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Knissp
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Homework Statement
A small block of mass m slides on a horizontal frictionless surface as it travels around the inside of a hoop of radius R. The coefficient of friction between the block and the wall is mu; therefore, the speed v of the block decreases. In terms of m, R. mu, and v, find expressions for each of the following.
b. The block's tangential acceleration dv/dt
c. The time required to reduce the speed of the block from an initial value v0 to vo/3
(A diagram is given here on page 4: www.swcp.com/~gants/calendars/ap%20physics/sept%20docs/(A)%20Newton's%20LawsC.doc)
Homework Equations
dv/dt = aT = tangential acceleration
aA = angular acceleration
aC = centripetal acceleration
v/r=w (angular velocity)
The Attempt at a Solution
First I tried to use aT = r * aA = r * d^2 (theta) / dt^2 but I don't think that's right because none of those values are given.
Then I tried to do
Fnet = m * (aC^2 + aT^2)^(1/2) = ((m*v^2/r)^2+(m*aT - mu*m*v^2/r))^(1/2)
but I think that's wrong because I'm taking taking the forces and finding the vector sum of them and I don't know if that's allowed like I can do with the (aC^2 + aT^2)^(1/2) to get acceleration.
Perhaps would it help for me to know that dv/dt = dv/dx * dx/dt = v*dv/dx?? I'm kind of lost, any help would be greatly appreciated.
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