Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

A uniform 1.8 m long rod with a mass of 1.20 kg is suspended vertically from a f

ID: 1378629 • Letter: A

Question

A uniform 1.8 m long rod with a mass of 1.20 kg is suspended vertically from a frictionless pin at its upper end. A 4 gram bullet with a speed of 260 m/s strikes the rod 1.3 m below the pivot point.

Determine how high the bottom of the rod swings above the datum if the bullet goes through the rod and leaves with a speed of 135 m/s.
(include units with answer)

Use COE for the swinging rod after the collision to find the change in height.

These are important values to calculate along the way. I can check them if need be

Hint #1:

Use COE for the swinging rod after the collision to find the change in height.

Explanation / Answer

moment of inertia of rod about pivot, I = M*L^2/3

= 1.2*1.8^2/3

= 1.296 kg.m^2

let w is the angular speed of rod after the collsion.

Apply consrvation of angular momentum

m*u*r = m*v*r + I*w

==> w = m*r*(u-v)/I

= 0.004*1.3*(260-135)/1.296

= 0.5 rad/s


let h is the height raise by the center of mass.
after the collsion apply energy conservation

M*g*h = 0.5*I*w^2


h = 0.5*I*w^2/(M*g)

= 0.5*1.296*0.5^2/(1.2*9.8)

= 0.0138 m or 1.38 cm <<<<<<-----Answer

Hire Me For All Your Tutoring Needs
Integrity-first tutoring: clear explanations, guidance, and feedback.
Drop an Email at
drjack9650@gmail.com
Chat Now And Get Quote