The solution to Problem 3, PSet 10 contains errors and inconsistencies. The problem states that the curve of the trough is given by z=(1/100)x**4, but the lower limit for the integral is given as (1/81)x**4. The length of the trough is stated as 200m, but the picture shows a length of 300m and the solution uses a length of 100m. Finally, the density of water is listed as 1kg/m*3. The solution uses 1000kg/m*3. Note that kg, not g are the correct units for finding energy in joules.

Question

The solution to Problem 3, PSet 10 contains errors and inconsistencies.  The problem states that the curve of the trough is given by z=(1/100)x**4, but the lower limit for the integral is given as (1/81)x**4.  The length of the trough is stated as 200m, but the picture shows a length of 300m and the solution uses a length of 100m.  Finally, the density of water is listed as 1kg/m*3.  The solution uses 1000kg/m*3.  Note that kg, not g are the correct units for finding energy in joules.

phi · Answer

yes, both the question and answer are a mess.

if z goes to 81
we get nicer x values using z= x^4/81
(x= -9 to +9)
and who knows what the length is.
further, evaluating the iterated integral given in the solution,  I get 1.14e9 J which does not match the quoted result of 5.14e10 Joules.

baru · Answer

.