- #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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