Speeding bullet, average force by post on bullet

[serendipityfox]

Homework Statement

bullet initial speed 600m/s, mass 15g, penetrates 10cm, average force exerted by post on bullet

Relevant Equations

f= delta p/t, d=vi+vf/2 *t

used a) change in momentum / time, time from from kinematics equation d = vi+vf/2 *t ... 0.1 = 300*t
=3.33*10^-4
then 600/0.00333 = 1.8*10 ^5
how to proceed?

 

[Delta2]

What you calculated as 1.8x10^5 is the average acceleration (or to be more accurate deceleration) of the bullet. How can you find the average force if you know the average acceleration? Newton's 2nd law of course! :D

 

[serendipityfox]

thankyou delta2
i bungled the second equation... should be 9 / 0.00033 of course
answer i get is 2.7*10^4

but the mcq answers are...
a) 9.0*10^3
b) 5.3*10^4
c) 2.4*10^5
d) 1.6*10^6

 

[Delta2]

I get the same answer as you, don't know what's going on, maybe recheck the data given.

 

[PeroK]

thankyou delta2
i bungled the second equation... should be 9 / 0.00033 of course
answer i get is 2.7*10^4

but the mcq answers are...
a) 9.0*10^3
b) 5.3*10^4
c) 2.4*10^5
d) 1.6*10^6

If you assume a constant force, hence constant acceleration, then the work done is $Fd$ and this must equal the initial KE of the bullet. So:

$F = \frac{mv^2}{2d}$

This agrees with the formula derived from the kinematics of constant acceleration.

Assuming SI units (units are important but missing from your work and your answers), then this should be $F = 27kN$.

 

[serendipityfox]

... average force exerted by post on bullet, will be same as the bullet on post?

 

[serendipityfox]

@Delta2 - thankyou for the assistance
@PeroK - sorry will endevour to be more precise

 

[PeroK]

... average force exerted by post on bullet, will be same as the bullet on post?

That's Newton's third law.

 

[serendipityfox]

so still no viable answer according to the exam sheet... well this discourse has been helpful anyway, thanks

 

[haruspex]

so still no viable answer according to the exam sheet... well this discourse has been helpful anyway, thanks

As @PeroK notes, the question embodies a blunder: you have to assume the force is constant.
Average force (a vector) is defined as change in momentum (a vector) divided by elapsed time (a scalar). Dividing work done by distance produces a scalar, and this does not in general match the magnitude of the average force. It is an interesting exercise to calculate the difference in the case of a spring.

 

[serendipityfox]

physics question section on an MCAT practice paper