thanks for answering the question
I got another one...
A 15.0 kg box is released on a 30 degree incline and accelerates down the incline at .30 m/s^2. Find the firctiopn force impeding its motion. What is the coefficient of kinetic friction?
SIGMA F_x = m a_x = F_g_x - F_fr_k = mg sin THETA - mg cos THETA MU
therefore
mg cos THETA MU = mg sin THETA - m a_x
I divided through by mass
g cos THETA MU = g sin THETA - a_x
I do not see what is wrong with this solution. This gave me 4.6 N. I'm suppose to get 69 N. I know that if I muliply 4.6 N by 15 (the mass that I canceled out) I get 69 N.
So apparently I don't know why I can not divide by the mass here and would like to know why...
Surpisingly enough when I rearanged for Mu I did this and got the right answer according to the back of the book
F_fr_k = 4.6 N = g cos THETA MU
therefore
MU = 4.6 N/(g cos THETA)
this gave me the right answer of .54
THANKS!
those are subscripts by the way
F_fr_k
is the force of kinetic friction
and the all capital letters are greek leters
You're welcome! I'm glad I could help. It seems like you were able to solve the problem by rearranging the equation in terms of the friction force and the coefficient of kinetic friction.
Let's discuss the part where you were dividing through by mass and why it didn't work in this case.
In the equation: g cos θ μ = g sin θ - a_x
You tried to divide both sides of the equation by the mass, but you encountered an issue. The reason for this is that the term "mg cos θ μ" represents the force of kinetic friction, which is a force acting on the box and is dependent on the mass. When you divided by the mass, you effectively canceled out the dependence on mass.
Dividing both sides of the equation by the mass would give:
g cos θ μ = g sin θ - a_x
Dividing by the mass cancels out the mass on both sides:
g cos θ μ = (g sin θ)/m - a_x/m
However, we know that the force of kinetic friction, F_fr_k, should not be affected by the mass of the object. The force of friction depends on the coefficient of kinetic friction and the normal force, not the mass itself. Therefore, in this particular problem, it is not valid to divide the equation by the mass.
To find the friction force impeding the motion, you can rearrange the equation as you did earlier:
F_fr_k = g cos θ μ
Then solve for the coefficient of kinetic friction:
μ = F_fr_k / (g cos θ)
By doing this, you correctly calculated the coefficient of kinetic friction as 0.54.
I hope this clarifies why dividing through by the mass didn't work in this case. If you have any more questions, feel free to ask!