1. A box slides a chute, which is bent in the shape of a hyperbola. When the box reaches the point x = 5m, it has a speed of 5m/s and the speed is decreasing at the rate of 0.5 m/s?. Determine the normal and 10 xy = 10 tangential components of the acceleration of the box. 10 x, (m) (u)

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1. A stopwatch starts while race car travels at 13 m/s from the pit area and accelerates at a uniform rate to a speed of 37 m/s in 5 s moving on a circular track of radius 548 m. Assuming constant tangential acceleration, find (a) the tangential acceleration, and (b) the radial acceleration,at the instant when the speed is v=7 Once you have both of those…. find the magnitude of a at any moment a= 2. A stopwatch starts while race car travels at 5 m/s from the pit area and accelerates at a uniform rate to a speed of 23 m/s in 16 s moving on a circular track of radius 466 m. Assuming constant tangential acceleration, find (a) the tangential acceleration, and (b) the radial acceleration,at the instant when the speed is v=15 Once you have both of those …. find the magnitude of a at any moment a= 3. A stopwatch starts while race car travels at 7.0 m/s from the pit area and accelerates at a uniform rate to a speed of 22 m/s in 3 s moving on a circular track of radius 491 m. Assuming constant…

4. Given the path, find a decomposition of the acceleration vector à(t) into tangential and normal components at the point indicated. T(t) = (cos t, sin t, t) : at t = T

Cross country runners must turn a corner around a tree obstacle, in the rain. a) The first runner takes a wide line to the tree and runs around a curve with a radius of 1.5 m and undergoes a radial acceleration of 10 m/s2. Determine their tangential velocity during the curve. b) The second runner is trying to catch up and so runs closer to the tree. If a loss of control (slip) occurs at a radial acceleration of 22 m/s2, does the runner manage to run around a curve with a radius of 0.50 m at a tangential velocity of 3.5 m/s?

Chapter 5 Problem 8: BIO Ultracentrifuge You are working in a biology lab and learning to use a new ultracentrifuge for blood tests. The specifications for the centrifuge say that a red blood cell rotating in the ultracentrifuge moves at and has a radial acceleration of 150,000 g’s (that is, 150,000 times ). The radius of the centrifuge is 0.15 m. You wonder if this claim is correct. Support your answer with a calculation.

Question 4. A single bead can slide without friction on a vertical hoop of radius r. The hoop rotates about its vertical axis and makes one complete revolution in T seconds. The position of the bead is described by the angle 0. At what 0 > 0 can the bead stay stationary while the hoop rotates? r

10. You're out in space, on a rotating wheel-shaped space station of radius 551 m. You feel planted firmly on the floor , due to artificial gravity. The gravity you experience is Earth-normal, that is, g = 9.81 m/s^2. How fast is the space station rotating in order to produce this much artificial gravity? Express your answer in revolutions per minute (rpm).      1.019 rpm      1.274 rpm      0.133 rpm      73.5 rpm