Question

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.

I thought the answer was (0.5v^2+gh)/(mu x g) but it is not correct apparently

Answer 1

Using energy conservation:

KEi + PEi + Wf = KEf + PEf

KEi = Initial kinetic energy of the chute + zebra = (1/2)*m*v^2

PEi = Initial potential energy of zebra = m*g*D

KEf = 0, since final velocity is zero

PEf = 0, since ground is reference point

Wf = work-done by friction force = Ff*d

Ff = Force due to friction = -*N = -*m*g

d = stopping distance of zebra = ?

W = -*m*g*d

Using above expressions

(1/2)*m*v^2 + m*g*D - *m*g*d = 0 + 0

*m*g*d = (1/2)*m*v^2 + m*g*D

divide by m

*g*d = (1/2)*v^2 + g*D

d = (0.5*v^2 + g*D)/(*g)

d = v^2/(2**g) + D/

Your above expression is correct but you've to give final answer in terms of given variables only

Since you've used 'h' in place of 'D', So that's why your answer was wrong. Also use '' in place of 'mu' too.