A solid 5.3 kg sphere of diameter 13 cm rolls up a ramp that is at 30° relative to the horizontal. At the bottom of the ramp the center of mass of the sphere has a translational speed of 1.2 m/s. a. What is the kinetic energy of the sphere at the bottom of the ramp? b. How far up the ramp does the sphere go? c. If the mass of the sphere doubles and the radius is tripled, how does the answer to part b change? Explain.
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A solid 5.3 kg sphere of diameter 13 cm rolls up a ramp that is at 30° relative to the horizontal. At the bottom of the ramp the center of mass of the sphere has a translational speed of 1.2 m/s.
a. What is the kinetic energy of the sphere at the bottom of the ramp?
b. How far up the ramp does the sphere go?
c. If the mass of the sphere doubles and the radius is tripled, how does the answer to part b change? Explain.
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- A uniform solid sphere with a radius of 0.120 m has a mass of 1.60 kg. The sphere is rolling along a horizontal surface, without slipping, at a constant speed of 4.75 m/s. a. What is the kinetic energy of the sphere due to its translational motion along the surface? b. What is the rotational inertia of the sphere about an axis of rotation through its center of mass?5. A child riding a merry-go-round that rotates with constant angular speed (radius r = 5.0 m) can hold onto the handle with a maximum grip force of FG = 0.01 N. The child has a mass of 40.0 kg. a. Draw a free-body diagram for the child and indicate the direction of their acceleration. b. Calculate the maximum linear speed of the edge of the merry-go-round that the child can withstand before falling off.A rigid object rotates in a counterclockwise sense around a fixed axis. Each of the following pairs of quantities represents an initial angular position and a final angular position of the rigid object. (i). Which of the sets can only occur if the rigid object rotates through more than 180°? a. 3 rad, 6rad b. -1 rad, 1 rad c. 1 rad, 5 rad (ii). Suppose the change in angular position for each of these pairs of values occurs in 1 second. Which choice represents the lowest average angular speed?
- A typical small rescue helicopter has four blades: Each is 4.00 m long and has a mass of 50.0 kg. The blades can be approximated as thin rods that rotate about one end of an axis perpendicular to their length (I = (Ml^2)/3). The helicopter has a total loaded mass of 1000 kg. a.) Calculate the rotational kinetic energy in the blades when they rotate at 300 rpm. b.) Calculate the angular momentum of the four combined blades when they rotate at 300 rpm (Hint: Find the angular momentum for one blade and multiply it by 4).7. You are asked to design a turntable that is 55.8 cm in diameter that has a kinetic energy of 0.250 J when it is turning at 45.0 rev/min. a. What must its moment of inertia be? b. If you make the turntable in the shape of a uniform solid disk, what mass would it have?4. A pinball of mass M and radius R is pushed against a spring of spring constant k. The spring is compressed a distance D and the pinball machine ramp is inclined at an angle 0. The spring is then released. The pinball is a solid metal sphere that rolls without slipping. a. Determine the speed of the pinball as it leaves the spring. Hint: the spring force is not constant so you cannot use constant acceleration kinematics. Use conservation of mechanical energy instead. b. What is the distance that the pinball would go up the ramp before coming back down?
- Ethan and Joseph are riding on a merry-go-round. Ethan rides on a horse at the outer rim of the circular platform, twice as far from the center of the circular platform as Joseph, who rides on an inner horse. i. When the merry-go-round is rotating at a constant angular speed, what is Ethan's angular speed? a. Twice Joseph's b. The same as Joseph's c. Half of Joseph's d. Impossible to determine ii. When the merry-go-round is rotating at a constant angular speed, describe Ethan's tangential speed from the same list of choices?A 4m board weighing 60 N extends out over the edge of the table with 40% of the board's length off the table. How far beyond the table can a 20N cat walk before the board begins to tilt Meow, O A. 1.2 m О В. 1.5 m о С. 1.1 m O D. 1.4 m O E. None of the abovea. What is the angular velocity of the two after the collision?b. What is the kinetic energy before and after the collision?c. What is the total linear momentum before and after the collision?
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