Cats Vector Application Problem

Question

My kittens Annie and Josie are at it again. This time, they have found the bag of cat food and are attempting to drag it out of the pantry by their teeth. Annie can pull with a force of 8 pounds and Josie can pull with a force of 12 pounds. It only takes 17 pounds of force in a single direction to overcome friction, but will the bag move if Annie and Josie are pulling at a 70° angle to each other?

Answer 1

Since they're pulling the bag at 70° from each other we can probably assume that the angle between each cat and the bag is 55°. (180-70)/2

For Annie, we have 18 sin 55 = 14.74 pounds of force.

For Josie, we have 12 sin 55 = 9.83 pounds of force.

Adding them, we get 24.57 pounds of force so yes, the two cats together will be able to drag the bag.

However if one of the cats is pulling at 0° and the other is pulling at 110° they will not be able to drag the bag.