Woocommerce get products

I used the following code to get the list of product categories form WooCommerce in my WordPress website:

 <?php
  $taxonomy     = 'product_cat';
  $orderby      = 'name';  
  $show_count   = 0;      // 1 for yes, 0 for no
  $pad_counts   = 0;      // 1 for yes, 0 for no
  $hierarchical = 0;      // 1 for yes, 0 for no  
  $title        = '';  
  $empty        = 0;
$args = array(
  'taxonomy'     => $taxonomy,
  'orderby'      => $orderby,
  'show_count'   => $show_count,
  'pad_counts'   => $pad_counts,
  'hierarchical' => $hierarchical,
  'title_li'     => $title,
  'hide_empty'   => $empty
);
?>
<?php $all_categories = get_categories( $args );

//print_r($all_categories);
foreach ($all_categories as $cat) {
    //print_r($cat);
    if($cat->category_parent == 0) {
        $category_id = $cat->term_id;

?>     

<?php       

        echo '<br /><a href="'. get_term_link($cat->slug, 'product_cat') .'">'. $cat->name .'</a>'; ?>


        <?php
        $args2 = array(
          'taxonomy'     => $taxonomy,
          'child_of'     => 0,
          'parent'       => $category_id,
          'orderby'      => $orderby,
          'show_count'   => $show_count,
          'pad_counts'   => $pad_counts,
          'hierarchical' => $hierarchical,
          'title_li'     => $title,
          'hide_empty'   => $empty
        );
        $sub_cats = get_categories( $args2 );
        if($sub_cats) {
            foreach($sub_cats as $sub_category) {
                echo  $sub_category->name ;
            }

        } ?>



    <?php }     
}
?>

This works fine and returns the list of product categories. I have been trying now to get a list of products for a particular category.

Example: get all the products for with cat_id=34.

I know products are stored as posts, and have been trying to get this done but can't seem to.

How do I get the list of products for a particular category?

<?php  
    $args = array(
        'post_type'      => 'product',
        'posts_per_page' => 10,
        'product_cat'    => 'hoodies'
    );

    $loop = new WP_Query( $args );

    while ( $loop->have_posts() ) : $loop->the_post();
        global $product;
        echo '<br /><a href="'.get_permalink().'">' . woocommerce_get_product_thumbnail().' '.get_the_title().'</a>';
    endwhile;

    wp_reset_query();
?>

This will list all product thumbnails and names along with their links to product page. change the category name and posts_per_page as per your requirement.