# Solving Amplitude Problem for Air Track Glider

• Liketothink
In summary, the conversation discusses solving a problem involving an air-track glider attached to a spring. The problem involves finding the amplitude of oscillation based on given information such as period and maximum speed. The conversation also touches on using equations and solving for initial phase in order to find position at a given time. The participants also discuss different modes (radians vs degrees) on a calculator and how it affects the solutions.
Liketothink

## Homework Statement

An air-track glider is attached to a spring. The glider is pulled to the right and released from rest at t=0 s. It then oscillates with a period of 1.5 s and a maximum speed of 40.4 cm/s. What is the amplitude of the oscillation?

x=Acos(wt+ro)

## The Attempt at a Solution

I really don't know how to start this problem because angular speed is not given and the length the air glider travels is not given either.

You can find the angular velocity from the period: T = 2π/ω.

I found it to be 4.19 rad/s. I don't see how it helps me though.

The maximum kinetic energy is ½mv2 where v = 40.4 cm/s, at the center where potential energy is zero. Now at the maximum displacement (x = A), all of this KE must be potential energy (KE is zero at this point), so

½mv2 = ½kA2

Write k in terms of ω and m, and solve for A. (m cancels out)

Ok so v^2/w^2=A^2. I have one question though. Why is it 1/2mv^2 instead of 1/2kx^2 if all the kinetic Energy is transferred to potential energy at the amplitude?

At x, the potential energy is given by ½kx2. If x = A, then the potential energy is ½kA2. This must be equal to the max kinetic energy, so ½mv2 = ½kA2.

I see. If I wanted to find the position at t=.5s for that question wouldn't I just take x=Acos(wt+ro)? I have tried that and it seemed to be wrong. I solved for ro when x=0, ro=pi/2 then I solved for x but that is wrong. I tried putting the calculator in degrees or radians mode it's still wrong. What am I doing wrong? What mode is the calculator suppose to be into solve for position.

r0 (initial phase) is zero in this case. How did you get π/2?

The position at t = 0.5 would just be x = Acos(0.5ω).

I set x=0 so that 0=Acos(wt+ro). Since t=0, 0=Acos(ro). Then 0=cos(ro), so I get ro=pi/2.

The glider is pulled to the right and released from rest at t = 0, so at t = 0 the positin is x = A.

A = Acos(r0)

cos(r0) = 1

so r0 = 0.

oh that's right! ok. But I am still getting the wrong answer though. x=.096cos(4.19*.5)=
.0963 m. The computer is telling me it's wrong. what am I doing wrong in this case?

Hm.. maybe it wants you to enter the answer in cm?

I got it. For some reason the answer was -.042 when the calculator was in radian. do you know why I have to put the calculator in radians? I have a test tomorrow and I would not have gotten this answer right.

Well you calculated the angular velocity in radians, so you must have the calculator in radian mode. If you want to use degrees, just multiply the angular velocity by (360)/2π.

## What is an air track glider?

An air track glider is a device used in physics experiments to study motion and forces. It is a small cart that moves along a track with very little friction, allowing for more accurate measurements.

## What is the amplitude problem for air track gliders?

The amplitude problem refers to the difficulty in accurately measuring the amplitude, or maximum displacement, of the glider's motion on the track. This is due to the air track's low friction, which can cause the glider to continue moving even after the initial force has stopped.

## How can the amplitude problem be solved?

One solution is to use a photogate sensor, which can accurately measure the time it takes for the glider to pass through a certain point on the track. This can then be used to calculate the amplitude of the glider's motion.

## What other factors can affect the accuracy of amplitude measurements for air track gliders?

Aside from low friction, other factors that can affect the accuracy of amplitude measurements include air resistance, uneven track surface, and external forces such as wind or vibrations.

## Why is solving the amplitude problem important in physics experiments?

Accurately measuring the amplitude of motion is crucial in understanding the behavior of objects in motion and the forces acting upon them. It allows for more precise calculations and analysis of data, leading to more accurate conclusions and theories.

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