Answer:
C = 17 i^ - 7 j^ + 16 k^
, | C| = 24.37
Explanation:
To work the vactor component method, we add the sum in each axis
C = A + B = (Aₓ + Bₓ) i ^ + (
+
) i ^ + (
+
) k ^
Cₓ = 12+ 5 = 17
= -37 +30 = -7
= 58 -42 = 16
Resulting vector
C = 17 i ^ - 7j ^ + 16k ^
The mangitude of the vector is
| C | = √ c²
| C | = √( 17² + 7² + 16²)
| C| = 24.37
Work needed: 720 J
Explanation:
The work needed to stretch a spring is equal to the elastic potential energy stored in the spring when it is stretched, which is given by

where
k is the spring constant
x is the stretching of the spring from the equilibrium position
In this problem, we have
E = 90 J (work done to stretch the spring)
x = 0.2 m (stretching)
Therefore, the spring constant is

Now we can find what is the work done to stretch the spring by an additional 0.4 m, that means to a total displacement of
x = 0.2 + 0.4 = 0.6 m
Substituting,

Therefore, the additional work needed is

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