How Much Kinetic Energy is Lost in a Bullet-Block Collision?

AI Thread Summary
In the bullet-block collision problem, a bullet embeds itself in a wooden block on a frictionless surface, raising questions about kinetic energy loss. The initial momentum is conserved, leading to the equation for final velocity after the collision. The initial kinetic energy is calculated using KE = 1/2 m v^2, while the final kinetic energy is derived from the combined mass of the bullet and block. The fraction of kinetic energy lost is determined to be M/(M+m), highlighting the importance of understanding both linear and angular momentum in such collisions. The mass of the rod is deemed irrelevant to the solution.
roeb
Messages
98
Reaction score
1

Homework Statement



A wooden block of mass M resting on a frictionless horizontal surface is attached to a rigid rod of length l and of negligible mass. The rod is pivoted at the other end. A bullet of mass m traveling parallel to the horizontal surface and perpendicular to the rod with speed v hits the block and becomes embedded in it.

What fraction of the original kinetic energy is list in the collision?

Homework Equations



KE = 1/2 m v^2
L = cross(r,p)

The Attempt at a Solution



The only way I can think of doing this problem is using linear momentum conservation.
Say if pi = m*v, pf = (m+M)v'
v' = v * m / (M+m)

final / initial Kinetic Energy = m / (M+m)

Unfortunately, the answer is M/(M+m).

I believe that I should be using conservation of angular momentum. According to part a of this problem (not stated) the angular momentum of the bullet+block = mvl.

If I were to use cons. of angular momentum, I don't really know to formulate it.
Initial Li = 0
Final Lf = mvl

Does anyone have any hints?
 
Physics news on Phys.org
fraction lost = (init - final)/init
=1 - m/(m+M)
=M/(m+M)

Read the question!

The rod is an irrelevance, since it's massless.
If it wasn't, you would indeed conserve angular momentum
to solve it.
 
Last edited:
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Thread 'Egg Drop Challenge! Need ideas for winning designs'

I was thinking using 2 purple mattress samples, and taping them together, I do want other ideas though, the main guidelines are; Must have a volume LESS than 1600 cubic centimeters, and CAN'T exceed 25 cm in ANY direction. Must be LESS than 1 kg. NO parachutes. NO glue or Tape can touch the egg. MUST be able to take egg out in less than 1 minute. Grade A large eggs will be used.
View full post »

Similar threads

A bullet collides perfectly elastically with one end of a rod
Replies
21
Views
2K
Angular momentum for a bullet and a rod attached to a ceiling
Replies
17
Views
1K
Body attached to a block by a spring, shaped like an inclined plane
Replies
1
Views
951
Angular momentum, block plus bullet
Replies
4
Views
3K
State whether the distance x for the block would be greater/less/same
Replies
25
Views
1K
A bullet hits a rod attached to a pivot at one of its ends....
Replies
10
Views
4K
Inelastic collision problem: Bullet striking a wood block
Replies
2
Views
3K
How Does Angular Momentum Conservation Affect Asteroid Collision Dynamics?
7
Replies
335
Views
14K
MCAT Collisions of a wooden block and bullet
Replies
5
Views
2K
Bullet shooting vertically into a block
Replies
9
Views
7K

Hot Threads

Recent Insights

Back
Top