Minimum speed of the bullet to penetrate a sphere

In summary, the conversation discusses determining the minimum speed of a bullet with mass m and charge q to penetrate through a solid uniformly charged sphere of radius R and total charge +q. The problem can be approached using either conservation of energy or work kinetic energy theorem. There may be a sign problem in the work energy equation, which can be corrected. The conversation also mentions another thread on "flux through a circular ring" for further discussion.
  • #1
Tanya Sharma
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Homework Statement



A bullet of mass m and charge q is fired towards a solid uniformly charged sphere of radius R and total charge + q. If it strikes the surface of sphere with speed u, find the minimum speed u so that it can penetrate through the sphere. (Neglect all resistance forces or friction acting on bullet except electrostatic forces)

Homework Equations


The Attempt at a Solution



I think if the bullet can just reach the center ,then it can penetrate through the sphere because the electric field inside a sphere is radially outwards .As it reaches the center and moves just a little bit outwards radially ,the electric field will push the bullet outwards .

The problem can be approached either by conservation of energy or by work kinetic energy theorem.

1) By conservation of energy

kq2/R+(1/2)mu2 = (3/2)kq2/R

2) By work energy theorem

## \int_{R}^{0}\frac{kq^{2}r}{R^3} \hat{r} \cdot dr\hat{r} = \frac{1}{2}mu^2 ##

Have I approached the problem correctly or is there something more in it ?
 
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  • #2
Both approaches look correct to me.

But in the work energy equation, there might be a sign problem. I think your integral on the left is correct for the work done by the electric force on the bullet as it goes from the surface to the center. But, is the sign correct on the right for the change in KE?
 
  • #3
Yes.. you are right.There should be a minus sign in the LHS .

Thanks TSny...

Would you mind having a look at the other thread :"flux through a circular ring " .
 
  • #4
Tanya Sharma said:
Yes.. you are right.There should be a minus sign in the LHS .

Thanks TSny...

Would you mind having a look at the other thread :"flux through a circular ring " .

I'll take a look tomorrow. It's that time again. :zzz:
 
  • #5
Okay :smile:
 

FAQ: Minimum speed of the bullet to penetrate a sphere

What factors affect the minimum speed of a bullet to penetrate a sphere?

The minimum speed of a bullet to penetrate a sphere is affected by several factors, including the density and thickness of the sphere, the shape and composition of the bullet, and the angle at which the bullet hits the sphere.

What is the formula for calculating the minimum speed of a bullet to penetrate a sphere?

The formula for calculating the minimum speed of a bullet to penetrate a sphere is v = √(2E/m), where v is the minimum speed, E is the elastic energy of the sphere, and m is the mass of the bullet.

How does the minimum speed of a bullet to penetrate a sphere change with different sphere materials?

The minimum speed of a bullet to penetrate a sphere is directly proportional to the elastic energy of the sphere, which is determined by the material's density and elastic properties. Therefore, a sphere made of a denser or more elastic material will require a higher minimum speed for the bullet to penetrate it.

Is the minimum speed of a bullet to penetrate a sphere the same for all types of bullets?

No, the minimum speed of a bullet to penetrate a sphere can vary depending on the shape, composition, and weight of the bullet. For example, a heavier and more streamlined bullet may require a lower minimum speed to penetrate a sphere compared to a lighter and less aerodynamic bullet.

What are some real-world applications of understanding the minimum speed of a bullet to penetrate a sphere?

Understanding the minimum speed of a bullet to penetrate a sphere is important in fields such as ballistics, forensic science, and military operations. It can also be useful in designing and testing bulletproof vests and other protective gear.

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