# Incline problem

1. Feb 10, 2008

### JonathanSnow

we have to design an entrance ramp for the new megamart. the maximum force customers will exert without complaint is 20N, ignoring friction at what maximum angle should the ramp be built assuming a full 20 kg grocery cart?

i've almost drawn at a blank it just seems like the question is missing something is there any other way besides trial and error, even miniscule hints would be appreciated

2. Feb 10, 2008

### Dick

The variable is angle of the ramp. On this incline the tangential force on a 20kg stationary grocery cart should be 20N. The gravitational force is mg. How much is tangential at an angle theta? Can you solve for the angle?

3. Feb 10, 2008

### JonathanSnow

im still confused a bit the angle is it 5.8ish im not sure exactly what im missing
f=mg sin(theta)

Last edited: Feb 10, 2008
4. Feb 10, 2008

### Dick

You didn't show much of your work there. Yes, it is 5.8ish if you mean degrees. It's hard to tell what you are missing if you don't say what you did or why you don't think it's right.

5. Feb 10, 2008

### JonathanSnow

ok what i did was used the formula F=mg sin(Theta) and punched in
20=20(9.81) sin (theta)
20/196.2=sin(theta)
sin-1(.101...)=theta
theta = 5.85
?
so when i get this angle is that the maximum it can be?

6. Feb 10, 2008

### Dick

At that angle holding a 20kg grocery cart at constant acceleration will need a force of 20N. If the angle is larger, the force is larger. And I guess that means the customers will complain. Well done.

7. Feb 10, 2008

thanks alot!