contestada

A boy shoves his stuffed toy zebra, which has mass m, down a frictionless chute, starting at a height D above the bottom of the chute and with an initial speed of v. The toy animal emerges horizontally from the bottom of the chute and continues sliding along a horizontal surface with coefficient of kinetic friction μ. At what distance d from the bottom of the chute does the toy zebra come to rest? Express your answer in terms of the given variables and g, the acceleration due to gravity.

Relax

Respuesta :

Manetho

Answer:

[tex]d=\frac{0.5v^2+gD}{\mu\times g}[/tex]

Explanation:

mass of the boy = m kg

staring height of the boy = D meters

initial velocity = v

coefficient of kinetic friction = μ

total energy of the toy is

E_total = K.E. +P.E.

= 0.5mv^2 +mgD

= m( 0.5v^2+ gD)

The work done by friction force

W= μ×F_normal ×distance

W= μ×m×g×d

hence, the distance d covered by the zebra toy

and since, the total energy is conserved

W= E_total

μ×m×g×d= m( 0.5v^2+ gD)

[tex]d=\frac{0.5v^2+gD}{\mu\times g}[/tex]

hence, the distance d from the bottom of the chute does the toy algebra comes to rest.

[tex]d=\frac{0.5v^2+gD}{\mu\times g}[/tex]