Energy needed to penetrate each object

[PhysicS FAN]

1. The problem statement, all variables and the known data
A bullet (mass m) is shot with an initial velocity (V) towards an object with mass M=3m as shown in the picture. The energy needed to penetrate the object is 30J.
The same bullet is shot with a velocity (v) heading to an identical object with the one mentioned above. If the coefficient of friction is μ=0 then what is the necessary energy so that the bullet penetrates the object.

Homework Equations

The Attempt at a Solution

.I tried to use energy theorems for the first case and I found some equations involving the speed of bullet. The same and for the 2nd case. The problem is that I can not find a way to connect the equations of the 2 cases. Please help me.

 

[Doc Al]

In the first case, where the object is up against the wall, all the energy goes into penetrating the object. But in the second case that cannot happen since the object is free to move and thus some of the energy of the bullet must be used for the overall KE after the collision. Hint: What's conserved in any collision?

 

[PhysicS FAN]

In the first case, where the object is up against the wall, all the energy goes into penetrating the object. But in the second case that cannot happen since the object is free to move and thus some of the energy of the bullet must be used for the overall KE after the collision. Hint: What's conserved in any collision?

I'm stuck I don't know how to continue. The reason is that I can not combine any equations and so I can't proceed

 

[TheMercury79]

Try using the relation $p^2=2Km$ in the first case and see how you can combine and use that in the second case

 

[PhysicS FAN]

Try using the relation $p^2=2Km$ in the first case and see how you can combine and use that in the second case

Well there is no difference since the Kinetic energy is different, the momentum is different and that won't lead anywhere

 

[TheMercury79]

But the momentum in the first case gives you some information on the maximum momentum the material in the object can withstand.
This limit will be the same in the second case, but you also need that additional momentum that makes it move. So yes, the momentum is different, but part of it from the first case is still there

 

[haruspex]

I'm stuck I don't know how to continue. The reason is that I can not combine any equations and so I can't proceed

In the second case the bullet flies at speed v. At what speed will the combined bullet and block move? How much energy is needed for that?

 

[neilparker62]

I'm not sure about the wording of this question and the significance of v vs V in respect of velocity. The question appears to be asking for a comparision of energy loss in a perfectly inelastic collision given a) 3m mass can't move b) 3m mass can move. We can't do such a comparision unless the bullet is fired with the same velocity in a) and b).

$$ ΔE = ½μΔv^2 $$

 

[haruspex]

We can't do such a comparision unless the bullet is fired with the same velocity in a) and b).

No, the question is ok. The energy to penetrate is the same in both cases. The question is asking how much extra energy (hence extra velocity) the bullet needs when the block is not restrained.

 

[neilparker62]

Ok - got it. Thanks for the clarification. Above equation should assist if the OP is familiar with it (probably not!)

 

[neilparker62]

Ok - got it. Thanks for the clarification. Above equation should assist if the OP is familiar with it (probably not!)

Apologies - no disparagement intended if OP doesn't know the formula $ΔE=½μΔv^2$ - it's just a geeky result which can be derived and which I have found useful solving problems of this nature.