Mass hanging in a boxcar accelerating

[brake4country]

1. Homework Statement
A mass of 1 kg hangs inside a boxcar of a train. If the train accelerates at 7 m/s^2, what is the approximate tension in the rope?

A: 12 N

Homework Equations

F=ma

The Attempt at a Solution

I originally thought of doing this problem as pythagorean theorem, but I wanted to work out the x and y components for practice. Breaking up the components:
ΣF_y=ma_y
T_y-mg = ma_y
T_y=10N

ΣF_x=ma_x
T_x=10*7
T_x=70N

Thus, T²=10²+70²
T=71 N

The problem sets it up just like I do but get 12 N for their answer:
T²=ma²+mg²

What am I doing wrong? Thanks in advance!

 

[berkeman]

1. Homework Statement
A mass of 1 kg hangs inside a boxcar of a train. If the train accelerates at 7 m/s^2, what is the approximate tension in the rope?

A: 12 N

Homework Equations

F=ma

The Attempt at a Solution

I originally thought of doing this problem as pythagorean theorem, but I wanted to work out the x and y components for practice. Breaking up the components:
ΣF_y=ma_y
T_y-mg = ma_y
T_y=10N

ΣF_x=ma_x
T_x=10*7
T_x=70N

Thus, T²=10²+70²
T=71 N

The problem sets it up just like I do but get 12 N for their answer:
T²=ma²+mg²

What am I doing wrong? Thanks in advance!

Can you show us your free body diagram for this problem? That is generally the first/best step on these problems.

 

[gneill]

Breaking up the components:
ΣF_y=ma_y
T_y-mg = ma_y
T_y=10N

ΣF_x=ma_x
T_x=10*7 ⇐
T_x=70N

Check the mass value used for the calculation of the x-component.