A 1.60 102-kg piano is being lifted at a steady speed from ground level straight up to an apartment 18.0 m above the ground. The crane that is doing the lifting produces a steady power of 4.00 102 W. How much time does it take to lift the piano?
2007-12-13 01:20:29 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Physics
By definition power is a rate of energy flow
P=E/t then
t=E/P
Energy equal to the work done against gravity or equal to potential energy Pe gained hence
E= Pe
Pe= mgh and finally
t=mgh/P
t= 1.60 E+2 x 9.81 x 18.0 / 4.00 E+2
t=70.6 sec
2007-12-13 01:40:42 · answer #1 · answered by Edward 7 · 1⤊ 0⤋
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Mass of piano =1.69*10^2=160 kg
Height = h =18.0 m .
Power = 4.00 *10^2 W
Power(P)*time(t) =work done = w = mgh
P*t=mgh
t = mgh / P
t = 160*9.8*18 / 4*10^2
t = 70.56 s
The crane takes 70.56 second to lift the piano at a steady speed from ground level straight up to an apartment 18.0 m above the ground.
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2007-12-13 01:49:34 · answer #2 · answered by ukmudgal 6 · 1⤊ 0⤋
i am going to assume that it is a 102kg piano and a 102W crane either way the method is the same!
The equations that you need are Power = energy / time.
Gravitational Potential Energy = mass * g * height
g is the acceleration due to gravity which is 9.8 m/s^-2
and height is the change in height.
The gravitational potential energy is the same value that you would use in the power equation.
Therefore
GPE = 102 * 9.8 * 18
P = E/t
102 = 102 * 9.8 * 18 / t
so divide both sides by 102 and multiply by t to get...
t = 9.8 * 18
t is for time taken...
2007-12-13 02:25:32 · answer #3 · answered by Anonymous · 1⤊ 1⤋
The work needed to lift the piano through a distance of 18m is Force x distance = mgh.
160*9.8*18. J
Power is rate of doing work = work / time
= 160*9.8*18 /t
It is given that the power is 400 W = 400 J/s.
160*9.8*18 /t = 400
t =160*9.8*18 / 400 = 70.56s.
2007-12-13 02:12:14 · answer #4 · answered by Pearlsawme 7 · 1⤊ 0⤋
Power = Energy Transferred / Time taken
Energy Transferred = Gain in G.P.E
G.P.E = mass x gravity acceleration x height
G.P.E = 1.60x10² x (9.8) x (18.0)
G.P.E = 28224 J
Power = 4.00 x 10²
Time = Energy Transferred / Power
Time = 28224 / 4.00 x 10²
Time = 70.56 s
2007-12-13 01:41:48 · answer #5 · answered by Murtaza 6 · 1⤊ 0⤋