Again consider the potential energy stored in a spring, U=12 kx2 . What variables could you plot against each other and expect a straight line (For full marks select ALL that work). Question 5Select one or more: a. U−−√ against x . b. U against kx . c. U−−√ against x2 . d. U against x2 . e. U against x .
Question
Again consider the potential energy stored in a spring, U=12 kx2 . What variables could you plot against each other and expect a straight line (For full marks select ALL that work).
Question 5Select one or more:
a. U−−√ against x .
b. U against kx .
c. U−−√ against x2 .
d. U against x2 .
e. U against x .
Solution
The potential energy stored in a spring is given by the equation U = 1/2 kx^2. To get a straight line graph, we need to plot variables such that one is directly proportional to the other.
a. U^1/2 against x: This will not give a straight line because U^1/2 is proportional to x, not x^2.
b. U against kx: This will not give a straight line because U is proportional to x^2, not x.
c. U^1/2 against x^2: This will give a straight line because U^1/2 is proportional to x, and x is the square root of x^2.
d. U against x^2: This will give a straight line because U is directly proportional to x^2.
e. U against x: This will not give a straight line because U is proportional to x^2, not x.
So, the correct answers are c. U^1/2 against x^2 and d. U against x^2.
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