Question

An incline plane has Ф = 40.0° and μ k = 0.15. Starting from rest, how long will it take a 4.0 kg block to reach a speed of 12 m/s?

Answer 1

The block on the action of two forces, the Force of Friction and the Tangential Weight. Using the Newton's Secound Law, we have:


`P_(t)-Fat=ma \\ mgsen\O-mgucos\O=ma \\ a=g(sen\O-ucos\O)`

Using the Velocity Hourly Equation, we get:


`V=V_(o)+a\Delta t \\ \Delta t= (V)/(a)`

Uniting the equations:


`\Delta t= (V)/(g(sen\O-ucos\O))`

Entering the unknowns:


`\Delta t= (V)/(g(sen\O-ucos\O)) \\ \Delta t= (12)/(10(sen40^o-0.15cos^o)) \\ \Delta t= (12)/(10(0,64-0.15x0.77)) \\ \Delta t= (12)/(5.27) \\ \boxed {\Delta t=2.28s}`

Obs: Approximate results

If you notice any mistake in my english, please let me know, because i am not native.