Question

A father lifts a toddler 1. 5 m up in the air. The child gains 187. 5 j of energy in her gravitational potential energy store as a result. What is the mass of the toddler?.

Answer 1

Approximately
`13\; {\rm kg}`, assuming that
`g = 9.81\; {\rm N \cdot kg^(-1)}`.

Step-by-step explanation:

The gravitational field is approximately uniform (
`g \approx 9.81\; {\rm N\cdot kg^(-1)}`) near the surface of the Earth.

Consider an object of mass
`m` in this gravitational field. If the height of this object increases by
`\Delta h`, this object would gain gravitational potential energy (
`\text{GPE}`)
`m\, g\, \Delta h`.

In this question, it is given that
`\Delta h = 1.5\; {\rm m}`. The object gained
`187.5\; {\rm J}` of
`\text{GPE}`. Rearrange the equation
`\text{GPE} = m\, g\, \Delta h` to find the mass of this object:

`\begin{aligned}m &= \frac{(\text{GPE})}{g\, \Delta h} \\ &= \frac{187.5\; {\rm J}}{(9.81\; {\rm N\cdot kg^(-1)})\, (1.5\; {\rm m})} \\ &\approx 13\; {\rm kg} \end{aligned}`.

(Note that
`187.5\; {\rm J} = 187.5\; {\rm N\cdot m}`.)