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!