Frank Key's Cafe supplies

how do you do this?

A machine in an ice factory is capable of exerting 3.06 102 N of force to pull a large block of ice up a slope. The block weighs 1.19 104 N. Assuming there is no friction, what is the maximum angle that the slope can make with the horizontal if the machine is to be able to complete the task?

First, I shall assume you meant 3.06 * 10^2 N, and 1.19 * 10^4 N.

Assuming this, you can say that if the sum of the forces = ma.

So, your two forces are the pull and your weight. Your acceleration is the minimum acceleration. We say that if we solve it for 0 acceleration, then that will give you the maximum angle. That is, you must be less than this angle to accomplish the task, no matter how long it takes — we don’t care.

Now, notice that the pull is at an angle. This also makes your weight at an angle. Draw a diagram and convince yourself that:

Force pull * cos (theta) – Weight * sin (theta) = ma = 0

Now, I’ll call Force pull F, and Weight W.

So, solve:

Fcos(theta) = W sin (theta)
F/W = sin(theta) / cos(theta) = tan (theta)
arctan(F/W) = theta

I came up with 1.47 degrees. You have a really small pulling force and a pretty heavy block, so this should make sense.

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