Question

A 15 g pellet is accelerated along the barrel of a rifle from rest to 133 m/s by a force of 222 N. a. Find the acceleration of the pellet. b. Find the length of the barrel. c. Find the time the pellet is in the barrel.

Answer 1

The acceleration of the pellet is 14,800 m/s². The length of the barrel is 1.127 m. The time the pellet is in the barrel is 0.009 sec.

Step-by-step explanation:

a. To find the acceleration, we can use Newton's second law, F = ma, where F is the force and m is the mass of the pellet. Rearranging the equation, we have a = F/m. Plugging in the values, we get a = 222 N / 0.015 kg = 14,800 m/s².

b. To find the length of the barrel, we can use the equation of motion, v² = u² + 2as, where v is the final velocity, u is the initial velocity (0 m/s since it starts from rest), a is the acceleration, and s is the distance. Rearranging the equation, we have s = (v² - u²) / (2a). Plugging in the values, we get s = (133²) / (2 * 14,800) = 1.127 m.

c. To find the time the pellet is in the barrel, we can use the equation of motion, v = u + at, where t is the time. Rearranging the equation, we have t = (v - u) / a. Plugging in the values, we get t = (133 - 0) / 14,800 = 0.009 sec.