# Maximum acceleration up ramp

1. Mar 18, 2009

### diffusion

You are trying to have your remote-controlled car leap off a ramp, which happens to be at a 20 degree incline to the ground. If the coefficients of static and kinetic friction are .70 and .50, repsectively, what is the maximum possible acceleration of the remote-controlled car up the ramp?

2. Mar 18, 2009

### Vuldoraq

Hi,

Have you drawn a free body force diagram? Also we need to see your attempt at the solution before we can help you.

3. Mar 19, 2009

### diffusion

Not sure how to find the solution, but I'll wing it.

Max acceleration = -mg(sin20) + max static friction / mass.

Max static friction = static coefficient x normal force = 0.70 x n

Find n (Net force in y-direction) = mgcos20.

Now you plug mgcos20 back into the original equation

-mg(sin20) + mgcos20 / mass.

Stuck here.

4. Mar 19, 2009

### Staff: Mentor

Looks like you knew more than you thought.

Looks good to me. Realize that mass = m, so it cancels. And use parentheses, to reduce mistakes. I'd write that as:

a = ( -mgsin20 + mgcos20 )/m

5. Mar 19, 2009

### diffusion

I realize this is going to be a stupid question, but how do they cancel? In the numerator you have two mg's, only one in the denominator. Isn't that going to leave you with another m?

6. Mar 19, 2009

### Staff: Mentor

No. Each term in the numerator has a single "m". It factors out like so:

mX + mY = m(X + Y)

7. Mar 19, 2009

### diffusion

Gotcha. Thanks.