# John Taylor Classical Mechanics Chapter 1 Problem 46

• karmonkey98k
In summary, the conversation discusses two problems related to inertial reference frames and a rotating turntable experiment. The first problem describes the path of a frictionless puck launched on the turntable from the perspective of an observer on the ground, while the second problem asks for the polar coordinates of the puck as measured by an observer on the turntable. The second problem also asks if the turntable observer's frame is inertial and to describe the path of the puck from their perspective.
karmonkey98k

## Homework Statement

Problem 27 Experiment needed first: The hallmark of inertial ref. frames is that any object subject to 0 net force travels in straight line at a constant speed. Consider the following experiment: I am standing on the ground (which we shall take to be an inertial frame) beside a perfectly flat horizontal turntable, rotating with constant ang. velocity w. I lean over and shove a frictionless puck so that it slides across turntable, straight through center. The puck is subject to 0 net force, and, as seen from my inertial frame, travels in straight line. Describe puck's path as observed by someone sitting at rest on turntable.
Now Problem 46: Consider experiment of Problem 27, where a frictonless puck is slid straight across a rotating turntable through the center O. a. Write polar coordinates r, phi, of the puck as functions of time as measured in the inertial frame S of an observer on the ground (Assume puck was launched along axis phi=0 at t=0). b. Now write down the polar coordinates rprime, phiprime of the puck as measured by an observer (Frame Sprime) at rest on tunrtable. (choose these coordinates so that phi and phiprime coincide at t=0). Describe and sketch path as seen by this second observer. Is frame Sprime inertial?

## The Attempt at a Solution

I had tried to find which polar coordinates would coincide with the regular cartesian ones; that's really all i can describe about my attempt

hi karmonkey98k!

show us how far you have got

(btw, you can write S' for Sprime etc)

## 1. What is the problem statement in Chapter 1 Problem 46 of John Taylor's Classical Mechanics?

The problem asks you to determine the maximum height reached by an object thrown vertically upward with a given initial velocity and air resistance.

## 2. What is the formula for calculating the maximum height in this problem?

The formula is h = v02/2g + (v0/g)(k/m)(1 - e-gt/m), where h is the maximum height, v0 is the initial velocity, g is the acceleration due to gravity, k is the air resistance constant, and m is the mass of the object.

## 3. How do you solve this problem using calculus?

First, you need to set up and solve the differential equation for the motion of the object. Then, use the initial conditions (position and velocity at t = 0) to find the constants of integration. Finally, plug in the values to the formula for maximum height and solve for h.

## 4. What are the assumptions made in this problem?

The problem assumes that the air resistance is proportional to the velocity, the object is thrown vertically upward, and the acceleration due to gravity is constant.

## 5. What is the significance of this problem in classical mechanics?

This problem demonstrates how air resistance affects the motion of an object and how it can be modeled using calculus and differential equations. It also shows the importance of considering initial conditions in solving problems in classical mechanics.

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