What Are the Mechanical Advantages and Efficiencies in an Inclined Plane System?

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The inclined plane system involves a 1-meter board at a 10-degree angle with a block of mass 122.5g and a 50g weight connected via a pulley. The ideal mechanical advantage (IMA) is calculated as 2450, while the actual mechanical advantage (AMA) is determined to be 2.45. The theoretical efficiency is approximately 41.76%, and the experimental efficiency is about 25.88%. The input force is derived from the IMA, resulting in a calculated input work of 2.7735J and an output work of 0.7177J. These calculations illustrate the differences between theoretical predictions and experimental results in mechanical advantage and efficiency.
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Homework Statement



a 1meter board is inclined at 10 degrees with a height of .3 meters. a block with mass of 122.5g is placed at the bottom connected to a string which is connected to a pulley at the top. if a weight of 50g is hung from the pulley and the block moves with constant velocity, what is the ideal and actual mechanical advantage(theoretical), predicted efficiency(theoretical), input force(tension), input work, output work, AMA(experimental), and efficiency(experimental).


Homework Equations





The Attempt at a Solution

 
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Ideal mechanical advantage= output force/input force=122.5g/.05g=2450Actual mechanical advantage= net output force/input force=22.5g/50g=0.45Theoretical efficiency= output work/input work=122.5g*9.8m/s^2*sin10°*.3m/50g*9.8m/s^2=.4176Input force=MA*input force=2450*.05g=122.5gInput work=input force*distance=122.5g*9.8m/s^2*sin10°*.3m=2.7735JOutput work=output force*distance=50g*9.8m/s^2*sin10°*.3m=.7177JAMA(experimental)= output force/input force=122.5g/50g=2.45Efficiency(experimental)= output work/input work=.7177J/2.7735J=.2588
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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