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A very slippery ice cube slides in a vertical plane around the inside of a smooth, 20-cm-diameter horizontal pipe. The ice cube’s speed at t
Question
A very slippery ice cube slides in a vertical plane around the inside of a smooth, 20-cm-diameter horizontal pipe. The ice cube’s speed at the bottom of the circle is 3.0 m/s. What is the ice cube’s speed at the top?
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Physics
2 years
2021-07-27T15:59:06+00:00
2021-07-27T15:59:06+00:00 1 Answers
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Answer:
Explanation:
Given that,
Diameter of pipe
d = 20cm
Then, radius =d/2 =20/2
r = 10cm =0.1m
The speed at the bottom is
Vi = 3m/s
Speed at the top Vf?
At the bottom the cube is at a height of 0m
Then, y1 = 0m
At the top the cube is at a height which is the same as the diameter of the pipe
y2 = 0.2m
Now, let us consider, the energy conservation equation , which is the sum of kinetic energy and gravitational potential energy, given by,
K2 + U2 = K1 + U1
½m•Vf² + m•g•y2 = ½m•Vi² + m•g•y1
Divide all through by m
½•Vf² + g•y2 = ½•Vi² + g•y1
Since y1 = 0
So we have,
½•Vf² + g•y2 = ½•Vi²
½•Vf² = ½•Vi² — g•y2
Multiply through by 2
Vf² = Vi² —2g•y2
Vf = √(Vi²—2g•y2)
g is a constant =9.81m/s2
Vf = √(3²—2×9.81×0.2)
Vf = √(9—0.981)
Vf = √8.019
Vf = 2.83m/s
The speed of the ice cubes at the top of the pipe is 2.83m/s