# Why would tension be smaller if the string were parallel to the lab bench?

##### 1 Answer

Let

Taking East as positive

External forces responsible for the magnitude of acceleration of masses when considered as single object

#(M+m)a=mgcostheta-mu(Mg-mgsintheta)# ......(1)

For Block it is

#a=T_x/M#

#=>a=(Tcostheta)/M#

#=>T=(Ma)/costheta#

#=>T=(M(mgcostheta-mu(Mg-mgsintheta)))/((M+m)costheta)# .....(2)

Rewriting it as

#T=a-b/costheta+ctantheta#

where#a,b and c# are system parameters defined with help of (2) not dependent on#theta#

We see that

#-1/costheta# . For#T# to be a smaller number#costheta# term must be maximum. We know that#costheta# has a maximum value#=1# for#theta=0^@# #tantheta# . For#T# to be a smaller number,#tantheta# term must be zero. We know that#tantheta# has a value#=0# for#theta=0^@# .

Hence, we see that tension will be smaller if the string connecting the block were parallel to the lab bench.