Answer to Question #289296 in Mechanics | Relativity for CosmoS

Question

1.) A 400 kg piano is lifted to the third story with a set of pulleys. The theoretical mechanical advantage is 4.00.

a.) Calculate the effort required to lift the piano.

b.) If the piano is lifted 10.0 m, how far does the effort move?

c.) How much work is done to lift the piano in 10.0 m?

d.) If the piano is lifted 10.0 m in 30.0 seconds, how much power is developed?

Answer 1

Explanations & Calculations

$\qquad\qquad \begin{aligned} \small MA&=\small 4=\frac{\text{load}}{\text{effort}}\\ \small \text{effort}&=\small \frac{400\times9.8\,N}{4}\\ &=\small 980\,N(or \,100\,kg\,\text{in kilogram notation}) \end{aligned}$

• The effort moves $\small4$ times the load since the MA is such.
• Therefore, it moves $\small 40.0\,m$

• Work done is how the effort works
• Therefore, the work is $\small W=F\times s=980\,N\times40.0\,m=39200\,J$
• This pulley system makes the work easier by changing how the quantities of the work equation (W = Fs) behave.
• It lowers the needed force while increasing the distance that force should move to deliver a particular amount of work.
• This delivered work still equals the needed work that is $\small mgh=400\times9.8\times10=39200\,J$

• Power is the ration of work to time taken, therefore,

$\qquad\qquad \begin{aligned} \small P&=\small \frac{39200\,J}{30.0\,s}\\ &=\small 1306.7\,W\\ &\approx\small 1.31\,kW \end{aligned}$