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Evil dead · Aug 16, 2007, 07:18 AM

A tractor leaves a muddy field throwing mud into the air with it's rear wheels. The wheels are 1m in radius and the tractor moves off at 8ms-1. What is the maximum height that the mud will reach? And where will this mud land relative to the tractor.

I only got far as using centripetal acceleration to calculate the acceleration of the mud assuming it leaves the wheels on a tangent.

a = v2 / r
a = 64ms-2.

I'm stuck I don't know what to do...

ebaines · Aug 16, 2007, 07:51 AM

To do this problem you have to first know at what angle relative to the ground the mud is thrown - do they give you this bit of information? Or do they tell you how deep into the mud the wheels are - from this you can calculate the angle. Given the angle you could then calculate the velocity of the surface of the wheel relative to the ground at the point where the mud leaves the wheel, and from that you could then calculate the rest.

Evil dead · Aug 16, 2007, 12:47 PM

No I was not given an angle or anything like that, just the above clues I stated

ebaines · Aug 16, 2007, 12:56 PM

OK, well in that case, we can assume the following: the mud would reach a maximum height if it is thrown with maximum possible velocity straight up. Imagine a clump of dirt coming off the wheel at the point where the tangential velocity of the wheel surface is directed straight up.. can you visualize where that is? Once you have that, you will need to figure out both the vertical and horizontal components of the clump's velocity. And then from that you can calculate the max altitude, and the horizontal velocity of the clump relative to the tractor. Post back if you 're still having difficulty.

One other hint - you don't need to worry about any centripetal acceleration with this problem- just the tangential velocity of the wheel rim.

Evil dead · Aug 16, 2007, 01:25 PM

I'm very stupid please explain in more explicit detail.

ebaines · Aug 16, 2007, 01:30 PM

Step 1.. Determine the velocity of a point on the rim of the wheel. You know that the tractor is moving at 8m/s -- so what is the velocity of a point on the rim of the wheel?
Step 2.. If a clump of dirt is thrown straight up at that velocity, how high would it rise?

Start on these two steps, and post back.

Evil dead · Aug 16, 2007, 03:41 PM

Well since the whole circumference of the wheel is moving at 8ms, then the rim of the wheel moves at 8ms no matter where the tangent is.

So therefore if the clump of dirt is moving in a tangent off that point, it's immediate velocity is 8ms, so it's maximum height is 8m... even though the solution said 4.2m was the maximum.

Where did I go wrong?

ebaines · Aug 17, 2007, 05:05 AM

You are correct that the clump of mud is thrown straight up at 8 m/s. To figure out how high it goes - the force of gravity will cause the clump to slow down, until at some point its velocity is 0, and after that it starts to fall back to earth. Do you know how to relate an object's velocity to its aceleration and distance traveled? There's an equation which you should memorize, which goes like this:

$<br /> v_f ^2 - v_i ^2\ =\ 2ad<br />$
Where:
$v_i$ = Initial Velocity
$v_f$ = Final Velocity
$a$ = acceleration (in this case the acceleration due to gravity is -9.8 m/s^2), and
$d$ = distance traveled.

So, set $v_i$ to 8m/s, $v_f$ to 0 (since the object's velocity is 0 at its maximum height), and $a$ = -9.8m/s^2, and calculate $d$ . Then don't forget that the height above the ground is $d+1$ meters.

Hope this helps.

Capuchin · Aug 17, 2007, 05:15 AM

I've been watching this, and I still don't really comprehend what it has to do with circular motion, or even where the radius of the wheel would have to be used.

ebaines · Aug 17, 2007, 05:22 AM

Originally Posted by Capuchin

I've been watching this, and I still don't really comprehend what it has to do with circular motion, or even where the radius of the wheel would have to be used.

You're right - nothing to do with circular motion. And the only reason you need to know the radius of the wheel is to add it onto the calculation of $d$ to determine the total height above the ground the mud is thrown (that's why there's the +1 in the solution).

Capuchin · Aug 17, 2007, 05:24 AM

Ah yes of course. :)

Evil, was this question in a circular motion part of your course or text book, or did you just assume that it was circular motion when starting the thread?

Evil dead · Aug 17, 2007, 07:18 AM

Part of my tectbook that was in the chapter: circular motion. It may be a projectile question though.