Chapter 17, Problem 6CQ

Consider the series M8 3 ཱ|༤༠ n=0 5n a. Find the general formula for the sum of the first k terms. Your answer should be in terms of k. Sk=3 1 5 5 k b. The sum of a series is defined as the limit of the sequence of partial sums, which means k 3 5n 1- = lim 3 k→∞ n=0 4 15 4 c. Select all true statements (there may be more than one correct answer): A. The series is a geometric series. B. The series converges. C. The series is a telescoping series (i.e., it is like a collapsible telescope). D. The series is a p-series.

A uniform ladder of length L and weight w is leaning against a vertical wall. The coefficient of static friction between the ladder and the floor is the same as that between the ladder and the wall. If this coefficient of static friction is μs : 0.535, determine the smallest angle the ladder can make with the floor without slipping. ° = A 14.0 m uniform ladder weighing 480 N rests against a frictionless wall. The ladder makes a 55.0°-angle with the horizontal. (a) Find the horizontal and vertical forces (in N) the ground exerts on the base of the ladder when an 850-N firefighter has climbed 4.10 m along the ladder from the bottom. horizontal force magnitude 342. N direction towards the wall ✓ vertical force 1330 N up magnitude direction (b) If the ladder is just on the verge of slipping when the firefighter is 9.10 m from the bottom, what is the coefficient of static friction between ladder and ground? 0.26 × You appear to be using 4.10 m from part (a) for the position of the…

Your neighbor designs automobiles for a living. You are fascinated with her work. She is designing a new automobile and needs to determine how strong the front suspension should be. She knows of your fascination with her work and your expertise in physics, so she asks you to determine how large the normal force on the front wheels of her design automobile could become under a hard stop, ma when the wheels are locked and the automobile is skidding on the road. She gives you the following information. The mass of the automobile is m₂ = 1.10 × 103 kg and it can carry five passengers of average mass m = 80.0 kg. The front and rear wheels are separated by d = 4.45 m. The center of mass of the car carrying five passengers is dCM = 2.25 m behind the front wheels and hcm = 0.630 m above the roadway. A typical coefficient of kinetic friction between tires and roadway is μk 0.840. (Caution: The braking automobile is not in an inertial reference frame. Enter the magnitude of the force in N.)…