Question

A U.S quarter is rolling on the floor without slipping in such a way that it describes a circular path of radius R=4 cm. The plane of the coin is tilted at an angle of θ=45∘ with respect to the horizontal plane (see the figure below). Find the coin's period T in seconds, that is, the time it takes for the coin to go around the circle of radius R. The radius of a U.S quarter is r=1.2 cm.

Answer 1

Newton’s 2nd law
vector(ma) = vector(mg ) +vector( N) +vector(Ffr)
Projections:
ma=F(fr)
0=N-mg

mv²/r =μN
N=mg

mv²/r = kN = μmg
μ=v²/gr.

tanα =F(fr)/N = μmg/mg = μ = v²/gr.
v=sqrt{gr•tanα}

T=2πR/v= 2πR/ sqrt{gr•tanα} = …

Answer 2

nope, 0.733 is wrong

Answer 3

wait, Elena, what is are R and r? Are they the same ones that I used?

Answer 4

R=0.04 m
t= 0.012 m
The solution is correct.May be there is mistake in calculations (or in your answer)...

Answer 5

net torque on the coin, answer not just force balance