Calculating Efficiency of an Inclined Plane

AI Thread Summary
The discussion focuses on calculating the efficiency of an inclined plane used to lift a washing machine weighing 1400N onto a truck bed 1.2m high, with a worker applying a force of 450N along a 4.3m ramp. The mechanical advantage (MA) is correctly calculated as 3.11, while the ideal mechanical advantage (IMA) was initially miscalculated but later corrected to 3.58. The efficiency is then determined using the formula e=(MA/IMA)100, resulting in an efficiency of 87%. Participants emphasize that MA and IMA are dimensionless numbers and clarify the correct relationship between effort and load distances. The final efficiency calculation demonstrates the effectiveness of the inclined plane in this scenario.
Jonathan Teas
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Homework Statement


A washing machine that weighs 1400N must be put into a delivery truck bed that is 1.2 m off the ground. A worker uses a force of 450N to push the machine up a ramp that is 4.3m long. What is the efficiency of the inclined plane?

Homework Equations


e=(MA/IMA)100---- efficiency of a machien in % is = to its mechanical advantage, divided by the ideal mechanical advantage, multiplied by 100.
MA=Fr/Fe---- mechanical advantage=the resistance of force divided by the effort force.
IMA=De/Dr----the ideal mechanical advantage of an ideal machien is=to the displacement of the effort force, divided by the displacement of the load.

The Attempt at a Solution


MA=1400N/450N=3.11N, I think i did that part right.
IMA=1.2m/4.3m=0.28m, I think i did this part wrong.
e=(3.11N/0.28m)100=1110.71joules.
 
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Hi Jonathan Teas, welcome to PF.
First of all MA or IMA are pure numbers. No units for them.
Next IMA = Distance traveled by effort/ distance traveled load. = ...?
In Ist or second type of machine IMA cannot be less than one.
 
rl.bhat said:
Hi Jonathan Teas, welcome to PF.
First of all MA or IMA are pure numbers. No units for them.
Next IMA = Distance traveled by effort/ distance traveled load. = ...?
In Ist or second type of machine IMA cannot be less than one.

If IMA= Distance traveled by effort/ distance traveled load
then IMA= 4.3m/1.2m=3.58 then no unit?
so the answer is 3.11no unit again/3.58=(0.87)100=87%
Thank you very much.
 
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