Question

please help with question 1 and 4a, 4b

1) A planet of mass 5 x 1024 kg is at location <1 x 1011,5 x 1011,0 > m. A star of mass 5 x 10" kg is at location < 7 X 10", 10 X 10",0 > m. What is the gravitational force exerted on the planet by the star? Express your answer as a 3-component vector. It may be useful to draw a diagram of the situation, including the relevant vectors. (5 pts)

Answer 1

(1) Directi on of force exerted on a planet by the star in the unit vector notati on can be expressed as follows: Ar = (7x10",10x10",0)- (1×10",5×10",0) = (6x10", 5x10",0)m Ar|= (6x10" m)" +(5x10" m) =7.81x10"m Ar Ar| (6x10",5x10", 0) 7.81x10"m = (0.768,0.64,0) Gravitati onal force exerted on the planet by the star is, Gm,m, F = (6.67x10-" N.m2/kg)(5x10* kg)(5×10º kg), (7.81×10" m) =(2.7337x10), = (2.7337x10")(0.768,0.64,0) = (2.0995x1021 1.749x1021,0) (2.1x101 1.75x101,0)N (or) (2.71x101)+(1.75x10")+0k N

(4) The youngs modulus of the materi al is, Stress Y= Strain Stress is the force acting per unit area. Stress=: Strain is the change length per original length. AL Strain= Therefore, AL Stress = y AL Ay F(L A AL mg (4 ()AL, (10kg) (9.8m/s*) 2.0m 2.1x103 m 1.0×10-3m) = 1.19x10" N/m? 81.2x10" N/m? (b) Bond length b/w atoms can be calculated as foll ows: 1/3 Zm ON 1/3 (29)64 8.9(6.023x103) = 7.02x10-10 m Relation b/w inter atomic spring stiffness (k) & bond length (1)is, k = Y! =(1.2x10" N/m?)(7.02x10-10 m = 84.2N/m