# Smudge#

Aliyah 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!), Aliyah decides to use dimensional analysis to figure out the power. Aliyah 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

## 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

Solve for the value of $$?$$.