Consider a homogeneous billiard ball of mass m and radius R that moves on horizontal table. Gravity acts downward. The coefficient of kinetic friction between the ball and the table is µ, and you are to assume that there is no work done by friction for pure rolling motion. At time t = 0, the ball is struck with cue, which delivers a force pulse of short duration. Its impulse is = F(t)dt a) The point of contact between the cue and the ball is at the "equator" and the direction of the force is toward the center of the ball. Calculate the time at which pure rolling begins. What is the final speed of the center of mass of the ball? b) At what height h above the center must the cue strike the ball so that rolling motion starts immediately (see Figure)

Consider a homogeneous billiard ball of mass m and radius R that moves on horizontal table. Gravity acts downward. The coefficient of kinetic friction between the ball and the table is µ, and you are to assume that there is no work done by friction for pure rolling motion. At time t = 0, the ball is struck with cue, which delivers a force pulse of short duration. Its impulse is = F(t)dt a) The point of contact between the cue and the ball is at the "equator" and the direction of the force is toward the center of the ball. Calculate the time at which pure rolling begins. What is the final speed of the center of mass of the ball? b) At what height h above the center must the cue strike the ball so that rolling motion starts immediately (see Figure)

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

A ring (2 kg, r = 1 m) rotates in a CW direction with initial angular velocity 20 s-1. A disk (4 kg, r = 1 m) rotates in a CCW direction with initial angular velocity 50 s-1. The ring and disk "collide" and eventually rotate together. Assume that positive angular momentum and angular velocity values correspond to rotation in the CCW direction.What is the initial angular momentum Li of the ring+disk system? kg m2 s-1 What is the final angular velocity ωf of the ring+disk system? s^-1
A basketball of mass 1.25 kg traveling with an initial speed of 8 m/sec bounces off of a backboard and comes back in the opposite direction with a speed of 7 m/sec. The ball is in contact with the backboard for 0.1 sec. What is the impulse on the ball?
can you please provide the equations and how to solve these problems, thank you
A 2.10 kg "particle" traveling with velocity = (3.7 m/s )i collides with a 4.70 kg "particle" traveling with velocity V = (1.7 m/s )j. The collision connects the two particles. What then is their velocity in (a) unit-vector notation and as (b) a magnitude and (c) a positive (counterclockwise) angle measured from the +x axis? (a) Number i+ į Units (b) Number Units (c) Number Units
Under many conditions, the center of mass of a system of particles can represent the system as a whole. But how far does this rule extend? Consider two identical particles traveling toward each other at the same speed. By examining this system, choose the correct response. 1)The momentum and kinetic energy of the center of mass is equivalent to that of the system of particles. 2)The kinetic energy, but not the momentum, of the center of mass is equivalent to that of the system of particles. 3)Neither the momentum nor the kinetic energy of the center of mass is equivalent to that of the system of particles. 4)The momentum, but not the kinetic energy, of the center of mass, is equivalent to that of the system of particles.
A basketball of mass 1.25 kg travelling with an initial speed of 8 m/sec bounces off of a backboard and comes back in the opposite direction with a speed of 7 m/sec. The ball is in contact with the backboard for 0.1 sec. (a) What is the impulse on the ball? (b) What is the force exerted on the ball?
Hi there! I need some help! I am really confused. I do not know how to solve this! A block of mass m = 4.4 kg, moving on frictionless surface with a speed vi = 9.2 m/s, makes a perfectly elastic collision with a block of mass M at rest. After the collision, the 4.4 kg block recoils with a speed of vf = 2.5 m/s. Mass m is closest to: Thank you!
Now let's consider the impulse associated with kicking a soccer ball (Figure 1). The ball has mass 0.40 kg . Initially it moves horizontally to the left at 20 m/s, but then it is kicked and given a velocity with magnitude 30 m/s and direction φ=45∘ upward and to the right. Find the impulse of the force and the average force on the ball, assuming a collision time Δt=0.010s a) Suppose the ball is moving at 30 ∘ downward from the horizontal before it is kicked. If all the numerical values are the same as before, find the magnitude of the average force on the ball. b)Find the direction of the average force on the ball found in Part A.
A golf ball is moving at speed vo to the East. After deflecting off a tree, it moves at a speed of 0.90vo in a direction which is 25° North of East. Check all the following answers which are true statements. There may be more than one correct answer! The impulse vector (delivered by the tree) has components which point North and West The ball's momentum vector has the same magnitude before and after the collision The impulse vector (delivered by the tree) points purely to the North The ball's momentum vector decreases in magnitude during the collision
Ball having mass 5.5kg and velocity 7.6m/s travels to the east. Impulse given at point O, makes it change direction to north with velocity 4.8 m/s. What is the direction of the given impulse, measured in unit of degrees, if the angle is defined as between the horizontal direction (east) and the impulse?
A 0.046 kg golf ball initially at rest is given a speed of 20 m/s when a club strikes. If the club and the ball are in contact for 0.003 s with an impulse of 0.92kg.m/s, What average force acts on the ball? Given: and Solution: The average force that acts on the ball is 306.67 N. What would be the required net force to achieve a 1.5 kg.m/s impulse? Given: and Solution:
A 1.0 kg ball drops vertically onto a floor, hitting with a speed (just before hitting floor) of 20 m/s. It rebounds with a speed (just after leaving floor) of 15 m/s. (a) What is the magnitude of the impulse that acts on the ball during the contact?(b) If the ball is in contact with the floor for 0.040 s, what is the magnitude of the average force exerted on the floor?