# Homework Help: Calculating constant velocity using work

1. Nov 22, 2011

### anonymous12

1. The problem statement, all variables and given/known data
A 25.6-kg boy pulls a 4.81-kg toboggan up a hill inclined at 25.7º to the horizontal. The vertical height of the hill is 27.3 m and the coefficient of friction of the hill surface is 0.4
a) Determine how much work the boy must apply on the toboggan to pull it at a constant velocity up the hill? (Hint: An FBD is needed to see all your forces acting on te toboggan)

2. Relevant equations
W = F x ∆d
Eg = mgh
Ek = 0.5mv^2
vf^2 - vi^2 = 2a∆d

3. The attempt at a solution

$$-mgsin25.7º - \mu Kmgcos25.7º = m * a$$
$$-(30.41 x 9.8 x sin 25.7º) - (.4 x 30.41 x 9.8 x cos 25.7) = 30.41 * a$$
$$-129.24 - 106.46 = 30.41a$$
$$a = -7.75 m/s^2$$

Calculating length of the hill:

$$\frac{27.3}{sin25.7º} = 62.95m$$

I don't really know what to do after this.

2. Nov 22, 2011

### cepheid

Staff Emeritus
If the boy is pulling the toboggan up the hill at a constant speed, then what must the acceleration be equal to? Hint: your mistake was that you forgot one of the forces in the force balance equation: the applied force from the boy!

Last edited: Nov 22, 2011
3. Nov 22, 2011

### LabGuy330

The reply above is spot on.