# Homework Help: Calculate the retarding force of a cyclist on a slope

1. Nov 17, 2014

### Nicaragua

1. The problem statement, all variables and given/known data
A cyclist attacks a 20% hill, the mass of the cyclist plus the bike is 100kg. Assuming g = 10 N kg^-1 , calculate the size of the retarding force due to gravity, acting along the slope.

2. Relevant equations
g = 10 N kg^-1 , Work = Force x Displacement,

3. The attempt at a solution
I was thinking that maybe resolving into vertical and horizontal components of the cyclists weight but am not quite sure how this would work. I have never worked a retarding force on a slope before. Some guidance please? Thanks

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2. Nov 17, 2014

### Staff: Mentor

You have the right idea. Draw the free body diagram (FBD) for the cyclist. The weight of the cyclist points down toward the center of the Earth, and that will give you components parallel to the slope and perpendicular to the slope. The component parallel to the slope is the retarding force. If the slope is horizontal (0%), there will be no retarding force, and all of the weight is straight down. If the slope is 100% (45 degrees), how much of the rider's weight is the retarding force?

3. Nov 17, 2014

### Nicaragua

If the slope was 100%, would the horizontal component be 0 and the vertical (retarding) be all of the rider's weight?

4. Nov 17, 2014

### Staff: Mentor

No. a 100% slope is 45 degrees. Rise/Run = 1.0 = 100%.

5. Nov 17, 2014

### Nicaragua

I'm struggling to see how to use that to find the two components :/

6. Nov 17, 2014

### Staff: Mentor

Well, one of the components varies as sin(angle) and the other varies as cos(angle). We said that on a horizontal slope, the retarding force is zero. Which of those trig functions is zero when angle=0....?

7. Nov 17, 2014

### Nicaragua

Sin(angle)? But it's not at a 0 degree angle?

8. Nov 17, 2014

### Staff: Mentor

9. Nov 17, 2014

### Nicaragua

There should be an image of it attached?

10. Nov 17, 2014

### Staff: Mentor

Ah, sorry. I missed that. So draw a horizontal line from the lower left point of the slope, and label that included angle θ. Now what?

11. Nov 17, 2014

### Nicaragua

Here is what I have came to so far. Not quite sure which trig function to use.

The gradient is 20% if that helps?

Btw thanks very much for going through this with me, with each reply I learn a bit more :)

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