take home quiz about simple machines?

Question

1.) a lever arm of a jackscrew is 2m and the pitch is 0.02m. a load of 35,000N is to be raised and this requires a force of 360N at the end of the lever arm. find the following:

a.) AMA
b.) IMA
c.) efficiency of this machine

Answer 1

What is AMA and IMA?

Thank you for the feedback
So now I know that
AMA=actual mechanical advantage
IMA=ideal mechanical advantage or theoretical mechanical advantage.

Since you have an ideal machine (no friction)
AMA=IMA
and efficience = 100%
**The information below is full of details. I hope it will not put you to sleep.**

Since you have no friction it is an ideal machine and
AMA =IMA

So energy in = energy out + zero in losses (ideal machine)
[We will get back to that again later when we consider efficiency n.]
IMA=?
A screw is similar to an incline. Imagine you have an object on a frictionless incline (ideal machine). The force responsible for hording this object from sliding has to appose only parallel to the plane component (Fd) of its weight (w)
Fd=w sin(angle the plane makes with the horizontal).
Or Fd/w=rise / run
Run of the path is the path the force takes as it turns the screw
Run=2 pi R where R=2m
And rise is 0.02m
Thus Fd=(rise/run) w
Fd=(.02/(2 pi 2) )35,000 = 55.7N
So 360 N is actually too much force
Finally the IMA=Fout/Fin=35000/55.7= 628 times
Also we should not be blindsided that
IMA= Run over rise
(c) So what is the efficience?
n=(energy out)/(energy in)
We could say also
n=(power out)/(power in) but power is not given that is we do not know how fast one turns the screw unless we want to use the 360 N force.
Let’s do energy first
E in = F s = Fd (2 pi R)= 55.7 (2 x 3.14159 x 2) = 700 Joules
E out = w h= 35000 0.02 = 700 Joules
So n=100% Surprised? You should not be it is an ideal machine and ideal machiens are 100% efficient.

And if you apply the 360N force you will get hurt since you will either slip or accelerate the system to oblivion.

I hope it helps.

Answer 2

a) AMA (actual mechanical advantage) is defined as
AMA = R/Ea where
R is resistance force
Ea actual force
so

AMA = 35000N/360N = 97.22

b) IMA (ideal mechanical advantage) is defined as

IMA = De/Dr where
De = effort distance
Dr = resistance distance

So the resistance distance for one revolution of the lever arm is
0.02 m and the motion of the lever arm is the circumference of the circle made by the 2m arm = 2Pix2m = 12.6m

so IMA = 12.6m/0.02m = 630

This is so much bigger than 630 that I have doubts about the operation of the jackscrew. You don't say what is the motion of the lever arm. For example, tt could be a full revolution or a quarter turn.

c) Efficiency is power output/power input

Power output is 0.02m x 35,000N = 700 J
Power input is 360N x 12.6m = 4536 J

Eff = 700/4536 = 15.4%

Again you might want to revise these numbers if you know the exact motion of the lever arm needed to lift the weight by one pitch.