How Much Work Does It Take to Push a Sled Up a Snowy Hill?

[cmarte01]

Homework Statement

A father pushes horizontally on his daughter's sled to move it up a snowy incline, as illustrated in the figure, with h = 3.9 m and = 11°. The total mass of the sled and the girl is 35 kg and the coefficient of kinetic friction between the sled runners and the snow is 0.20. If the sled moves up the hill with a constant velocity, how much work is done by the father in moving it from the bottom to the top of the hill?

m=35 kg
h=3.9 m
angle= 11 degrees
kf= .20

Homework Equations

F=Uk
W=Fd
W=mg
sin=OPP/HYP

The Attempt at a Solution

W= mg, W=(35)(9.8) = 343
Fx= 343 sin 11 = 65.45
Fy= 336.70
.2*336.7 = 67.34
67.34+65.45 = 132.79
sin 11 = 3.9/HYP, HYP = 3.9/sin 11 = 20.44
132.79* 20.44 = 2714.23 J

What did I do wrong? Help!

 

[Shooting Star]

I can't see any figure. I assume that the vertical height of the hill is h = 3.9 m.

Component of mg acting along the slope is mgsin x, where x= 11 deg.
Normal reaction is mgcos x.
So, frictional force is kmgcos x along the slope.

Total force along the slope is the sum of these two forces, both acting downward.

W = f*d, where h/d = sin x.

Plug in the values now.

 

[ogb p]

As a scientist, it is important to carefully analyze the given problem and apply the appropriate equations and concepts. In this case, you correctly identified the relevant equations for calculating work (W=Fd) and friction (F=Uk), as well as the given values for mass, height, angle, and coefficient of kinetic friction. However, your calculation for the work done by the father (132.79 J) is incorrect.

To calculate the work done by the father in moving the sled up the hill, we need to consider the forces acting on the sled. The father's push creates a horizontal force (Fx) while the force of gravity acts vertically (Fy). The sled's movement up the hill is opposed by the force of kinetic friction (Ff). In order for the sled to move at a constant velocity, these forces must be balanced, meaning that the horizontal force (Fx) must be equal and opposite to the force of kinetic friction (Ff).

Using the given values, we can calculate the horizontal force (Fx) as 343 sin 11 = 65.45 N. This is also equal to the force of kinetic friction (Ff), which can be calculated as 0.2*336.7 = 67.34 N. Therefore, the work done by the father in moving the sled up the hill is the product of the horizontal force (65.45 N) and the distance traveled (h=3.9 m). This gives us a work done of 65.45 N * 3.9 m = 255.255 J.

It is important to carefully consider all the forces and their directions when solving a physics problem. Additionally, double-checking your calculations and units can help avoid errors. In this case, the final units for work should be Joules (J), not Newtons (N). I hope this helps clarify the solution to the problem.