A bucket containing water is tied to one end of a rope 8 m long and rotated about the other end in vertical circle. Find the minimum number of rotations per minute in order that water in the bucket may not spill? (g = 9.8 m/s²)
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- A planet orbits a star, in a year of length 3.58 x 107 s, in a nearly circular orbit of radius 2.02 x 10¹¹ m. With respect to the star, determine (a) the angular speed of the planet, (b) the tangential speed of the planet, and (c) the magnitude of the planet's centripetal acceleration. (a) Number i (b) Number (c) Number i Units Units UnitsA planet orbits a star, in a year of length 2.88 x 107 s, in a nearly circular orbit of radius 1.85 x 10¹¹ m. With respect to the star, determine (a) the angular speed of the planet, (b) the tangential speed of the planet, and (c) the magnitude of the planet's centripetal acceleration.The International Space Station has a mass of 440,725 kg and is located 420 km away from the surface of the earth. Earth has a mass of 5.97 x 1024 kg and a radius of 6371 km. How quickly does the ISS travel as it orbits the earth, assuming uniform circular motion? Express your answers in rev/day (for angular velocity) and mph (for tangential velocity). Define ALL variables.
- George swings a ball around him, in uniform circular motion. The circle's radius is r. George inadvertently releases the string, and the ball goes outward. He catches the string again, and now the ball goes around him at a new rotation rate, with a new radius r + Δr. Calculate the new rotation rate (in rev/s). r = 3.0 m Δr = 1.0 m Original rotation rate = ωi = 1.1 rev/s The ball's mass is m = 160 gramsA bucket containing water is tied to one end of a rope 5 m long and it is rotated in a vertical circle about the other end. Find the number of rotations per minute in order that the water in the bucket may not spill.A centrifuge is a common laboratory instrument that separates components of differing densities in solution. This is accomplished by spinning a sample around in a circle with a large angular speed. Suppose that after a centrifuge in a medical laboratory is turned off, it continues to rotate with a constant angular deceleration for 10.7s before coming to rest.How many revolutions did the centrifuge complete after being turned off?Δθ= (?) rev
- A parachutist jumps out of an airplane and accelerates with gravity to a maximum velocity of 68.6 m/s in 7.00 seconds. She then pulls the parachute cord and after a 2.7-second constant deceleration, descends at 10.5 m/s for 3.6 * 10' seconds, reaching the ground. From what height did the parachutist jump? answer in meters. (assume g = 9.8 m/s? )An air puck of mass 0.30 kg is tied to a string and allowed to revolve in a circle of radius 1.3 m on a frictionless horizontal table. The other end of the string passes through a hole in the center of the table, and a mass of 1.5 kg is tied to it. The suspended mass remains in equilibrium while the puck on the tabletop revolves. (a) What is the tension in the string? N (b) What is the force causing the centripetal acceleration on the puck? (c) What is the speed of the puck? m/s Need Help? Read ItA rocket powered car is set inside a circular track and ignited. Pressure sensors on the wall of the track measure the centripetal acceleration of the car as a function of time to be ac (t) = (9 m/s®) tª + (42 m/s*) t² + (49 m/s³) If the radius of the track is 2.28 m, what is the tangential acceleration of the rocket car at t = 6.76 s? tangential acceleration: m/s?
- You are swinging a 0.45 kg water balloon vertically. The distance from your shoulder (acting as the center of rotation) and the water balloon is about 0.70 m. You estimate the water balloon is traveling at 6.0 m/s. At the very bottom of the circular path, how much force is your hand holding the water balloon?A small object of mass 0.500 kg is attached by a 0.840 m-long cord to a pin set into the surface of a frictionless table top. The object moves in a circle on the horizontal surface with a speed of 8.80 m/s. What is the magnitude of the radial acceleration of the object?