# HW13 - homework 13 PAPAGEORGE MATT Due 4:00 am Solution The...

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homework 13 – PAPAGEORGE, MATT – Due: Feb 19 2008, 4:00 am 1 Question 1, chap 6, sect 2. part 1 of 1 10 points A load of 66 N attached to a spring hanging vertically stretches the spring 2 cm. The spring is now placed horizontally on a table and stretched 12 cm. What force is required to stretch it by this amount? Correct answer: 396 N (tolerance ± 1 %). Explanation: Given : F = 66 N , x 1 = 2 cm , and x 2 = 12 cm . The force exerted by the spring is F 1 = k x 1 k = F 1 x 1 . When stretched 12 cm, F 2 = k x 2 = F 1 x 2 x 1 = (66 N) (12 cm) 2 cm = 396 N . Question 2, chap 6, sect 2. part 1 of 2 10 points A 0 . 56 kg mass is attached to a spring with a spring constant 101 N / m so that the mass is allowed to move on a horizontal frictionless surface. The mass is released from rest when the spring is compressed 0 . 137 m. Find the maximum force on the mass. Correct answer: 13 . 837 N (tolerance ± 1 %). Explanation: Basic Concepts: F = m a F = k x The maximum force and acceleration occur at the maximum amplitude of the motion. Solution: The force on the mass is F = k x = (101 N / m) (0 . 137 m) = 13 . 837 N . Question 3, chap 6, sect 2. part 2 of 2 10 points Find the maximum acceleration. Correct answer: 24 . 7089 m / s 2 (tolerance ± 1 %). Explanation: The acceleration is a = F m = 13 . 837 N 0 . 56 kg = 24 . 7089 m / s 2 . Question 4, chap 6, sect 3. part 1 of 2 10 points The coefficient of static friction between the person and the wall is 0 . 75 . The radius of the cylinder is 6 . 12 m . The acceleration of gravity is 9 . 8 m / s 2 . An amusement park ride consists of a large vertical cylinder that spins about its axis fast enough that any person inside is held up against the wall when the floor drops away. ω 6 . 12 m What is the minimum angular velocity ω min needed to keep the person from slip- ping downward? Correct answer: 1 . 46119 rad / s (tolerance ± 1 %). Explanation:

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homework 13 – PAPAGEORGE, MATT – Due: Feb 19 2008, 4:00 am 2 Let : R = 6 . 12 m and μ = 0 . 75 . Basic Concepts: Centripetal force F = m v 2 r . Frictional force f μ N = f max .
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