- #1
ChrisBrandsborg
- 120
- 1
Homework Statement
A child is at a playground, and chooses to try the spinning disc (see figure). The radius of the disc is 2.00 m, and the coefficient of static friction between child-surface and disc-surface is μs = 0.350.
In the following questions, you must provide algebraic equations as well as final numbers.
a) If the child sits 1.50 m from the centre, how fast can the spinning disc turn, without her slipping off?
b) The evil big brother now spins the disc with ω = 2.00 rad/s. At what distance from the centre of the disc should the kid sit, to avoid falling off?
Having safely moved to the radius 0.500 m, the child starts complaining, becau- se she cannot get off the ride. The evil big brother decides to stop the rotating disc, by providing a constant tangential force.
c) How quickly can he stop the disc, without her sliding in any direction (neither forwards, backwards, inwards or outwards)?
Homework Equations
(possibly)[/B]1. m⋅ν2/r (centrifugal force)
2. ω = ν/r (angular velocity)
3. a = -ν2/r (accelration)
3. F = ma (Newton Law)
The Attempt at a Solution
Relevant information:
r = 2.00m (radius of the disc)
μs = 0.350 (static friction)
Fs = μs⋅mg
ra = 1.50m (distance from centre - in a)
My attempt:
mν2/r = μsmg
μs = νmax2/rg
vmax = √μsrg
vmax = √0.350⋅1.50m⋅9.80m/s2 = 2.27 rad/s
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