We're asked to determine the **tension in the string** attached to the top block and **magnitude of the acceleration** of the bottom block, as well as i**dentifying action-reaction force** pairs.

This is a **system-of-objects** type problem: Stacked Blocks With Friction. We'll follow these steps to solve:

- Draw a
**free-body diagram**for each body we're interested in - Write our Newton's Second Law Equations
**∑***F*=*ma* - Solve for the
**target variable**

Obviously, we'll be using the equation for Newton's Second Law:

$\overline{)\begin{array}{rcl}\mathbf{\sum}\stackrel{\mathbf{\rightharpoonup}}{\mathit{F}}& {\mathbf{=}}& \mathit{m}\stackrel{\mathbf{\rightharpoonup}}{\mathit{a}}\end{array}}$

We'll also need to relate the normal force and kinetic friction force:

$\overline{){{\mathit{f}}}_{{\mathit{k}}}{\mathbf{=}}{{\mathit{\mu}}}_{{\mathit{k}}}{\mathit{N}}}$

A 5.00-kg block is placed on top of a 10.0-kg block as shown in the figure. A horizontal force of 45.0 N is applied to the 10-kg block, and the 5.00-kg block is tied to the wall. The coefficient of kinetic friction between all moving surfaces is 0.200.

(a) Draw a free-body diagram for each block and identify the action–reaction forces between the blocks.

(b) Determine the tension in the string.

(c) Determine the magnitude of the acceleration of the 10.0-kg block.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Systems of Objects with Friction concept. You can view video lessons to learn Systems of Objects with Friction. Or if you need more Systems of Objects with Friction practice, you can also practice Systems of Objects with Friction practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Gentile's class at RUTGERS.