Question

A 2.0 kg block is given an initial speed of 8.0 m/s up an incline plane of angle 30° where the coefficient of friction is 0.35. Calculate the maximum distance the block moves along the incline plane.

Answer 1

4.1 m

Step-by-step explanation:

Given :

Mass of the block = m = 2 kg.

Initial velocity =
`v_(i)` = 8 m/s

Angle of the incline = α = 30°

Coefficient of friction = μ = 0.35

Distance moved up the incline is calculated using the work energy theorem.

Work done by the net force = change in kinetic energy of the object.

Net work = work done by friction + work done by the gravity component.

(- mg sin 30 - μ mg cos 30 ) d =
`1/2m v_(f)^(2) - 1/2 m v_(i)^(2)`

m cancels out when divided on both sides with m.

- [(9.8 sin 30 - ( 0.35 × 9.8 × cos 30) ] d = 1/2 ( 0² - 8² )

⇒ -7.87 d = -32

⇒ Distance traveled up the incline = d = 4.0658 m = 4.1 m