**Problem 5: Friction and Motion of Blocks***Description of the Problem:*Two blocks, each with mass \( m \), are stacked on each other. A hand applies a push with an unknown magnitude \( P \) to the bottom block, moving it to the left. Friction exists between the two blocks and between the floor and the bottom block. The frictional force is sufficient for the blocks to move together to the left, with the top block on the verge of slipping to the right on the bottom block. Both blocks are observed to have moved a distance \( d \).*Task:*Determine the magnitude of the force \( P \) and the speed of each block after they have moved the distance \( d \).*Given Variables:*- \( m \): mass of each block- \( g \): acceleration due to gravity- \( d \): distance moved by the blocks*Important Notes:*- Do not calculate the horizontal accelerations of the blocks.- Hint: The blocks undergo only horizontal motion, with no vertical displacement.*Diagram Explanation:*The accompanying diagram shows:- Two blocks, each labeled with mass \( m \), stacked one on top of the other.- A hand applying a force \( P \) to the bottom block, moving it to the left.- Frictional coefficients are provided: - Static friction coefficient \(\mu_s = 1/2\) between the blocks. - Kinetic friction coefficient \(\mu_k = 1/5\) between the bottom block and the floor.- An arrow indicates the direction of the applied force and the frictional force acting in the opposite direction at the hand’s point of contact. This problem explores concepts of friction, force, and motion within a physics context.

Answered: Image /qna-images/answer/00c52d93-98bc-4086-a1df-10f21322f5ea.jpg

Two blocks, both with mass m, are at rest on top of each other when a hand pushes the bottom block to the left with an unknown magnitude P. There is friction between the two blocks and between the floor and the bottom block. There is enough friction between the two blocks so that they move together to the left, with the top block about to slip to the right on the bottom block. Both blocks are observed to move a distance d. Find the magnitude of P and the speed of each block when they have moved the distance d. The knowns are m, g, and d. Do not solve this problem by finding the horizontal accelerations of the block. Hint: both block have no vertical motion during their motion, just horizontal motion.

Two blocks, both with mass m, are at rest on top of each other when a hand pushes the bottom block to the left with an unknown magnitude P. There is friction between the two blocks and between the floor and the bottom block. There is enough friction between the two blocks so that they move together to the left, with the top block about to slip to the right on the bottom block. Both blocks are observed to move a distance d. Find the magnitude of P and the speed of each block when they have moved the distance d. The knowns are m, g, and d. Do not solve this problem by finding the horizontal accelerations of the block. Hint: both block have no vertical motion during their motion, just horizontal motion.