Find the Distance of a Toy Zebra from a Chute

[becky_marie11]

Homework Statement

A boy shoves his stuffed toy zebra down a frictionless chute, starting at a height of 1.05 m above the bottom of the chute and with an initial speed of 1.71 m/s. The toy animal emerges horizontally from the bottom of the chute and continues sliding along a horizontal surface with coefficient of kinetic friction 0.263. How far from the bottom of the chute does the toy zebra come to rest? Take g = 9.81 m/s2.

h=1.05m
Vi=1.71m/s
μk=.263
g=9.81m/s^2

Homework Equations

K=1/2mv^2
W=-μmgd
W(non conservative)=Ef-Ei

The Attempt at a Solution

I don't even know where to start... I solved for the final velocity using regular kinematic equations, but without a mass, I have no idea how to go about this... please help!

 

[BruceW]

There's essentially two parts to the question. So the first part is calculating the speed which the object gets to when it gets to the bottom of the chute. I'm guessing you've done the regular kinematic equations for this part? Which equations did you use, and what answer did you get to?

 

[I like Serena]

Welcome to PF, becky_marie11!

I'm missing the relevant equation for potential energy.
Conservation of energy says that the total initial energy must have been canceled by the work done by friction.

 

[becky_marie11]

Ohhh...Wait I figured it out. Nevermind! Thanks though!

 

[asteriatic]

I would first identify the relevant equations and variables in this problem. The initial height of the toy zebra can be represented by the variable h, the initial velocity by Vi, the coefficient of kinetic friction by μk, and the acceleration due to gravity by g. The mass of the toy zebra is not given, but it is not needed to solve this problem.

Next, I would use the conservation of mechanical energy equation, which states that the initial kinetic energy plus the initial potential energy equals the final kinetic energy plus the final potential energy. In this case, the initial potential energy is equal to the final potential energy because the toy zebra starts and ends at the same height. Therefore, we can set the initial kinetic energy equal to the final kinetic energy and solve for the final velocity.

Using the equation K=1/2mv^2, we can solve for the final velocity by plugging in the given values for the initial velocity and the coefficient of kinetic friction. This will give us the final velocity of the toy zebra as it reaches the bottom of the chute.

Next, we can use the equation W=-μmgd to find the work done by friction as the toy zebra slides along the horizontal surface. We can then use the work-energy theorem, which states that the net work done on an object is equal to the change in its kinetic energy, to solve for the distance d traveled by the toy zebra before it comes to rest.

Finally, we can plug in the values for g and the final velocity to solve for the distance d. This will give us the distance from the bottom of the chute where the toy zebra comes to rest.