Question

An old rubber band is used to hold together a pack of playing cards by looping twice around the deck. Assuming that tension is distributed equally throughout the band ,how much tension is required to keep the center cards from slipping out under their own weight when the deck is held vertically? The mass of a deck of cards is roughly 80 and the coefficient of friction is roughly 0.1.

Answer 1

For the cards to not fall, the net force vertically must be zero. The upward force here will be the force of friction which will be equal to the gravitational force.

F_friction = mg

=>

here, m = mass of the deck = 80g = 0.08 kg

so,

this is the normal force on the cards.

Also, the net force horizontally must be zero. Therefore, this normal contact force R must be equal to the tension in the rubber band.

Therefore, T = R = 7.84 N.

This is the tension required to keep all the cards from slipping.