Answer to Question #250777 in Classical Mechanics for Mr Amazing

Question

A metal block starts from rest and slides 12 m down a chute that is inclined at 40° to the horizontal. It then continues to slide along a horizontal length of the chute and eventually comes to rest. If μ = 0,2 between the chute and the block, calculate the horizontal length of the chute. Use conservation of energy to solve this question.

Clearly show the following values in their respective sections

Section A:

E_k=?

E_p=?

E_TR=?

E_TE=?

Energy equation=??

v=??

Section B:

E_k=?

E_p=?

E_TR=?

E_TE=?

Distance=??

Answer 1

$m\vec g+\vec{F_{fr}}+\vec N=m\vec a,$

$ma=mg\sin \alpha-\mu mg\cos \alpha,$

$a=g(\sin\alpha-\mu\cos\alpha)=0.49~\frac m{s^2},$

$v=\sqrt{2al}=3.43~\frac ms,$

$\frac{mv^2}2=\mu mg,$ $\implies$

$d=\frac{v^2}{2\mu g}=3~m.$