# Why resistive force will vary with speed?

1. Jul 4, 2014

### sta6a2411

I have been working on the following question. I have finished part (a) and (b) and checked the answer. But I'm confused by the answer of part(c).

A metal stake of mass 2kg is driven vertically into the ground by a blow from a sledgehammer of mass 10kg. The sledgehammer falls vertically on to the stake, its speed just before impact being 9m/s. In a model of the situation it is assumed that , after impact, the stake and the sledgehammer stay in contact and move together before coming to rest.

(a) Find the speed of the stake immediately after impact.

The stake moves 3cm into the ground before coming to rest. Assuming in this model that the ground exerts a constant resistive force of magnitude R newtons as the stake is driven down,
(b) find the value of R.

(c) State one way in which this model might be refined to be more realistic.

The answer of (c) is "the resistance (R) could be modeled as varying with speed". However, I cannot figure out the explanation of it. Since the stake is moving, the frictional force should be limiting all the time until the stake stops. Have I confused that resistive force with frictional force? Can anyone help explain it to me?

2. Jul 4, 2014

### Simon Bridge

Welcome to PF;
It can be quite tricky to think about.
You can see that resistive forces do vary with speed simply by rubbing something with your fingers - the faster you rub, the hotter your fingers get, the more it hurts, the faster the flesh wears off etc depending on the surface and the speed. (Recommend using someone elses fingers...)

But one of the things to consider is friction as a drain of energy ... and the relationship between work and energy and the rate that energy gets drained.

There should be a force present, pointing the opposite direction to the motion, all the time - but it does not have to be a constant force.

When the instantaneous speed is highest, the instantaneous friction/resistance force is also highest.
When the speed is zero - the resistance force is zero.

Now in (a) - that is the effect before any resistance can come into play.
In (b) you are explicitly told to use a model of resistive forces where the force does not depend on speed.
In (c) you are only asked for a simple statement...