How much time does it take to lift the piano?

[BlackMamba]

Hello,

I thought I knew how to solve for this problem but alas I was wrong. I'm hoping someone will be able to point me in the right direction.

Here's the problem: A 1.40x10^2 kg piano is being lifted at a steady speed from ground level straight up to an apartment 18.0m above the ground. The crane that is doing the lifting produces a steady power of 4.00x10^2 W. How much time does it take to lift the piano?

So here's what I did:

The equation for power is P = W/t.

The equation for W (work done) is W = (Fcos0)s.

I have P (at least this is my thinking here). P is 4.00x10^2 and I would need to find W and then I could solve for t.

F = ma, however I don't know what my acceleration is. I calculated it with 9.80 but my answer was incorrect. So if all my original thinking in finding t is correct then all I really need help with is finding F.

Any help provided will be greatly appreciated.

 

[Pyrrhus]

Stunner, that does not equal work.

Conservation of Mechanical Energy
$$\Delta K + \Delta \Omega = 0$$

By the way, if the speed is steady(i suppose it means constant) what will be the change of kinetic energy?

You could apply (Conservative System Work)

$$W = -\Delta \Omega$$

Alternatively,

Newton's 1st Law

$$\sum_{i=1}^{n} \vec{F}_{i} = 0 \rightarrow \vec{v} = constant$$

You could use this to establish the force exerted to lift it is equal to the weight of the piano, in magnitude.

 

[wais]

Hi there,

To solve this problem, it would be helpful to use the equation P = Fv, where P is power, F is force, and v is velocity. In this case, we know that P = 4.00x10^2 W and v = 18.0 m/s (since the piano is being lifted at a steady speed of 18.0m above the ground). Therefore, we can rearrange the equation to solve for F: F = P/v. Plugging in the values, we get F = (4.00x10^2 W)/(18.0 m/s) = 22.22 N.

Now, we can use the equation F = ma to solve for the acceleration. We know that m = 1.40x10^2 kg, so we can rearrange the equation to solve for a: a = F/m. Plugging in the values, we get a = (22.22 N)/(1.40x10^2 kg) = 0.159 m/s^2.

Finally, we can use the equation v = at to solve for the time (t) it takes to lift the piano. We know that v = 18.0 m/s and a = 0.159 m/s^2, so we can rearrange the equation to solve for t: t = v/a. Plugging in the values, we get t = (18.0 m/s)/(0.159 m/s^2) = 113.21 seconds.

Therefore, it would take approximately 113.21 seconds (or 1 minute and 53 seconds) to lift the piano. I hope this helps and please let me know if you have any further questions.