---
title: Rope Tension Between Blocks
topic: Force
author: Jake Bobowski
source: 2013 Final Q7
template_version: 1.4
attribution: standard
outcomes:
- 6.1.1.4
- 6.2.1.2
- 6.3.1.3
- 6.12.1.1
difficulty:
- Hard
randomization:
- undefined
taxonomy:
- undefined
span:
- undefined
length:
- Medium
tags:
- MP
assets:
- q7image.png
part1:
  type: multiple-choice
  pl-customizations:
    weight: 1
part2:
  type: multiple-choice
  pl-customizations:
    weight: 1
myst:
  substitutions:
    params:
      vars:
        title: Rope Tension Between Blocks
        units: $\rm{ \frac{m}{s^2} }$
      part1:
        ans1:
          value: $T_3$ > $T_2$ > $T_1$
        ans2:
          value: $T_3$ > $T_2$ = $T_1$
        ans3:
          value: $T_3$ = $T_3$ = $T_1$
        ans4:
          value: $T_3$ < $T_2$ < $T_1$
        ans5:
          value: $T_3$ < $T_2$ = $T_1$
      part2:
        ans1:
          value: $a = \frac{4}{21} g$
        ans2:
          value: $a = \frac{g}{4}$
        ans3:
          value: $a = \frac{g}{2}$
        ans4:
          value: $a = g$
        ans5:
          value: $a = \frac{2}{3} g$
---
# {{ params.vars.title }}
As pictured, two blocks of mass $2m$ are connected by a rope of tension $T_3$ and pulled along a frictionless surface.
Another (massless) rope of tension $T_2$ connects the two blocks to a (frictionless) pulley of mass $m/2$, which is a disk of radius $R$.
The (massless) rope continues with tension $T_1$ on the other side of the pulley to a hanging mass of mass $m$.

<img src="q7image.png" alt="Ropes and Pulleys">

## Part 1

Referring to the image, the tensions in the ropes satisfy:

### Answer Section

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- {{ params.part1.ans3.value }}
- {{ params.part1.ans4.value }}
- {{ params.part1.ans5.value }}

## Part 2

Referring to the image, the magnitude of the acceleration of the system is:

### Answer Section

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- {{ params.part2.ans2.value }} {{ params.vars.units }}
- {{ params.part2.ans3.value }} {{ params.vars.units }}
- {{ params.part2.ans4.value }} {{ params.vars.units }}
- {{ params.part2.ans5.value }} {{ params.vars.units }}

## Attribution

Problem is licensed under the [CC-BY-NC-SA 4.0 license](https://creativecommons.org/licenses/by-nc-sa/4.0/).<br> ![The Creative Commons 4.0 license requiring attribution-BY, non-commercial-NC, and share-alike-SA license.](https://raw.githubusercontent.com/firasm/bits/master/by-nc-sa.png)