I-sol - Chapter I - Problems Blinn College - Physics 2425 -...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Chapter I - Problems Blinn College - Physics 2425 - Terry Honan Problem I.1 A 200 kg mass sits at x = 0 and a 500 kg mass sits at x = 0.4 m. (a) What is the net gravitational force on a 50 kg mass at the midpoint of the two, x = 0.2 m. (b) Where on the x axis would the net force on a third mass be zero. Solution to I.1 m 1 = 200 kg and m 2 = 500 kg (a) The force on m = 50 kg is the sum of the forces of m 1 and m 2 on m . F 1 = G m 1 m r 1 2 = 6.67 μ 10 - 11 200 μ 50 0.2 2 = 1.6675 μ 10 - 5 N F 2 = G m 2 m r 1 2 = 6.67 μ 10 - 11 500 μ 50 0.2 2 = 4.1688 μ 10 - 5 N F net = F 1 + F 2 . Since the forces are in opposite directions we should subtract their magnitudes. F net = F 2 - F 1 = 2.50 μ 10 - 5 N (b) Take the distances from m 1 and m 2 to be x and x - d , where d = 0.4 m . F 2 = F 1 ï G m 1 m x 2 = G m 2 m H d - x L 2 ï d - x x = m 2 ê m 1 ï d = x + x m 2 ê m 1 ï x = d 1 + m 2 ë m 1 = 0.4 1 + 5 ê 2 = 0.155 m Problem I.2 Consider a 80000 kg uniform solid sphere with a 1.2 m. What is the gravitational field a distance of r from the center for the values: (a) r = 0, (b) r = 0.6 m, (c) r = 1.2 m, (d) r = 2.4 m Solution to I.2 The gravitational field g is defined as the force per test mass, g = F ë m 0 . Here we are just looking for the magnitude of the field. The shell theorem implies the force and field at r go as F = G M inside m 0 r 2 ï g = F m 0 = G M inside r 2 where M inside is the total mass inside a sphere of radius r . Here take M = 80000 kg and R = 1.2 m. When outside the sphere M inside is just M .
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
r ¥ R ï M inside = M When inside the sphere M inside depends on the fraction of the total volume inside r : call this V inside . r
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 5

I-sol - Chapter I - Problems Blinn College - Physics 2425 -...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online