P10: An object of mass m slides from initial height h down a curved ramp, onto a
ID: 1778360 • Letter: P
Question
P10: An object of mass m slides from initial height h down a curved ramp, onto a flat area. There is a patch of length L with coefficient of kinetic friction , on the flat portion, but the ramp is frictionless everywhere else. Beyond the patch, there is a spring of constant k a) Assume friction is high enough to stop the mass half way across the patch. What value of p will do this? Please be sure to answer in terms of the other given variables and g. b) Instead, assume that friction is low enough for the mass to reach the spring, how much is the spring compressed? Please be sure to answer in terms of the given variables and g.Explanation / Answer
(a) kinetic friction uk is
the energy Ef = uk * m * g * d
uk = Ef / mgd = 0.0509*v^2 / d
K.E. = 0.5 * m*v^2 = Ef
m = mass of object
g = 9.81 m/s^2
d = the distance the object moves along
(b) the spring compress is
Ethermal = 0
KEi + PEi = KEf + PEf
0 + mgh = 0 + (1/2)kx^2
x = sqrt(2mgh/k)
k is the spring constant
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