5.8) *** A carnival ride consists of a vertical cylinder...

5.8) *** A carnival ride consists of a vertical cylinder that spins around its axis fast enough that any person in side is held against the side of the wall once the floor drops away (see figure). The coefficient of static friction between the person and the wall is $\mu_s$ and the radius of the cylinder is R. a. Draw a free body diagram, write out Newton's laws, and then explain why a person will fall from the wall when the cylinder is spinning slowly, but will stick to the wall when it is spinning fast. b. Show that the maximum period of revolution necessary to keep the person from falling is $T = (4\pi^2 R\mu_s / g)^{1/2}$ c. What is the value of $T$ if the radius of the cylinder is 4m and $\mu_s$=0.4. How many revolutions does the cylinder make per minute?

Transcript

00:01 Hi there.

00:02 Given problem here are this is a large cylindrical drum having a radius.

00:13 Oh, and the person remains stick.

00:27 I mean, this one, the weight of the person you'd be acting vertically don't work under which the person will be having a tendency to slide down or the wall of the slender so ah, force of friction will act on him in a direction worded belly up as the cylinder will rotate, a centrifugal force will act on the person they're really outward given by an expression mp scored by our which will create a normal reaction on the person you do this wall given by n.

01:10 So in the first part of the problem, we have toe find the rate off rotation off the slender good witch.

01:21 The partisan will remain.

01:23 Stick with the wall.

01:25 So the normal reaction acting on the person will be equal to centrifugal force acting on him, which is empty squad by art and as the person is not falling down.

01:41 So the weight of the person mg really just equal to four so static creation which we begin by new s times, the normal reaction or we can see mgi is equal to us.

01:59 Stine's off envy.

02:01 Square by up there must got cancer.

02:06 So we square comes out to be g times off our means, regis with a slender divided by new s so this week finally becomes squire rode off g times off radios divided by us and hence, you know the being at a speed in a circular motion may also be given us the product off really us with angular velocity.

02:41 So this week is going to our times, amigo is equal to g into our divided by a new s.

02:51 So the angular velocity here comes out to be one by our square root off g into our divided by us.

03:02 No, this angular velocity is giving us to buy divided by the time period so two pi bitey becomes one by our into g multiplied by r divided by a new s to the power ho.

03:21 So finally we can write the time period a period of rotation off the slender is equal to four times the to buy times.

03:34 It's the stool...

Question

Please give Ace some feedback