Question

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 desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20N .

Ignoring friction, at what maximum angle θ should the ramps be built, assuming a full 30kg grocery cart?

Express your answer using two significant figures.

Answer 1

3.90 degrees

Step-by-step explanation:

Let g= 9.81 m/s2. The gravity of the 30kg grocery cart is

W = mg = 30*9.81 = 294.3 N

This gravity is split into 2 components on the ramp, 1 parallel and the other perpendicular to the ramp.

We can calculate the parallel one since it's the one that affects the force required to push up

F = WsinΘ

Since customer would not complain if the force is no more than 20N

F = 20

`294.3sin\theta = 20`

`sin\theta = 20/294.3 = 0.068`

`\theta = sin^(-1)0.068 = 0.068 rad = 0.068*180/\pi \approx 3.90^0`

So the ramp cannot be larger than 3.9 degrees