Interactions and Potential Energy

[CJoy]

Homework Statement

The Cubarb parasite, having pursued Defiance Drake this far was not expecting either her sudden acrobatics, or to be shot by her futuristic slug throwing pistol. Nevertheless, Cubarbs have naturally flexible skin that afford them protection from projectiles, depending of course, on the amount of kinetic energy that the projectiles are carrying. The parasite's skin acts as a spring, with constant k=1.8 x 10^6 N/m, and as long as the deflection is less than 3cm (more than that and the skin breaks, and the parasite likely dies. If the bullet has a mass of 50g, and travels at 300 m/s, does the bullet bounce off the creature, or does it penetrate? How do you know?

Relevant Equations

Usp=1/2K(total s)^2
Ke=1/2mv^2
Esys=total Ke+total U+total Ethermal=Wext
Emech=total Ke+total U+ total Ethermal

Usps=1/2(1.8x10^6)(0.03)^2=810J
Ke=1/2mv^2=1/2(0.05)(300)^2=2250J
I don't know how to take it farther than this, or if this is the correct way to start the problem. If this is correct, would it be correct to assume that the bullet does penetrate the creature because Ke overcomes Usps?

 

[phinds]

If the bullet has a mass of 50g, and travels at 300 m/s, does the bullet bounce off the creature, or does it penetrate?

Uh ... you think maybe it matters whether the bullet is a hollow point or sharp-nosed or armor-piercing ?

 

[jbriggs444]

Usps=1/2(1.8x10^6)(0.03)^2=810J
Ke=1/2mv^2=1/2(0.05)(300)^2=2250J
I don't know how to take it farther than this, or if this is the correct way to start the problem. If this is correct, would it be correct to assume that the bullet does penetrate the creature because Ke overcomes Usps?

Yes, that is pretty clearly the intended approach. I agree with your calculations and your prediction for penetration.

As @phinds suggests, the armored skin specification in the problem statement does not seem very realistic or complete since it ignores the size of a projectile's pointed tip.