A) A 48 g ice cube can slide without friction up and down a 30 slope. The ice cu
ID: 1411194 • Letter: A
Question
A) A 48 g ice cube can slide without friction up and down a 30 slope. The ice cube is pressed against a spring at the bottom of the slope, compressing the spring 10 cm. The spring constant is 20 N/m . When the ice cube is released, what total distance will it travel up the slope before reversing direction?(height=21cm and distance is 43cm the part im intrested is in part B).
B) The ice cube is replaced by a48 g plastic cube whose coefficient of kinetic friction is 0.20. How far will the plastic cube travel up the slope?
(show all steps please)
Explanation / Answer
A)
The energy from the spring is:
kx^2 / 2 = 20*0.10^2 / 2 = 0.1 J.
Equating the energy above to the potential energy of the cube at its maximum height h cm:
0.048* 9.81*h = 0.1
h = 21.27 cm.
If x is the distance along the slope:
h = x sin(34)
x = h / sin(30)
x = 42.54 cm.
B)
the stored spring energy is converted into height energy and frictional heat energy.
The height energy is m*g *d*sin(30)
where d is the distance the cube moves along the slope.
The Frictional energy converted is F*d
F(the frictional force) = µ*N
N ( the reaction to the component of the gravity force perpendicular to the surface of the slope ) = m*g*cos(30)
Total energy converted
0.5*k *x^2 = (m*g*dsin(30) + (µ*m*g*cos(30)*d )
0.5 x 20 x 0.10^2 = d*((0.048 x 9.81 x 0.5) + (0.20 x 0.048 x 9.81 x 0.8660)
0.1 = d(0.23544 + 0.08156)
0.1 = 0.316996d
d = 31.55 cm
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