A 29.0-g object is placed against the free end of a spring (k equal to 25.0 N/m)
ID: 1780591 • Letter: A
Question
A 29.0-g object is placed against the free end of a spring (k equal to 25.0 N/m) that is compressed 12.0 cm (see the figure below). Once released, the object slides 1.25 m across the tabletop and eventually lands 1.60 m from the edge of the table on the floor, as shown. Is there friction between the object and the tabletop? If there is, what is the coefficient of kinetic friction? The sliding distance on the tabletop includes the 12.0-cm compression of the spring, and the tabletop is 1.00 m above the floor level. 1) Is there friction between the object and the tabletop? Yes, coefficient of kinetic friction is 0.100 Yes, coefficient of kinetic friction is 0.300 Yes, coefficient of kinetic friction is 0.600 Yes, coefficient of kinetic friction is 0.900
Explanation / Answer
from the edge of the table
along vertical
initial velocity voy = 0
acceleration ay = -g = - 9.8 m/s^2
displacement y = -1 m
y = voy*t + (1/2)*ay*t^2
-1 = 0 -(1/2)*9.8*t^2
time t = 0.452 s
along horizontal
velocity v = d/t = 1.6/0.452 = 3.54 m/s
on the table top
initial potential energy Ei = (1/2)*k*x^2
final energy at the edge of table Ef = (1/2)*m*v^2
work done by friction Wf = uk*m*g*d
Wf = Ef - Ei
uk*m*g*d = (1/2)*m*v^2 - (1/2)*k*x^2
uk*0.029*9.8*1.25 = (1/2)*0.029*3.54^2 - (1/2)*25*0.12^2
coefficent of friciton uk = 0.005 <<<------ANSWER
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