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 is obviously desired this not be too difficult., an engineer has done a survey and found that almost no one complains if the force required is no more than 50 n. will a slope θ = 5o be too steep, assuming a 30 kg grocery carts (full of groceries)? assume friction (wheels against ground, wheel on the axles, and so on), can be accounted for by a coefficient μk = 0.10

No, the slope won't be too steep

Explanation:

Force is an external agency that causes a body to change its position while friction is a force that causes a body to slide over another. This force is called the frictional force (Ff). The force that causes a body to move is the moving force (Fm).

The slope will be too steep if the frictional force is greater than the moving force since the frictional force tends to oppose the moving force.

According to the explanation, we need to get Ff and compare with the moving force along the plane.

If Ff>Fm it means the slope will be too steep but if Ff<Fm, the slope won't be too steep and as such the body can easily be moved along the plane.

Resolving forces acting along the plane we have FmSintheta + Ff = Fm (FmSintheta and Ff are added because they act in the same direction along the plane)

Fm=50N, theta=5°

Imputing this into the formula to get Ff;

50sin5°+Ff =50

Ff= 50-50sin5°

Ff= 50-4.35

Ff= 45.65N

Since Ff<Fm, this means the slope is not too steep and as such the 30kg load can be moved along the plane easily.

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