Nonuniform ball. In the figure, a ball of mass M and radius R rolls smoothly from rest down a ramp and onto a circular loop of radius 0.51 m. The initial height of the ball is h = 0.40 m. At the loopbottom,the magnitude of the normal force on the ball is 1.95M.. The ball consists of an outer spherical shell (of a certain uniform density) that is glued to a central sphere (of a different uniformdensity). The rotational inertia of the ball can be expressed in the general form I = BMR2, but B is not 0.4 as it is for a ball of uniform density. Determine B.

Write a given values of this question. R=0.51mh=0.40mI=βMR2 Normal force on a ball. FN=1.95Mg…

Nonuniform ball. In the figure, a ball of mass M and radius R rolls smoothly from rest down a ramp and onto a circular loop of radius 0.51 m. The initial height of the ball is h = 0.40 m. At the loop bottom, the magnitude of the normal force on the ball is 1.95Mg. The ball consists of an outer spherical shell (of a certain uniform density) that is glued to a central sphere (of a different uniform density). The rotational inertia of the ball can be expressed in the general form I = BMR2, but B is not 0.4 as it is for a ball of uniform density. Determine B.

Nonuniform ball. In the figure, a ball of mass M and radius R rolls smoothly from rest down a ramp and onto a circular loop of radius 0.51 m. The initial height of the ball is h = 0.40 m. At the loop bottom, the magnitude of the normal force on the ball is 1.95Mg. The ball consists of an outer spherical shell (of a certain uniform density) that is glued to a central sphere (of a different uniform density). The rotational inertia of the ball can be expressed in the general form I = BMR2, but B is not 0.4 as it is for a ball of uniform density. Determine B.

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter11: Dynamics Of Rigid Bodies

Section: Chapter Questions

Problem 11.10P

See similar textbooks

Similar questions

Consider the Atwood machine, where two masses m1 = 12.6 kg and m2 = 4.2 kg are connected by an ideal wire that passes through a pulley of mass M = E of radius R = 0.15 m. The pulley is attached, but can rotate freely around its axis of symmetry. As shown in the Figure below, at the initial instant the mass m1 is at a height h= 3.29 m in relation to m2. Knowing that the system starts from rest, and that the magnitude of the linear velocity of m1 when the masses pass through the same vertical position is v=3.31 m/s, what is the mass M of the pulley? Here, assume the acceleration due to gravity as g=10 m/s², the pulley moment of inertia as I=MR2 and, finally, that the wire does not slide on the pulley. Choose one: a. 4,2 kg b. 14,7 kg c. 10,5 kg d. 6,3 kg e. 12,6 kg f. 16,8 kg g. 8,4 kg h. None of the other alternatives.
Prove that the moment of inertia of a solid cylinder of uniform density, when rotating around its central axis,is MR2/2, where M is the mass of the cylinder and R is its radius. Hint: integrate the infinitesimal volume element in cylindrical coordinates
Consider two blocks glued to the top of a disk that is turning at a non-zero angular speed, one block 10 cm out from the center, one 20 cm out from the center. The magnitude of the linear acceleration of the block 20 cm out is the magnitude of the linear acceleration of the block 10 cm out from the center. Group of answer choices a) half b) the same as c) twice
You are the technical consultant for an action-adventure film in which a stunt calls for the hero to drop off a 19-m-tall building and land on the ground safely at a final vertical speed of 5 m/s. At the edge of the building's roof, there is a 100-kg drum that is wound with a sufficiently long rope (of negligible mass), has a radius of 0.4 m, and is free to rotate about its cylindrical axis with a moment of inertia I0. The script calls for the 76-kg stuntman to tie the rope around his waist and walk off the roof. (a) Determine an expression for the stuntman's linear acceleration in terms of his mass m, the drum's radius r, and moment of inertia I0. (b) Determine the required value of the stuntman's acceleration if he is to land safely at a speed of 5 m/s.
Note: Because the arguments of the trigonometric functions are unitless in this question, your calculator must be in radian mode if you use it to evaluate any trigonometric functions. When powered up, a disk drive starts at rest and spins up with non-uniform angular acceleration according to the following formula: =asin(bt) where a = 708 radians/s2 and b = 1.74 s-1. This lasts for the first 1.81 seconds, after which the drive does not accelerate. How many meters of disk surface have passed underneath the head in 0.79 seconds?
a particle of mass m is dropped from a height h, located at latitude λ (north), find an expression for the distance S from the point on the ground directly below the point where the body is dropped to the point at which the body reaches the ground neglecting air resistance and the quadratic terms of the angular velocity of the earth
Compute for the total moment of pt. A and pt. B Ps. with complete solution without any shortcuts, please
a solid brass ball of mass 0.280 g will roll smoothly along a loop-the-loop track when released from rest along the straight section. The circular loop has radius R = 14.0 cm, and the ball has radius r < R. (a) What is h if the ball is on the verge of leaving the track when it reaches the top of the loop? If the ball is released at height h = 6.00R, what are the (b) magnitude and (c) direction of the horizontal force component acting on the ball at point Q?
Consider the system in the figure, in which a small mass m = 1.95 kg is sliding off the top of a cylindrical object. There is no friction between the mass and the cylinder, which has a radius of r = 0.46 m. At what height, relative to the bottom of the cylinder, will the mass leave the surface of the cylinder?
A ball is dropped from height h by someone standing still on the earth’s equator. (a) Does it fall to the east or west of a point just beneath the position from which it was dropped? (b) When it strikes the ground, how far is the ball from the point originally directly beneath it, in terms ofg, h, and ω, earth’s angular velocity? (Pretend there is no air resistance.) (c) Explain the direction found in (a) using conservation of the ball’s angular momentum in the inertial frame in which earth rotates toward the east.
A ship's wheel can be approximated as an annular cylinder (different from a ring) of mass 6.7 kilograms, inner radius 25 centimeters, and outer radius 32 centimeters; and eight spokes of mass 0.50 kilograms and length 49 centimeters. a. What is the moment of inertia? Include units in your answer. b. Disagreeing over which way to go, the captain and the helmsman try to turn the wheel in opposite directions. The captain applies a force of 311 newtons at the inner radius, while the helmsman applies a force of 287 newtons at the outer radius. What is the magnitude of the angular acceleration of the wheel? Include units in your answer. PLEASE ANSWER IN HANDWRITING
A child of mass m stands at rest nearthe rim of a stationary merry-go-round of radius R and moment ofinertia I. The child now begins to walk around the circumference ofthe merry-go-round with a tangential speed v with respect to themerry-go-round’s surface. (a) What is the child’s speed with respectto the ground? Check your result in the limits (b) I S 0 and (c) I S ∞.