Answer:
(a) To find the equation connecting P and W, we can set up a system of equations using the given information.
Given: P = 2.32 when W = 2
and P = 3.19 when W = 5
Let's assume that the constant part of the effort is represented by K, and the varying part of the effort is represented by M.
So, the equation relating P and W can be written as:
P = K + M * W
Substituting the given values, we get:
2.32 = K + M * 2
3.19 = K + M * 5
Solving these two equations simultaneously will give us the values of K and M.
Subtracting the first equation from the second equation, we get:
3.19 - 2.32 = K + M * 5 - (K + M * 2)
0.87 = 3M
Dividing both sides by 3, we get:
M = 0.29
Substituting the value of M in the first equation, we can solve for K:
2.32 = K + 0.29 * 2
2.32 = K + 0.58
K = 2.32 - 0.58
K = 1.74
Therefore, the equation connecting P and W is:
P = 1.74 + 0.29 * W
(b) To find P when W = 12, we can substitute W = 12 into the equation we found in part (a):
P = 1.74 + 0.29 * 12
P = 1.74 + 3.48
P = 5.22
Therefore, when W = 12, P = 5.22 kg.