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.