A child sits in a wagon with a pile of 0.42 kg rocks. If she can throw each rock with a speed of 14 m/s relati

Question

A child sits in a wagon with a pile of 0.42 kg rocks. If she can throw each rock with a speed of 14 m/s relative to the ground, causing the wagon to move, how many rocks must she throw per minute to maintain a constant average speed against a 3.1 N force of friction?

Answer 1

The work she does to accelerate the rocks from 0 to 14 m/s is
.5*.42*14^2
=41.16 J

The work done by friction over the distance the wagon moves is 3.1*d

at a constant velocity, v, the distance traveled in one minute is v*60
so the work is
3.1*60*v
so the number of rocks will be a function of the average velocity
N*41.16=186*v
N=4.52 * v
or v=N/4.52

Just for fun, I looked at a few other equations to see what can be derived.

First, the distance the wagon travels between throws is v*60/N
this distance can be expressed as
v*60/N=vmax*60/N-
(.5*3.1/m)*3600/N^2

and Vmax and Vmin have the following relationships
v=(Vmax+Vmin)/2
and
Vmin=Vmax-(3.1/m)*60/N

combining
Vmax=N/4.52+93/(m*N)
and Vmax and Vmin have the following relationships
v=1/(4.52*m)

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