0 \, \frac{m}{s}, \quad s = 1.01 \, m$$

Work-energy theorem in conservative system:

$$A_{total} = \Delta(E_k) = \Delta\left(\frac{m v^2}{2}\right) = \frac{m v_1^2}{2} - \frac{m v_0^2}{2} = \frac{m v_1^2}{2}$$ $$A_{total} = F_{net} \cdot s$$ $$F_{net} = \frac{m v_1^2}{2s} = \frac{0.0099 \, kg \cdot 933^2 \, \frac{m^2}{s^2}}{2 \cdot 1.01 \, m} \approx 4266 \, N$$

Answer:

$$F_{net} \approx 4266 \, N$$