How Do You Calculate the Resistance of the Ground in a Physics Problem?

[Inertialforce]

Homework Statement

A camper let fall a heavy mallet of mass "M" from a height y upon the top of a tent stake of mass "m" and drives it into the ground a distance d. Find the resistance of the ground (f), assuming it to be constant and the stake and the mallet to stay together upon impact.

Homework Equations

The Attempt at a Solution

For this question I know that it asks me to find what the resistance force (f) is and I know that I can find it out by figuring out what the total force acting downward would be because (according to Newton's laws), total force downward must equal the total force upward or in other words, the force of the stake and mallet combination acting downward must equal the resistance force (f) acting upward.

However I do not know exactly how or where (with what equations) I should start my calculations, as all the values given to me are letters.

 

[ak1948]

Usually when you see masses dropping from some height, you want to think how you can use the energy Mgy to solve your problem. This is dissipated by the resistance of the ground to the movement of the stake.

 

[Inertialforce]

Because many people were having problems with this question we were given a hint to solve this question. The hint was that, what we are ultimately trying to find in this question is the impulse of the system and to find that impulse you would need to first go through the energy (conservation of energy) calculations and then apply what you got in the energy calculation into a momentum (conservation of momentum) calculation, then finally use what you got from both calculations and plug it into the impulse equation and solve.

Because there are no numbers in this entire question it is hard to know if I am going in the correct path. But the answer I got in the end after going through all three calculations is:

I = (Ff)*[(d/√(2gy) - (mm)(√(2gy)]

note: "mm" in the equation above is the mass of the stake.

Could someone please take a glance at this and tell me if I am at least going in the right direction or not?

 

[ak1948]

The equation is incorrect. Are you looking for a force or an impulse? If an impulse, its just equal to the change in momentum of the mallet, which you can easily calculate since you know the kinetic energy of the mallet when it strikes (from conservation of energy).

If you are looking for the constant resistive force as first stated, you can't find that from the impulse, because you don't know how long the force is applied. So you would look at the work done in driving in the stake, which must be equal to the energy given up by the mallet. Since you know the distance its driven, you can calculate the force.