My Physics Teacher Must Really Hate Pianos

[Medgirl314]

Homework Statement

A 350 kg piano is dropped from a stationary helicopter. As it falls, it picks up speed and the air resistance increases, causing its acceleration to be less than 9.8 m/s² What is the piano's acceleration at the moment that the air resistance is exerting an upward force of 1400 N?

Homework Equations

w=mg

The Attempt at a Solution

a=w-f_air /m

w=mg
w= 350 kg*9.8 m/s²
w=3430 N
a=3400-1400 N / 350 kg
a=2030/350 kg =5.8 m/s²

This is less than the force of gravity, ans seems reasonable. Could someone confirm?

Thanks!

 

[Simon Bridge]

a=3400-1400 N / 350 kg

... so like the other one, you should do the algebra before you start using numbers then it is easier to see what is going on.

F = air resistance, mg = weight, and a is the acceleration ... then,
draw a free body diagram and picking down as positive:

mg-F=ma means that a=(mg-F)/m ...

... putting the numbers in now gets you the same thing ... but now you can tell if it is right or not because the setup and the algebra are all there without the numbers to hide things.

 

[Medgirl314]

Thanks! I didn't have to mess with the equation too much, because my teacher had a similar one in an example. I usually find it harder to do the algebra first, but I can try it and see if it's easier in the end. Thank you!

 

[Simon Bridge]

Yah - if you just copy the examples, it'll bite you in the long run.
It takes a bit to get used to moving the variables around, but it pays off.

 

[Medgirl314]

Thanks for the help!