Determine mass of a glider on an air track

[idlackage]

Determine mass of a glider on an air track [solved]

Homework Statement

A 20.0 g mass is stringed to a glider on an air track through a pulley (https://www.physicsforums.com/attachment.php?attachmentid=30478&stc=1&d=1291794499"). I'm supposed to find the mass of said glider, assuming that the air track and pulley are frictionless and the string is massless.

Data from a graph:

V₁ = 0.143 m/s
V₂ = 0.377 m/s
Δt = 0.24 s

Homework Equations

a = (V2 – V1) / Δt
F_net = ma

The Attempt at a Solution

a = (V2 – V1) / Δt
= (0.377 – 0.143) / 0.24
= 0.975 m/s²

Mass 1 (https://www.physicsforums.com/attachment.php?attachmentid=30479&stc=1&d=1291794499"):

Fnet = ma
F_n1 + Fg₁ + T₁ = -m₁a
-m₁g + T₁ = -m₁a
-9.8m₁ + T₁ = -0.975m₁
+T = 8.825m₁

Mass 2 (https://www.physicsforums.com/attachment.php?attachmentid=30480&stc=1&d=1291794499"):

Fg₂ + T₂ = m2a
+m₂g – T₂ = +m2a
(20.0)(9.80) – T₂ = 20.0(0.975)
196 – T₂ = 19.5
-T₂ = -176.5

Final Calculations:

+ T = 8.825m₁
(+) – T = -179.84
---------------------
0 = 8.825m₁ – 179.84
8.825m₁ = 179.84
m₁ = 179.84/8.825
= 20 g

When the glider was weighted on a scale, it was said to be 429 g. So I have no idea what I'm doing wrong--am I getting the mass of the "20.0 g mass" here, or is this number just coincidental and irrelevant? Are the equations used incorrect? Thanks for any help.

 

[Kikora]

Homework Statement

Mass 1 (https://www.physicsforums.com/attachment.php?attachmentid=30479&stc=1&d=1291794499"):

Fnet = ma
F_n1 + Fg₁ + T₁ = -m₁a
-m₁g + T₁ = -m₁a
-9.8m₁ + T₁ = -0.975m₁
+T = 8.825m₁

You do not have to add in F_n1 and Fg₁ because they cancel each other out + they are in the vertical direction. You only need to take into account the horizontal forces(which in this case is the tension from the string).

 

[Yafa]

The tensions are equal

 

[idlackage]

You do not have to add in F_n1 and Fg₁ because they cancel each other out + they are in the vertical direction. You only need to take into account the horizontal forces(which in this case is the tension from the string).

It works now, thank you so much!

 

[rwisz]

Based on the data and calculations provided, it seems that the mass of the glider on the air track is indeed 20 grams. This is consistent with the given information of a 20.0 g mass being attached to the glider. It is possible that the discrepancy between the calculated mass and the weight measured on the scale could be due to experimental error or other factors not accounted for in the calculations. However, based on the given information and the equations used, the mass of the glider on the air track appears to be 20 grams.