How Does Friction Affect the Acceleration of Stacked Blocks?

[vjnmath]

Homework Statement

A block of mass m1 is on top of a block of mass m2. The lower block is on a horizontal surface, and a rope can pull horizontally on the lower block. The coefficient of kinetic friction for all surfaces is μ. What is the resulting acceleration of the lower block if a force F is applied to the rope? Assume that F is sufficiently large so that the top block slips on the lower block.

Homework Equations

F = ma
Frictional Force = Normal Force * μ

The Attempt at a Solution

Normal Force (for lower block) = (m1 + m2) g
Frictional Force (for lower block) = μ * (m1 + m2) g
F - (μ * (m1 + m2) g) = m2 * a
a = ((F - (μ * (m1 + m2) g)) / m2

Correct Answer should be: a2 = (F - μg(2m1 + m2)) / m2

 

[tiny-tim]

welcome to pf!

hi vjnmath! welcome to pf!

… Assume that F is sufficiently large so that the top block slips on the lower block.

… sooo, you'll need to include the friction force from the top block