[Physics] Two Block Pulley Emergency

acceleration

ProblemImage

So I took AP Physics last year, and am taking a more advanced AP Physics course this year. However my teacher from last year solves the following problem with one method and my current teacher solves it with a different method. The problem is both methods disagree, and I cannot decern which is flawed and why. Can somebody please help me understand which of these two methods is correct and why the other method is flawed?

Method one:

MethodOne

You can view both blocks as a system shown in the above image.

Fn=ma –> Fn=m2g –> m2g=(m1+m2)a –> a=m2g/(m1+m2)

This seems to be how the collegeboard does it.

Method two:

MethodTwo

You set up a system of equations based on the above image.

Fn=ma –> Fn=Ft –> Ft=ma –> Ft=(m1+m2)a

Fn=ma –> Fg-Ft=Fn –> Fg=m2g –> Fg-Ft=ma –> m2g-Ft=(m1+m2)a

Substitute: m2g-(m1+m2)a=(m1+m2)a –> m2g=2(m1+m2)a –> a=m2g/2(m1+m2)

Best Answer

In method two,you are writing $F_{net}=ma$ separately for each block.So it should be $F_t=m_1a$ and $m_2g-F_t=m_2a$,that is,you must use the mass of just the one block you are considering,not both the blocks together.This agrees with method 1,which is also correct.

Related Question