calculate the thickness of a 30cm by 30 cm sheet of aluminum foil (density 2.7g/cm^3) if it has a mass of four grams.
Mass of piano 1.6910^2160 kg Height h 18.0 m Power 4.00 10^2 W Power(P)time(t) work done w mgh Ptmgh t mgh / P t 1609.818 / 410^2 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
4 g / 2.7g/cm? 1.48 cm?, the volume Volume L x W x thickness thickness 1.48 / 3030 0.00165 cm or 0.0165 mm or 16.5 ?m
Power Energy Transferred / Time taken Energy Transferred Gain in G.P.E G.P.E mass x gravity acceleration x height G.P.E 1.60x10? x (9.8) x (18.0) G.P.E 28224 J Power 4.00 x 10? Time Energy Transferred / Power Time 28224 / 4.00 x 10? Time 70.56 s
The work needed to lift the piano through a distance of 18m is Force x distance mgh1609.818J Power is rate of doing work work / time 1609.818 /t It is given that the power is 400 W 400 J/s1609.818 /t 400 t 1609.818 / 400 70.56s.
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 / timeGravitational 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 heightThe gravitational potential energy is the same value that you would use in the power equationTherefore 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 gett 9.8 18 t is for time taken.
