Dynamics: impulse and momentum

[Mesmerr]

Homework Statement

a 200-g projectile is fired with a velocity of 900m/s towards the center of the 15-kg wooden block, which rests on a rough surface. If the projectile penetrates and emerges from the block with a velocity of 300m/s, determine the velocity of the block just after the projectile emerges. How long does the block slide on the rough surface, after the projectile emerges, before it comes to rest again? the coefficient of kinetic friction between the surface and the clock is μk=0.2.

Homework Equations

conservation of momentum

∫ƩFdt=∫mdv

Fr=N*μk

N=W

W=m*g

and maybe ƩF=ma?

The Attempt at a Solution

Attempt is an attached pdf. I am stuck on how to find the force the bullet applied to the block. With that I could do Fb-Fr=ƩF, ƩF(t2-t1)=∫mdv where Δt would be my answer. Any guidance would be appreciated. Thank you!

 

[SammyS]

Homework Statement

a 200-g projectile is fired with a velocity of 900m/s towards the center of the 15-kg wooden block, which rests on a rough surface. If the projectile penetrates and emerges from the block with a velocity of 300m/s, determine the velocity of the block just after the projectile emerges. How long does the block slide on the rough surface, after the projectile emerges, before it comes to rest again? the coefficient of kinetic friction between the surface and the clock is μk=0.2.

Homework Equations

conservation of momentum

∫ƩFdt=∫mdv

Fr=N*μk

N=W

W=m*g

and maybe ƩF=ma?

The Attempt at a Solution

Attempt is an attached pdf. I am stuck on how to find the force the bullet applied to the block. With that I could do Fb-Fr=ƩF, ƩF(t2-t1)=∫mdv where Δt would be my answer. Any guidance would be appreciated. Thank you!

Hello Mesmerr. Welcome to PF !


For what length of time is the bullet passing through the block? You can answer this if you assume that the bullet experiences the same force throughout its path through the block.

 

[Mesmerr]

The question was how long does the block slide on the surface after the bullet leaves it. I noticed though that it said "after the bullet leaves the block". This means that the bullet is no longer acting on the block meaning you can use the equation of impulse to give you.

ƩF_blockΔt=m_blockΔv where ƩF = F_friction

Thanks for the help though! I do see how if you are given the time through the block you can get impulse on the bullet. Then because of Newton's laws the block would experience the same force.

 

[cepheid]

Why can't you just use conservation of momentum (for the bullet-block system) to solve this?

EDIT: I see. Because external forces (friction) act on the system. OK. I don't see a problem with SammyS's approach. Using the impulse momentum theorem, you can at least figure out how much force the bullet applies to the block.

 

[rezeew]

I would approach this problem by first identifying the relevant equations and principles. In this case, we are dealing with dynamics, specifically impulse and momentum. The impulse-momentum theorem states that the change in momentum of an object is equal to the impulse applied to it. In this problem, the projectile applies an impulse to the block, causing it to change its momentum.

To solve this problem, we can use the conservation of momentum principle, which states that the total momentum of a system remains constant unless an external force acts on it. In this case, we can consider the projectile and the block as a system, and use the conservation of momentum to solve for the velocity of the block after the projectile emerges.

We can also use the equations for friction (Fr = μkN) and the weight of the block (W = mg) to calculate the normal force (N) acting on the block and the force of friction (Fr) acting on the block as it slides on the rough surface.

Using these equations, we can set up a system of equations to solve for the velocity of the block after the projectile emerges, and the time it takes for the block to come to rest again. I have attached an image with the solution to this problem.

In summary, as a scientist, I would approach this problem by identifying the relevant principles and equations, setting up a system of equations, and solving for the unknown variables. I would also carefully consider any assumptions and approximations made in the solution.