Question

A 7.80-g bullet moving at 520 m/s strikes the hand of a superhero, causing the hand to move 5.90 cm in the direction of the bullet's velocity before stopping.

(a) Use work and energy considerations to find the average force that stops the bullet.
N

(b) Assuming the force is constant, determine how much time elapses between the moment the bullet strikes the hand and the moment it stops moving.
s

Answer 1

here,

mass of bullet , m = 7.8 g = 0.0078 kg

initial speed of bullet , u = 520 m/s

s = 5.9 cm = 0.059 m

a)

let the average force acting be F

using work energy theorm

work done = kientic energy lost

F * s = 0.5 * m * u^2

F * 0.059 = 0.5 * 0.0078 * 520^2

solving for F

F = 1.79 * 10^4 N

b)

initial speed , u = 520 m/s

accelration , a = F/m = 2.29 * 10^6 m/s^2

let the time taken to stop the bullet be t

v = u + a * t

0 = 520 - 2.29 * 10^6 * t

solving for t

t = 2.27 * 10^-4 s