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 mu. 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.

Answer 1

Initial kinetic energy and potential energy of the toy is lost to friction while sliding across the rough horizontal surface

KE+ PE = W friction

KE; + PE; = F friction *d

Frictional force = coefficient of friction * Normal reaction

KE; + PE; = 4N*d

mV? + mgD = umg *d

Cancel mass m

p*6rt = 76 +247

Divide all terms with $\mu g$

vo 2μg 9D μg μgd μg

2μg μ

ANSWER: ${\color{Red} d=\frac{V^{2}}{2\mu g}+\frac{D}{\mu }}$

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