Please show all work for a high rated answer ( I want to check my work as well a

Question

Please show all work for a high rated answer ( I want to check my work as well as my answer).

Thank you.

You are testing the GRAVITRON (a.k.a, Starship 3), a spinning carnival ride that has been popular since its debut in 1983. Riders of the GRAVITRON lean against the inclined wall and are subjected to a 'centrifugal force' that can cause riders to slide up the wall. (This centrifugal force is one example of the fictitious or inertial forces that can arise in non-inertial frames of reference. The spinning ride is a non-inertial frame of reference.) The floor of the ride has radius R = 3. m, and the lower wall makes an angle theta = 4. degree with respect to the vertical, as shown. While fine-tuning the ride, you see that a test-mass (a block of mass m) is 'stuck to the walla distance L = .16 m up the wall as measured from the floor. Being the well-seasoned GRAVITRON tester that you are, you know that this really means that the block is moving in a horizontal circle at a constant speed, as shown below. At the moment, the block is moving with a constant speed = 9.55 m/s. What is ac the centripetal acceleration of the block as it moves along the horizontal path shown? How does your answer compare to g, the acceleration due to gravity? Solve the problem symbolically before calculating a numerical answer. You speed the ride up ever so slightly and notice that the box immediately begins to slide up along the wall. (This means that the block was on the verge of sliding upward when it was moving with speed in part (a).) What is mu s the coefficient of static friction between the block and the wall? Draw and label an appropriate free body diagram for this part, clearly indicating your choice of coordinate system. Solve the problem symbolically before calculating a numerical answer. Suppose that instead of speeding the ride up, you had slowed the ride down. What is the minimum speed at which the block could have moved and still remained at its original height above the floor? Draw and label an appropriate free body diagram for this part, clearly indicating your choice of coordinate system. Solve the problem symbolically before calculating a numerical answer.

Explanation / Answer

a. here net r =R +lsin theta =3 +0.16sin40 =3.103

centripetal acc =v^2/r =9.55^2/3.103=29.392 m/s^2

where g is 9.8 m/s^2 hence centripetal acc is 3 times g

..........

b)mv^2/r sin40 -mgcos40 =u*(mv^2/r cos40 +mgsin40)

v^2/r =29.392

g =9.8

hence friction coefficient u = 0.395

..........

c) mgcos40 =u*(mv^2/r cos40 +mgsin40) +mv^2/r sin40

V =Vmin =4.058

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