A mass of 100kg is lifted with a constant acceleration of 1m/s^2. Find the power delivered in lifting after 2s

Question

Also find the power delivered by gravity

Displacement of the object $$s=\frac 12 at^2$$ $$s=\frac 12.4$$ $$s=2m$$ Work done $$W=F.s$$ Force applied is $$F=ma$$ $$F=100$$ Therefore $$W=200J$$ Power $$P=200/2=100W$$ But the answer is $2200W$. What’s going wrong?

Answer 1

We have that

$$F-mg =ma\implies F=1100 N \implies dW=F\cdot tdt \implies P(t)=\frac{dW}{dt}=F\cdot t$$

Note that

• the mean power is $\frac{W_{tot}}{t_{fin}}=1100 W$

• the power at time $t=2$ is $P(2)=F\cdot 2=2200 W$