Is a 5° Ramp Slope Too Steep for Pushing a 30kg Cart?

[TrpnBils]

Homework Statement

In the design of a supermarket, there are to be several ramps connecting different parts of the store. Customers will have to push grocery carts up the ramps and it can't be too difficult. An engineer has done a survey and found that no one complains if the force required is no more than 50N. Will a slope of θ=5° be too steep, assuming the cart has a mass of 30kg? Assume μ_k=0.10

Homework Equations

Ff = μ_kFn

The Attempt at a Solution

Yes, it is too steep. Why? I have no idea...

Below is my diagram...forgive the fact that Fp is not parallel to the ramp's surface. It's supposed to be, but it's the best I can do in MS Paint right now.

Ff = μ_k * FN
= 0.1 * 299N
= 29.88 N

FNet = Ff + Fp = 55.88N (greater than the required 50N limit)

Is that right? I've been sitting here looking at this stupid thing for over an hour and I think I may have just gotten it. The one thing I don't like about these textbooks is that they give the answers to selected problems but no explanation. Just because my answer here is over 50N doesn't necessarily mean that it's right. So is it?

 

[ehild]

FNet = Ff + Fp = 55.88N (greater than the required 50N limit)

Is that right? I've been sitting here looking at this stupid thing for over an hour and I think I may have just gotten it. The one thing I don't like about these textbooks is that they give the answers to selected problems but no explanation. Just because my answer here is over 50N doesn't necessarily mean that it's right. So is it?

It is over 50 N, the numerical result is almost right, and yes, the slope is too steep. You did it well, why do you not trust in yourself? one small mistake: mg = 30*9.8cos5=293 instead of 299. What value have you used for g? ehild

 

[Simon Bridge]

According to the diagram he used g=10m/s/s. May have been told to use that. The 299 is mg.sin(5deg). The reasoning shown is sound - needs to draw the friction in the free-body diagram but that's a quibble. Just a tidy up.

One of the ways to gain confidence in your calculations is to keep track of your reasoning at each step. If your initial attempt looks kinda all over the place it can help to pretend you are explaining how to do it to someone else (like us :) ) and you need to keep the explanation simple and short as you can.