Solve the problem.
-A glass has circular cross sections that taper (linearly) from a radius of 7 cm at the top of the glass to a radius of 6 cm at the bottom. The glass is 15 cm high and full of lemonade. How much work is required to drink all the lemonade through a straw if your mouth is 8 cm above the top of the glass? Assume the density of lemonade equals the density of water. Round to two decimal places when appropriate.
A) 2.96 J
B) 0.94 J
C) 55.65 J
D) 4.32 J

Question

Solve the problem.   
-A glass has circular cross sections that taper (linearly) from a radius of 7 cm at the top of the glass to a radius of 6 cm at the bottom. The glass is 15 cm high and full of lemonade. How much work is required to drink all the lemonade through a straw if your mouth is 8 cm above the top of the glass? Assume the density of lemonade equals the density of water. Round to two decimal places when appropriate.
A) 2.96 J
B) 0.94 J
C) 55.65 J
D) 4.32 J

Quizplus · Accepted Answer

The work done is equal to the change in potential energy of the lemonade. The potential energy of the lemonade is equal to the mass of the lemonade times the acceleration due to gravity times the height of the lemonade. The mass of the lemonade is equal to the density of the lemonade times the volume of the lemonade. The volume of the lemonade is equal to the area of the circular cross section of the glass times the height of the lemonade. The area of the circular cross section of the glass is equal to pi times the radius of the circular cross section squared. The height of the lemonade is equal to the height of the glass minus the height of the straw. The acceleration due to gravity is 9.8 m/s^2.Plugging in the given values, we get:mass of the lemonade = (1000 kg/m^3) * (pi * (0.07 m)^2 * 0.15 m) = 0.226 kgheight of the lemonade = 0.15 m - 0.08 m = 0.07 mwork done = (0.226 kg) * (9.8 m/s^2) * (0.07 m) = 0.15 JTherefore, the work required to drink all the lemonade through a straw is 0.15 J.

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