Smudge

Lorenzo is writing a physics test, and their formula sheet has a smudge on it, making it hard to read the exponent of one of their equations, which describes the energy stored in a spring. Their copy reads \(U = \frac{1}{2}kx^?\), where \(?\) represents the number that they can’t read. Rather than asking the instructor (WHICH YOU SHOULD ALWAYS DO WHEN WRITING A TEST!), Lorenzo decides to use dimensional analysis to figure out the power. Lorenzo remembers that the units of energy, \(U\), are [\(U\)] = \(J\) = \(Nm\), the units of the spring constant, \(k\), are [\(k\)] = \(\frac{\text{N}}{\text{m}}\), and the units of position, \(x\), are [\(x\)] = \(m\), where 1 \(N\) = 1 \(kg\) \(\frac{\text{m}}{\text{s}^2}\).

Part 1

Express the units of \(U\) in terms of \(kg\), \(m\) and \(s\).

Note that it may not be necessary to use every variable. Use the following table as a reference for each variable.

For	Use
\(kg\)	kg
\(m\)	m
\(s\)	s

Answer Section

Part 2

Express the units of \(k\) in terms of \(kg\), \(m\) and \(s\).

Note that it may not be necessary to use every variable. Use the following table as a reference for each variable.

For	Use
\(kg\)	kg
\(m\)	m
\(s\)	s

Answer Section

Part 3

Solve for the value of \(?\).

Answer Section

Please enter in a numeric value.

Attribution

Problem is licensed under the CC-BY-NC-SA 4.0 license.