A dog with mass M has its string attached to one end of a spring which runs without friction along a horizontal overhead rod. The other end of the springs is fixed to a wall The spring constant is K. The string is massless and inextensible and it maintains a constant angle `theta` with the overhead rod, even when the dog moves. There is friction with coefficient mu between the dog and the gound What is the maximum distance (in cm) that the dog moving slowly can stretch the spring beyond its natural length? Use M=30 kg,`theta=400N//m and mu=1/3`

Answer

`0020`

Explanation

For the dog, `N+ Tsintheta-Mg=0` (vertical)
`F-Tcostheta=0` (horizontal)
For maximum extension `f=muN`
For spring `Tcostheta -kx=0` (horizontal)
We have four unknows (N,T,F,x) and four equations Solve for T `Tcostheta=kx Rightarrow T=kx//costheta`
Substitute for F and solve for N `muN-Tcostheta=0 Rightarrow N=Tcostheta//mu=kx//mu`