Concept explainers
(a)
The acceleration of the center of mass of the spherical shell
(a)
Answer to Problem 90P
Explanation of Solution
Given:
The coefficient of static friction =
Angle of inclination =
Formula used:
Torque is defined as,
F is the applied force on the object and r is the position vector from axis of rotation to the applied force
Acceleration of the object in terms of
Here I is the moment of inertia and
Calculation:
Consider the static friction on the shell is
Torque on the shell by static friction,
Now, by second law of motion for rotation:
Net force along the x axis,
By second law of motion
Conclusion:
The center of mass of the spherical shell is
(b)
The frictional force acting on the ball
(b)
Answer to Problem 90P
The frictional force acting on the ball is
Explanation of Solution
Given:
From part a),
Expression for the frictional force,
Acceleration of the center of mass of the spherical shell,
Calculation:
Since expression of the static friction,
Substitute the values:
Conclusion:
The static friction on the shell is
(c)
The maximum angle of the inclination for which the ball rolls without slipping
(c)
Answer to Problem 90P
Explanation of Solution
Given:
From part a),
Expression for the frictional force,
Acceleration of the center of mass of the spherical shell,
Calculation:
Net force along the y axis,
Since, there is no any acceleration along the y axis, so,
Maximum static friction,
Now, torque on the shell,
By 2nd law of motion for rotation, we get,
Now, net force along the x axis,
Now, by 2nd law of motion, we get,
Now, let’s plug the value of
At the maximum acceleration,
Conclusion:
The maximum angle is
Want to see more full solutions like this?
Chapter 9 Solutions
Physics for Scientists and Engineers
- A skateboarder is attempting to make a circular arc of radius r = 19 m in a parking lot. The total mass of the skateboard and skateboarder is m = 98 kg. The coefficient of static friction between the surface of the parking lot and the wheels of the skateboard is μs = 0.66. The maximum speed he can go without slipping is 11.09 m/s. He speeds up very slightly and begins to slide. The coefficient of kinetic friction is μk = 0.11. What is the new magnitude of his radial acceleration in m/s2?arrow_forwardA wheel of radius 0.269 m, which we can model as a thin disk, is mounted on a frictionless horizontal axis. The mass of the wheel is 2.44 kg. A massless cord wrapped around the wheel is attached to a block of 4.16 kg that slides on a horizontal frictionless surface. If a horizontal force P with a magnitude of 10.1 N is applied to the block as shown below. If the wheel and block start at rest, and the block is moved through a displacement of 2.60 m what is the final angular velocity of the wheel in rad/s, assuming the cord does not slip. Parrow_forwardA block of mass m₁ = 1.60 kg and a block of mass m₂ = 5.75 kg are connected by a massless string over a pulley in the shape of a solid disk having a mass of M = 10.0 kg. The fixed, wedge-shaped ramp makes an angle of 8 = 30.0° as shown in the figure. The coefficient of kinetic friction is 0.360 for both blocks. M, R m₁ m2 (a) Determine the acceleration of the two blocks. (Enter the magnitude of the acceleration.) m/s² (b) Determine the tensions in the string on both sides of the pulley. left of the pulley N right of the pulley Narrow_forward
- One end (A) of a thin rod rests on a floor, with coefficient of static friction μs. The other end (B) of the rod leans against a frictionless wall. The rod has a length of L and a mass of m. The rod has a uniform density, so the center-of-mass is a distance L/2 from either end. The rod does not move. variables only (m, g, L, θ, μs) a) Draw a free body diagram for the rod clearly showing all forces and where they are applied. Hint: There are four forces! b) On your diagram, draw and label the line of action and lever arm for the weight force about point A. c) What is the torque produced by the weight force about point A? d) Using static equilibrium equations, find the three support forces (two at A, one at B). e) Given the coefficient of static friction μs, what is the smallest possible angle before the rod starts to move?arrow_forwardA solid round wheel is mounted on a frictionless horizontal axis. A light string is wrapped around the wheel and supports a block of mass m = 2.50 kg . The block is released from rest and falls down with acceleration a = 4.10 m/s?. M (a) Find the tension in the string. T = 4.0 N (b) Find the mass of the wheel. M = 4.0 kgarrow_forwardA block with mass m1 = 3.00 kg sits on a horizontal table and is attached to a rope. The rope then passes over a MASSIVE pulley this time and is attached to a block of mass m2 = 2.00 kg, which hangs vertically. The coefficient of kinetic friction of the interface between the table and m1 is 0.1. You may assume the pulley section is a disk with a mass of 2 kg. We will keep the pulley frictionless for brevity. Find the acceleration of the blocks using your choice of either Newton’s Laws or the energy conservation method.arrow_forward
- A roller (mass m, mass moment of inertia Os, radius r) is wrapped around by a rope. A block (mass m2) is connected to the center of gravity of the roller by a massless rod. The block and the roller slide downwards on the rough inclined plane (coefficient of friction H). a) What acceleration i does the roller center of gravity experience? b) What is the maximum coefficient of friction u that a sliding motion starts from rest? Given: r, a, m1 = m2= m, Os, µ, g.arrow_forwardThe pendulum is connected to the vertical shaft by a clevis at A. Themass of the bob B is 1.2 kg, and the mass of the arm AB is negligible. The shaft rotates with a constant angular speed, causing the bob to travel in a horizontal circle. If θ = 85◦, determine (a) the tensile force in AB; and (b) the speed v of the bob.arrow_forwardA uniform disk with mass m = 8.75 kg and radius R = 1.41 m lies in the x-y plane and centered at the origin. Three forces act in the +y- direction on the disk: 1) a force 315 N at the edge of the disk on the +x-axis, 2) a force 315 N at the edge of the disk on the -y-axis, and 3) a force 315 N acts at the edge of the disk at an angle 0 = 38° above the -x-axis. +y +x F3 IF, F2arrow_forward
- A ball of mass m, =5.7 kg and a block of mass m, =3.1 kg are connected with a lightweight string over a pulley with moment of inertia I and radius R=0.25m. The coefficient of kinetic friction between the table top and the block of mass m, is uy = 0.5. If the magnitude of the acceleration is a=3.0 m/s2. a)What are the tensions T, and T, in the string. N T2= N b)Calculate the moment of inertia of the pulley. I= kg m2 c) What is the change of the kinetic energy of the system if the system is released from rest and the ball decends a distance h=5.4 m downward. ΔΚ -arrow_forwardChapter 12, Problem 037 GO In the figure, a uniform plank, with a length L of 6.83 m and a weight of 386 N, rests on the ground and against a frictionless roller at the top of a wall of height h = 2.78 m. The plank remains in equilibrium for any value of e = 70.0° or more, but slips if e < 70.0°. Find the coefficient of static friction between the plank and the ground. Roller Number Units the tolerance is +/-2% Click if you would like to Show Work for this question: Open Show Workarrow_forwardA 1 470-kg automobile has a wheel base (the distance between the axles) of 3.10 m. The automobile's center of mass is on the centerline at a point 1.00 m behind the front axle. Find the force exerted by the ground on each wheel. each front wheel: each rear wheel:arrow_forward
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON