# Finding acceleration on a slope

1. Oct 21, 2008

### jchipwpunj

1. The problem statement, all variables and given/known data
A child sits on a sled that rests on a snow-covered hill making an angle of 30 degree with the horizontal. The mass of the child and sled is 50 kg. if the coefficient of friction is 0.15, what is the acceleation of the sled down the hill?

2. Relevant equations
I'm trying to double check my work. My tutor gave me one answer, but I keep getting another. He gave the answer 2.9 m/s^2. I keep getting 3.63 m/s^2.

3. The attempt at a solution
First, the sum of the forces in the X direction...
1. ∑(Fx)=m*g*sinθ+ (-μ*m*g*cosθ) = ma
where m is mass; g is acceleration due to gravity (9.8); μ is the coefficient of frictions; and a is the acceleration in the x direction

We know these...
2. m = 50 ; g=9.8; θ=30; μ=-.15

Substitute
3. (50)*(9.8)*sin30 + [(-.15)*(50)*(9.8)*(cos30)] = (50)a
(245) + (-63.65) = (50)a
(181.35) = (50)a

I also did the problem by factoring out and canceling 'm'
4. ∑(Fx)=m*g*sinθ+ (-μ*m*g*cosθ) = ma

m*g*sinθ+ (-μ*m*g*cosθ) = ma
(m*g)*[sinθ - (μ*cosθ)] = ma the masses cancel so we're left with...
g*[sinθ - (μ*cosθ)] = a

(9.8)*[sin30 - (.15*cos30)] = a
(9.8)*[sin30 - (.1299)] = a
(9.8)*(.3701) = a
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Oct 21, 2008

### einstein_a_go_go

I get the same as you