Pennsylvania State University MATH 141 ALC ANLY GEOM II . In-Class Worksheet Week 6. Winter 2023.

Math 141 In-Class Worksheet Week 6 Page 1 of 4 Question 1 (a) A 3 kg book is lifted vertically 8 m. Calculate the work done. (b) A 10 lb object is lifted vertically 3 ft. Calculate the work done. Question 2 A 20-foot chain with density 4 lb/ft hangs off the roof of a building. How much work is required to pull the chain to the roof? I ft T Math 141 In-Class Worksheet Week 6 Page 2 of 4 Question 3 A trough with trapezoidal cross sections is 8 m long. The trapezoidal cross sections have a height of 2 m, a bottom width of 2 m, and a top width of 5 m. It is full of water. Recall water has a density of ρ = 1000 kg/m3, the acceleration due to gravity is 9.8 m/s2, so that the weight density of water is δ = 9800 N/m3. (a) Calculate the work needed to pump the water out of the top of the trough. Hint: instead of thinking in terms of similar triangles, you can use the fact that the slice width is a linear function of the slice’s vertical position. (b) Write a definite integral that calculates the work needed to pump the water to a height of 5 m above the top of the trough. K EI Math 141 In-Class Worksheet Week 6 Page 3 of 4 K EI i 4 140 Math 141 In-Class Worksheet Week 6 Page 4 of 4 Question 4 A solid pyramid is 140 m in height, and has a square base with side length 200 m. It is made of stone with a density of 1600 kg/m3. How much work did it take to build the pyramid? (This is like a water pumping problem, but instead of “lifting” the water to a particular height, the material to build each part of the pyramid is lifted from the ground.) EI i 4 140 K EI i 4 140 Math 141 In-Class Worksheet Week 6 Page 5 of 4