A spring with a spring-constant 2.2 N/cm is compressed 28 cm and released. The 5 kg mass skids down the frictional incline of height 31 cm and inclined at a 18◦ angle.

Question

A spring with a spring-constant 2.2 N/cm is compressed 28 cm and released. The 5 kg mass skids down the frictional incline of height 31 cm and inclined at a 18◦ angle.
The acceleration of gravity is 9.8 m/s2 .
The path is frictionless except for a distance of 0.8 m along the incline which has a coefficient of friction of 0.3.
k = 2.2 N/cm
What is the final velocity vf of the mass? Answer in units of m/s

Elena · Answer

k = 2.2 N/cm =220 N/m. x =0.28 m, h=0.31 m, s =0.8 m, μ=0.3, α=18º. PE(spring)=PE +W(fr) +KE, k•x²/2=m•g•h+ μ•m•g•cos α•s +m•v²/2, v=sqrt{kx²/m – 2g(h+ μ• s•cos α)}