Thread: Radians & Angles

The attached shows the angle to be 65° , but that now is in radians where .

Then the normal reaction depend on ; we let the normal reaction from the lift have magnitude newtons. We assume that the domain of is

1) Use a triangle of force to show that the has the rule



2) find the value of and explain why this value makes sense in situation modelled

It's not clear from the figure, but I'm going to guess that the ball m has a weight of 1.5N. The force of gravity is pulling down on the ball, and its weight is counter-acted by the normal force of the ramp. That normal force acts at angle x. There is also a third force at play here - the reaction force from the side wall, which I will call . See the attached figure - it shows how all three forces fit together to balance. From this you can see that , so .

2. If , you have the situaton where the ball is simply resting on a table, so of course the normal force is equal to the weight.

ok great - thank you for that. So how can we draw this as a graph. i.e with a table of values?

Then from that graph, explain why has an inverse function? leading from there - whats its domain and image set? can we then draw a graph?

You already know that the function of the reaction force for a given angle x is is f = 1.5N/sin(x). Make up a table of x and f where x varies from 0 to 90 degrees and see how f behaves. You can then plot f versus x.

To find the inverse function of f=1.5/sin(x) you need to rearrange this to get x by itself:

f = 1.5N/sin(x)
sin(x) = 1.5N/f
x = arcsin(1.5N/f)

This tells you what the angle x is to achieve a given reaction force f. The domain of 1.5N/f is limited to values less than or equal to 1 (since the arcsin of a value greater than 1 is not allowed). So if 1.5N/f must be less than or equal to 1, that means that f must be geater than or equal to 1.5N.

Any help on what the domain and image set is?

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