HW 013 - hanna (brh687) – hk 13 – Opyrchal – (11105)...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: hanna (brh687) – hk 13 – Opyrchal – (11105) 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points An artificial satellite circling the Earth com- pletes each orbit in 94 minutes. What is the value of g at the location of this satellite? The mass of the earth is 5 . 98 × 10 24 kg and the universal gravitational constant is 6 . 67259 × 10- 11 N · m 2 / kg 2 . Correct answer: 8 . 50223 m / s 2 . Explanation: Let : M earth = 5 . 98 × 10 24 kg , T = 94 min , and G = 6 . 67259 × 10- 11 N · m 2 / kg 2 . ω = 2 π T = 2 π 94 min parenleftbigg 1 min 60 s parenrightbigg = 0 . 00111404 rad / s . The centripetal force is F c = mr ω 2 = GM earth m r 2 , so r = 3 radicalbigg GM earth ω 2 = 3 radicalBigg 6 . 67259 × 10- 11 N · m 2 / kg 2 (0 . 00111404 rad / s) 2 × 3 radicalbig 5 . 98 × 10 24 kg = 6 . 85064 × 10 6 m is the radius of the satellite’s orbit. At this distance from the Earth, F = GM earth m r 2 = mg , so g = GM earth r 2 = 6 . 67259 × 10- 11 N · m 2 / kg 2 (6 . 85064 × 10 6 m) 2 × (5 . 98 × 10 24 kg) = 8 . 50223 m / s 2 . 002 10.0 points Planet X has a mass 7 . 17 times that of the Earth and a radius 2 . 77 times the radius of the Earth. What is the acceleration due to gravity on the surface of Planet X, measured in units of g (the gravitational acceleration on the surface of the Earth)? Correct answer: 0 . 934458 g . Explanation: Let : M X = 7 . 17 M E and R X = 2 . 77 R E . The acceleration due to gravity is a = GM R 2 ∝ M R 2 , so g X g E = R 2 E R X 2 M X M E g X = parenleftbigg R E 2 . 77 R E parenrightbigg 2 parenleftbigg 7 . 17 M E M E parenrightbigg g Earth = . 934458 g ....
View Full Document

This note was uploaded on 04/07/2012 for the course PHYSICS 121 taught by Professor James during the Spring '12 term at University of Texas.

Page1 / 4

HW 013 - hanna (brh687) – hk 13 – Opyrchal – (11105)...

This preview shows document pages 1 - 2. Sign up to view the full document.

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