0
$\begingroup$

I have the question:

A baby of mass $9.0\;$kg bounces with a period of $1.2\;$s in a baby bouncer. What is the spring constant of the bouncer?

I rearranged the equation $T = 2\pi$ $\sqrt{\frac{m}{k}}$ to make $k$ the subject.

$$k = \frac{4 \pi^2 m}{T^2}$$

The answer I got for this is $k= 246.74$.

However, I am not sure what the units should be.

  • 1
    Great question! Should be on https://physics.stackexchange.com though. – 2017-01-06
  • 1
    The spring exerts force (Newtons or pounds) and that force increases as the spring compresses (units of distance). $N/m$ – 2017-01-06
  • 2
    Your derived formula suggests units of $kg\, s^{-2}$, which is the same as @DougM's $N \, m^{-1}$ – 2017-01-06
  • 0
    @setholopolus Please do not recommend physics.SE as a migration target unless you are sure the question is on-topic there. In this case, it is clearly off-topic by our homework policy. – 2017-01-07

1 Answers 1

2

The units are both $\text{N}\cdot \text{m}^{-1}$ or $\text{kg}\cdot \text{s}^{-2}$.

The units of the mass $m$ is $\text{kg}$ and the units of the period $T$ is $\text{s}$.

Substituting the units into your formula, you get:

$$\frac{\text{kg}}{\text{s}^{2}}=\text{kg}\cdot \text{s}^{-2}$$

We can ignore the $4\pi^2$, since it is a dimensionless (unitless) constant.

Note that $\text{N}\cdot \text{m}^{-1}$ is equivalent to $\text{kg}\cdot \text{s}^{-2}$ because the units for force can be written as $\text{kg} \cdot \text{m} \cdot {\text{s}^{-2}}$ and so, substituting this into $\text{N} \cdot \text{m}^{-1}$ gives $\text{kg} \cdot \text{m} \cdot {\text{s}^{-2}} \cdot \text{m}^{-1}=\text{kg} \cdot {\text{s}^{-2}}$, which was the result obtained.

  • 1
    Very detailed answer thank you (: – 2017-01-06