A light, rigid rod is 50.2 cm long. Its top end is pivoted on a frictionless horizontal axle. The rod hangs straight down at rest with a small, massive ball attached to its bottom end. You strike the ball, suddenly giving it a horizontal velocity so that it swings around in a full circle. What minimum speed at the bottom is required to make the ball go over the top of the circle? m/s
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- A car is traveling at constant speed of v = 29 m/s. Its tires have a diameter of d = 0.53 m.v = 29 m/sd = 0.53 m Consider a point on the outer edge of the tire. What is the centripetal acceleration, ac, at this point in m/s2? ac = If the car was traveling twice as fast, what would be the numerical value of the ratio of the new centripetal acceleration, an, to the old centripetal acceleration? an/ac =A motorcycle, starting from rest, accelerates at 2.87 m/s2 on a circular track with a 205 m diameter. What is the elapsed time, in seconds, at which the centripetal acceleration of the motorcycle has the same magnitude as its tangential acceleration?The drawing shows a version of the loop-the-loop trick for a small car. The radius of the loop r = 0.46 m. What is minimum initial speed (v) that the car needs to have in order to remain in contact with the circular track at all times? m/s
- A car travels at a constant speed around a circular track whose radius is 3.82 km. The car goes once around the track in 246 s. What is the magnitude of the centripetal acceleration of the car? Number i UnitsA car initially traveling eastward turns north by traveling in a circular path at uniform speed as shown in the figure below. The length of the arc ABC is 257 m, and the car completes the turn in 39.0 s. 35.0° (a) Determine the car's speed. m/s (b) What is the magnitude and direction of the acceleration when the car is at point B? magnitude |m/s² direction ° counterclockwise from the +x-axisWhich is the correct option?
- A particle is moving in a circle of radius R. At t = 0, it is located on the x-axis. The angle the particle makes with the positive x -axis is given by 0 = At² + Bt³ What is the magnitude of the tangential acceleration, atan of the particle at a time t > 0? Express your answer in terms of R, t, A, and B as needed. What is the magnitude of the radial acceleration, larad of the particle at a time t > 0? Express your answer in terms of R, t, A, and B as needed.In a laboratory test of tolerance for high acceleration, a pilot is swung in a circle 15.0 m in diameter. It is found that the pilot blacks out when he is spun at 30.6 rpm (rev/min). At what acceleration (in SI units) does the pilot black out? acceleration: 77.01 m/s? Express this acceleration in terms of a multiple of g. acceleration as a multiple of g: 7.858 If you want to decrease the acceleration by 22.0% without changing the diameter of the circle, by what percent must you change the time for the pilot to make one circle? percent of time change:E. The centripetal acceleration of a particle moving in a circle is given by the formula a = s²/r where r is the radius and s is the speed of the particle. a) Consider a as a function of s and r. Compute the differential of a. b) Suppose that the particle is moving with speed 50cm/sec and the radius is 10cm. Use the differential to estimate the change in centripetal acceleration if the radius is changed to 9.80cm and the speed is changed to 51cm/sec. (Answ: 15) c) Suppose that the speed can be measured to within +3% and the radius can be measured to within +2%. Use the differential to approximate the maximum percent error in a. (Hint: The percent error in a quantity is the error in the quantity (da) divided by the quantity (a).) (Ans: 8%)
- An object is moving counterclockwise around a circular track at a constant speed of 3 m/s. The track is centered at the origin and has a radius of 1 m. What is the object's acceleration vector when it is at point P shown? y. P -(3플)i ○금3 + (3프) i a = +(9) i m Oa = 0 -(9플)iYou re out in space, on a rotating wheel-shaped space station of radius 679 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). 0.120 rpm 81.6 rpm 0.459 rpm 1.148 rpmIn the movie Kill Bill the character Gogo Yubari fights with a meteor hammer, which is a bladed metal sphere on the end of a chain. Let’s assume Gogo is spinning the meteor hammer in a vertical spin, as shown below, with a radius of motion as 1 m. She spins the weapon at 18 m/s. Gogo then lets out more chain, increasing the radius to 1.62 m. What is the new velocity of her weapon?