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=mgcosθ−μ(Mg−mgsinθ) ......(1)
For Block it is
a=TxM
⇒a=TcosθM
⇒T=Macosθ
⇒T=M(mgcosθ−μ(Mg−mgsinθ))(M+m)cosθ .....(2)
Rewriting it as
T=a−bcosθ+ctanθ
wherea,bandc are system parameters defined with help of (2) not dependent onθ
We see that
−1cosθ . ForT to be a smaller numbercosθ term must be maximum. We know thatcosθ has a maximum value=1 forθ=0∘ tanθ . ForT to be a smaller number,tanθ term must be zero. We know thattanθ has a value=0 forθ=0∘ .
Hence, we see that tension will be smaller if the string connecting the block were parallel to the lab bench.