Three uniform spheres of masses m₁ = 3.00 kg, m₂ = 4.00 kg, and m3 = 6.50 kg are placed at the corners of a right triangle (see figure below). Calculate the resultant gravitational force on the object of mass m2, assuming the spheres are isolated from the rest of the Universe. Ĵ) × 10-11 N Î + (0, 3.00) m 1)x m₁ (-4.00, 0) m F12 m3 32 0 x m2

A spring with unstretched length of 14.3 cm has a spring constant of 4.63 N/m. The spring is lying on a horizontal surface, and is attached at one end to a vertical post. The spring can move freely around the post. The other end of the spring is attached to a puck of mass m. The puck is set into motion in a circle around the post with a period of 1.32 s. Assume the surface is frictionless, and the spring can be described by Hooke's law. (a) What is the extension of the spring as a function of m? (Assume x is in meters and m is in kilograms. Do not include units in your answer.) x = Find x (in meters) for the following masses. (If not possible, enter IMPOSSIBLE.) (b) m = 0.0700 kg m (c) m = 0.140 kg (d) m 0.180 kg m m (e) m = 0.210 kg m

A stuntman whose mass is 62 kg swings from the end of a 4.1-m-long rope along the arc of a vertical circle. Assuming that he starts from rest when the rope is horizontal, find the magnitudes of the tensions in the rope that are required to make him follow his circular path at each of the following points. (a) at the beginning of his motion KN (b) at a height of 1.5 m above the bottom of the circular arc KN (c) at the bottom of the arc KN

(a) A luggage carousel at an airport has the form of a section of a large cone, steadily rotating about its vertical axis. Its metallic surface slopes downward toward the outside, making an angle of 24.5° with the horizontal. A 30.0-kg piece of luggage is placed on the carousel, 7.46 m from the axis of rotation. The travel bag goes around once in 37.5 s. Calculate the magnitude of the force of static friction between the bag and the carousel. N (b) The drive motor is shifted to turn the carousel at a higher constant rate of rotation, and the piece of luggage is bumped to a position 7.94 m from the axis of rotation. The bag is on the verge of slipping as it goes around once every 30.5 s. Calculate the coefficient of static friction between the bag and the carousel.

Shown below is a waterslide constructed in the late 1800's. This slide was unique for its time due to the fact that a large number of small wheels along its length made friction negligible. Riders rode a small sled down the chute which ended with a horizontal section that caused the sled and rider to skim across the water much like a flat pebble. The chute was 9.76 m high at the top and 54.3 m long. Consider a rider and sled with a combined mass of 81.0 kg. They are pushed off the top of the slide from point A with a speed of 2.90 m/s, and they skim horizontally across the water a distance of 50 m before coming to rest. 9.76 m Engraving from Scientific American, July 1888 A (a) 20.0 m -54.3 m 50.0 m (b) (a) Find the speed (in m/s) of the sled and rider at point C. m/s (b) Model the force of water friction as a constant retarding force acting on a particle. Find the magnitude (in N) of the friction force the water exerts on the sled. N (c) Find the magnitude (in N) of the force the…

You have an internship working at a company that designs and produces washing and drying equipment. Your supervisor is in the process of designing a new, very large dryer to be used in commercial establishments with intense laundry needs, such as restaurants (tablecloths, napkins) and hotels (sheets, towels). In a dryer, a cylindrical tub containing wet material is rotated steadily about a horizontal axis as shown in the figure below. 0 So that the material will dry uniformly, it is made to tumble. The rate of rotation of the smooth-walled tub is chosen so that a small piece of cloth will lose contact with the tub when the cloth is at an angle of 0 = 71.0° above the horizontal. Your supervisor's tub is designed to have a radius of r = 1.23 m and she asks you to determine the appropriate rate of revolution. (Give your answer in rev/min.) rev/min

A golf tee is located at precisely ; = 46.5° north latitude, as shown in the figure below. The hole that the golfer is aiming for is directly south of the tee, a distance of 370 m. The golfer hits the ball from this tee with an initial velocity that is 48.0° above the horizontal, and the horizontal component of the ball's initial velocity is directly south. The horizontal range that the golf ball travels in flight is also 370 m, but the golfer is surprised to find that the golf ball does not land in the hole. We will assume that air resistance is negligible for the golf ball. The questions below analyze how the Earth's rotation affects the golf ball's apparent trajectory. North Pole Radius of circular path of tee RECOS ; RE Tee Golf ball trajectory -Hole Equator (a) For what length of time is the ball in flight (in s)? S (b) From the point of view of the golf tee, the ball's horizontal velocity is directed south. However, the golf tee, and therefore the golf ball, are moving east due…

One end of a cord is fixed and a small 0.450-kg object is attached to the other end, where it swings in a section of a vertical circle of radius 3.00 m as shown in the figure below. When 0 = 23.0°, the speed of the object is 7.00 m/s. At this instant, find each of the following i (a) the tension in the cord T = × Your response differs from the correct answer by more than 10%. Double check your calculations. N (b) the tangential and radial components of acceleration a₁ = Your response differs from the correct answer by more than 10%. Double check your calculations. m/s² inward a₁ = m/s² downward tangent to the circle (c) the total acceleration a total = × Your response differs from the correct answer by more than 10%. Double check your calculations. m/s² inward and below the cord at Your response differs from the correct answer by more than 100%.° (d) Is your answer changed if the object is swinging down toward its lowest point instead of swinging up? ○ Yes No ×

One of the more challenging elements in pairs figure skating competition is the "death spiral" (see the figure below), in which the female figure skater, balanced on one skate, is spun in a circle by the male skater. The axis of rotation of the pair is vertical and through the toe of the skate on the male skater's leg that is bent backward, the toe being planted into the ice. During the one-armed maneuver first developed in the 1940s, the outstretched arm of the male skater must apply a large force to support a significant fraction of the female skater's weight and also to provide her centripetal acceleration. This force represents a danger to the structure of the wrist of the male skater. (a) Modeling the female skater, of mass 47.0 kg, as a particle, and assuming that the combined length of the two outstretched arms is 129 cm and that arms make an angle of 45.0° with the horizontal, what is the magnitude of the force (in N) exerted by the male skater's wrist if each turn is completed…