Dockerfile for Rails app - Permission Denied - ruby-on-rails

Question

I am attempting to create a docker image of a rails app using rvm (as non-root) and am running into permission errors:
Dockerfile:
FROM ubuntu
RUN apt-get update -q
RUN apt-get install -qy curl
RUN apt-get install -y libpq-dev
RUN apt-get install -y imagemagick --fix-missing
RUN apt-get install -y curl patch gawk g++ gcc make libc6-dev patch libreadline6-dev zlib1g-dev libssl-dev libyaml-dev libsqlite3-dev sqlite3 autoconf libgdbm-dev libncurses5-dev automake libtool bison pkg-config libffi-dev
RUN useradd -ms /bin/bash app
USER app
RUN gpg --keyserver hkp://keys.gnupg.net --recv-keys 409B6B1796C275462A1703113804BB82D39DC0E3
RUN curl -sSL https://get.rvm.io | bash -s stable
RUN /bin/bash -c -l 'rvm install 2.2.1'
RUN /bin/bash -c -l 'rvm use 2.2.1'
RUN /bin/bash -l -c "echo 'gem: --no-ri --no-rdoc' > ~/.gemrc"
RUN /bin/bash -c -l 'gem install bundler --no-ri --no-rdoc'
RUN /bin/bash -c -l 'mkdir /home/app/rails_app'
WORKDIR /home/app/rails_app
ADD Gemfile /home/app/rails_app/Gemfile
ADD Gemfile.lock /home/app/rails_app/Gemfile.lock
RUN /bin/bash -c -l 'bundle install'
ADD . /home/app/rails_app
EXPOSE 3000
CMD /bin/bash -c -l 'RAILS_ENV=production rails server -p 3000'
The image builds fine but when I run the container with docker run
I get the following error:
/home/app/.rvm/gems/ruby-2.2.1/gems/rack-1.6.4/lib/rack/server.rb:367:in `delete': Permission denied # unlink_internal - /home/app/rails_app/tmp/pids/server.pid (Errno::EACCES)
If I add:
USER root
RUN /bin/bash -c -l 'chmod -R 777 /home/app/rails_app/'
RUN /bin/bash -c -l 'chown -R app:app /home/app/rails_app/'
USER app
The container runs but the rails server did not start and there is nothing in the logs. Executing /bin/bash on the running container and trying to start the rails server ends in rails: command not found while logged in as app. Any Ideas?
Thanks