- #1

Callista

- 5

- 2

## Homework Statement

Two objects are connected by a string that passes over a frictionless pulley, where m1<m2 and a1 and a2 are the magnitudes of the respective accelerations. Which mathematical statement is true regarding the magnitude of the acceleration a2 of the mass m2?

(a) a2<g

(b) a2>g

(c) a2=g

(d) a2<a1

(e) a2>a1

## Homework Equations

F(net)=ma

## The Attempt at a Solution

for m1:

F(net)=m1a

Fx=0

Fy=T-m1g=m1a1

##a1= \frac{T}{m1}-g##

for m2:

F(net)=m2a

Fx=0

Fy=-T+m2g=m2a2

##a2=g- \frac{T}{m2}<g##

Answer= (a)

While the book confirms my answer is right, I wanted to try applying my derived formulas to the situation where m1=5kg, and m2=10kg to see what the result would be. However, when I do this I run into a problem.

##a2=g- \frac{T}{m2}##

->##Fy=-T+m2g=m2a2##

->##T=m2g-m2a2##

->##a2=g- \frac{m2g-m2a2}{m2}##

->##a2=g- g+a2##

->##a2=a2##

A similar thing happens when I try to use the equation I derived for a1. What am I missing?

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