Bullet Hits Disc: Velocity of Inelastic Collision

[satishinamdar]

A bullet of mass m hits a disc of radius R on its periphery at speed v.What will be the velocity of disc if the collision is inelastic?

 

[Doc Al]

A bullet of mass m hits a disc of radius R on its periphery at speed v.What will be the velocity of disc if the collision is inelastic?

You tell us. Hint: What's conserved?

 

[satishinamdar]

momentum is conserved.pl help

 

[OlderDan]

momentum is conserved.pl help

The problem statement does not give all the needed information. Is the disk at rest? What is its mass? This almost sounds like it could be a rotation problem. Is there more you have not told us?

 

[Doc Al]

Dan is correct, some information is missing. State the problem exactly as given.

(I assumed it was a rotation problem, and that angular momentum would be conserved, but failed to point out the missing info. Sorry.)

 

[Andrew Mason]

A bullet of mass m hits a disc of radius R on its periphery at speed v.What will be the velocity of disc if the collision is inelastic?

There are different ways that a collision can be inelastic. The bullet could compress and deflect off. The bullet could stick to the disc. Since the question does not give you the final speed of the bullet, let's assume that it sticks to the disc. In this case, the question is asking for the velocity of the centre of mass of the disc + bullet and this is just a matter of applying conservation of linear momentum:

$$v_{disc} = \frac{mv}{m_{disc} + m}$$

AM

 

[satishinamdar]

Assume the mass of disc as M.how it is a case of conservation of linear momentum?

 

[Doc Al]

Please state the full problem exactly as given.

For example: Is the disk fixed about an axis, or free to move? Are you asked to find the speed of the disk's center of mass? or it's rotational speed?

 

[satishinamdar]

it is fixed to axis.Angular speed to be calculated.

 

[Doc Al]

Angular (not linear) momentum will be conserved, assuming there's no friction about the axis. What's the initial angular momentum of the bullet? What's the rotational inertia of the "disk + bullet"?

Use that to find the angular speed of the disk after the collision, assuming the collision is perfectly inelastic--the bullet imbeds itself to the rim of the disk.

 

[OlderDan]

it is fixed to axis.Angular speed to be calculated.

Why do you insist on not stating the problem? You have been asked to do it repeatedly. You still have not given us enough information to find a result. If you want help, state the problem exactly the way it was given to you.

 

[Doc Al]

It's like pulling teeth, eh Dan?

 

[satishinamdar]

Dear Guruji
the problem as appearing in the textbook is as follows
"A bullet of mass m collides inelastically at the periphery of a disc of mass M and RADIUS r, with a speed v.The disc rotates about a fixed horizontal axis.Find theangular velocity of the disc bullet system just after the impact."
Now I request you to help.

 

[matthew baird]

This is hilarious if that is truly exactly as it appears in the textbook! The only way you will find the angular velocity is by knowing the Inertia of the system. In that calculation you will have to know the radius or distance from the center of mass at which the bullet hits. Unless I am blind, that little piece of information is missing. Is there a picture or diagram in the book?

 

[satishinamdar]

yes there is a diagram it shows,
a circle with radius r, centre O,
says mass M, THE ARROW TOUCHING THE CIRCLE PERIPHERY TANGENTIALLY . WITH VELOCITY v AND MASS m
I thought the text was quite sufficient.
Now nothing more to share

 

[matthew baird]

"THE ARROW TOUCHING THE CIRCLE PERIPHERY TANGENTIALLY"
Once again I am tired, is the arrow hitting the face of the circle as a real arrow strikes a target, or the arrow somehow sticks on the edge of the circle , as if a car wheel was hit with a falling rock on the edge and caused it to spin?

 

[Andrew Mason]

"THE ARROW TOUCHING THE CIRCLE PERIPHERY TANGENTIALLY"
Once again I am tired, is the arrow hitting the face of the circle as a real arrow strikes a target, or the arrow somehow sticks on the edge of the circle , as if a car wheel was hit with a falling rock on the edge and caused it to spin?

One has to assume the disk is perpendicular to the path of the bullet, the bullet strikes at a distance R above the horizontal axis about which the disk rotatates and sticks to the disk.

In this case, you have to determine the angular impulse received from the bullet:

$$\Delta L = I_{bullet+disk}\Delta \omega = \Delta p_{bullet}R$$

The moment of inertia of the disk + bullet is just the moment of inertia of the disk + mR^2

AM

 

[Doc Al]

Dear Guruji
the problem as appearing in the textbook is as follows
"A bullet of mass m collides inelastically at the periphery of a disc of mass M and RADIUS r, with a speed v.The disc rotates about a fixed horizontal axis.Find theangular velocity of the disc bullet system just after the impact."
Now I request you to help.

You have been provided with all the hints you need: See my last post and Andrew's post. Now it's your turn.