An ice cube (m = 400 grams) starts from rest at an initial height of h_o = 50 cm

Question

An ice cube (m = 400 grams) starts from rest at an initial height of h_o = 50 cm above the kitchen table and slides frictionlessly down a cookie sheet and across the table. What type of energy does the ice cube have before it starts to move? Describe the changes in energy as the ice cube travels down the cookie sheet, across the mustard and into the spring. Be sure to name the types of energy involved and describe what happens to energy as the ice cube crosses the mustard. Determine the speed of the ice cube at the bottom of the frictionless cookie sheet. The ice cube continues sliding and crosses an 8 cm patch of dried mustard that has a coefficient of kinetic friction mu_k = 0.5. How much energy is lost as the ice cube slides across the cried mustard? Determine the speed of the ice cube after it has crossed the mustard patch. Finally, the ice cube bumps into a spring and compresses it a distance of 10.0 cm before stopping and rebounding back. Determine the spring constant k of the spring.

Explanation / Answer

a) Initially it had gravitational potential energy.

as block comes down this gravitational potential energy converts into kinetic enertgy of block.

then it wil move with constant speed. then it comes across rough patch.

as it passes through it, some of KE get lost against work done by friction and converted in to

thermal energy.

after that remaning Ke will converts into potential energy of spring.

then back to KE energy and block moves toward incline.

b) using energy conservation,

PEi + KEi = PEf + KEf

mgh + 0 =   0 + mv^2 / 2

v =srt(2gh) = sqrt(2 x 9.8 x 0.50) = 3.13 m/s

c) N = mg

friction = uN = 0.5 mg

work done by friction = - f.d = - 0.5 x 0.400 x 9.8 x 0.08 = - 0.1568 J

d) initial energy = mgh = 0.400 x 9.8 x 0.50 = 1.96 J

KE after patch = 1.96 - 0.1568 = 1.8032

0.4 v^2 /2 = 1.8032

v = 3 m/s

e) now this KE = 1.8032 J will converts into spring PE.

1.8032 = k (0.10^2 ) /2

k = 360.64 N /m

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