What formula do you use??

Question

An 19.8 g rifle bullet traveling 249 m/s buries itself in a 3.50 kg pendulum hanging on a 2.78 m long string, which makes the pendulum swing upward in an arc. Determine the horizontal component of the pendulum's displacement.

What formula do you use on this type of problem and how do you set it up?

Answer 1

This is a conservation of energy/momentum problem.

mV = (m + M)v; where m and M are the masses of the bullet and pendulum, V = the bullet velocity before impact, and v = velocity of the bullet and pendulum after the bullet embeds in the pendulum. You have enough to solve for v, which you will need next.

KE = 1/2 (m+M)v^2; same variables as before. This is the kinetic energy imparted into the pendulum/bullet mass upon impact. As the pendulum swings upward and outward, it will convert the KE into PE (potential energy)...this is conservation of energy.

PE = (m + M)gh; where g = 9.81 m/sec^s and h can be calculated by setting KE = PE and solving for h = the height of the pendulum/bullet above its low point when the bullet first struck the pendulum

Now it's just a matter of trigonometry. h is the vertical direction the loaded pendulum swings, r = 2.78 m (the radius of the pendulum). You can solve for x, the horizontal displacement, by x = sqrt(h^2 + (r-h)^2). Draw out the pendulum at rest and then swung out and up. You will be able to see why one side of the right triangle I used is (r-h).

Watch out...if h>r, then the maximum horizontal displacement (x max) will have been reached and x will be less than x max.

Answer 2

good question