At the surface of a certain planet, the gravitational accelerationg has a magnitude of 12.0 m/s2. A 13.0-kg brass ball istransported to this planet. What is (a) the mass of the brassball on the Earth and on the planet, and (b) the weight ofthe brass ball on the Earth and on the planet?
× ⃗⃗1⃗⃗2⃗⃗⃗3⃗ } ⃗3⃗ 2⃗⃗ ⃗1⃗⃗ ⃗3⃗⃗ = 1 1⃗⃗ +2 2⃗⃗⃗ 1⃗⃗2⃗⃗3⃗ } ⃗1⃗⃗2⃗⃗ } ⃗1⃗⃗2⃗ } = { , ,…, } ⃗⃗⃗⃗ 1 2 = 1 1 2 2⋯+ ⃗⃗ 1,2,…, ⃗ 1 [] = [ ] ⋮ ↦ [ ] ↦ => 3 −1 1= [6],2= [0 ] 2 1 3 −1 = {6 ] [0 ]} 2 1 ⃗ = ⃗ ( − ) 3. det( − ) = 0 1 3 −5 [0 2 4 ] 0 0 7 − ) = 0 1 − 3 −5 ( 0 2 − 4 ) = 0 0 0 7 − − 1 − 2 − 7 − = 0 => = 1,2,7 1,2,…, 1,2,…, 1,2,…, 10 0 0 0 1 0 0 [0 −4 0] [−2 0 ] [0 −5 0 0] 0 0 5 0 4 0 0 −7 0 0 0 0 6 1,2,…, , ,…, × ⃗ ⃗ ,) | ⃗ − | ⊥ ⊥ ⊥ ⊥ ( ) = ( ) = . = − = = ̂ + ̂ ⃗ ) ̂ = 1 1⃗⃗ +2 2⃗⃗ + ⋯+ ⃗⃗ .⃗⃗ = 2 | ⃗⃗ | = − ̂ 6 −2 −1 [−2 6 −1] −1 −1 5 −1 −1 1 = 8,⃗1⃗⃗ =1[]; = 6,⃗2⃗⃗ −1[]; = 3,⃗3⃗ = 1 ] 0 2 1 1⃗⃗2⃗ ⃗3⃗ 1 1 1 − − 2 √6 √3 √ 1 1 ⃗1⃗ = 1 ; ⃗2⃗⃗ =− √6 ; ⃗3⃗⃗ =√3 √ 2 [ ] 2 1 0 [ √6 ] [√3] − 1 − 1 1 8 0 0 √2 √6 √3 1 1 1 = [0 6 0 ] = √2 − √6 √3 0 0 3 2 1 [ 0 √6 √3] ×
