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?

The final velocity of the sugar cube at the top is 2.25 m/s.

The given parameters;

The final velocity of the sugar cube at the top is calculated by applying the principle of conservation of energy;

Thus, the final velocity of the sugar cube at the top is 2.25 m/s.

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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

emily ruth's annual premium is $1058.50

step-by-step explanation:

emily ruth is a female of 27 years age purchasing 20 year endowment insurance with face value $25000.

from the given table,

for females, the age of a male 3 years younger should be used.

so, we have to check for 24 year male for 20 year endowment.

it is 42.34 for every $1000 face value.

for a face value of $25000,

it is 25 * 42.34 = $1058.50

∴ emily ruth's annual premium is $1058.50