solC3-1sample08

solC3-1sample08 - SOLUTIONS TO CALCULUS III SAMPLE MIDTERM...

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

View Full Document Right Arrow Icon
SOLUTIONS TO CALCULUS III SAMPLE MIDTERM 1 Problem 1. (10 points) A clothesline is ted between two poles, 8 m apart. The line is quite taut and has negligible sag. When a wet shirt with a mass of 0.8 kg is hung at the middle of the line, the midpoint is pulled down 8 cm. Find the tension in each half of the clothesline. Solution: 0.8 x 9.8 N b 8 cm 4 m 4 m x y θ θθ θ T 2 T 1 The angle θ is determined by tan θ = 8 cm 4 m = 0 . 08 4 = 0 . 02 . Denote the tensions by v T 1 and v T 2 . In the coordinate system, the Newton’s ±rst law gives two equations, in x -component and y -component respectively. −| v T 1 | cos θ + | v T 2 | cos θ = 0 | v T 1 | sin θ + | v T 2 | sin θ = 0 . 8 × 9 . 8 (N) . The ±rst equation says | v T 1 | = | v T 2 | , and then the second becomes 2 | v T 1 | sin θ = 0 . 8 × 9 . 8 (N). Compute sin θ , sin θ = 1 csc θ = 1 1 + cot 2 θ = 1 r 1 + ( 1 0 . 02 ) 2 = 1 1 + 2500 1 2500 = 0 . 02 The magnitudes of the tensions are | v T 1 | = | v T 2 | = 0 . 8 × 9 . 8 2 sin θ = 0 . 8 × 9 . 8 0 . 04 = 20 × 9 . 8 = 196 N 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
2 Problem 2. (10 points) Given two planes z = x + y, 2 x 5 y z = 1 .
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.

This note was uploaded on 11/02/2009 for the course MATH V1201 taught by Professor Perutz during the Spring '08 term at Columbia.

Page1 / 3

solC3-1sample08 - SOLUTIONS TO CALCULUS III SAMPLE MIDTERM...

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