Question

How far will 560 J raise a block with a mass of 4.5 kg
and the acceleration is 9.8m/s²?

Answer 1

Approximately
`13\; {\rm m}`.

Step-by-step explanation:

Let
`g` denote the gravitational field strength (free fall acceleration.) Assume that an object of mass
`m` is lifted up with a height change of
`\Delta h`. The gravitational potential energy of that object will increase by:

`\Delta \text{GPE} = m\, g\, \Delta h`.

Assume that the entire
`560\; {\rm J}` of energy is turned into the gravitational potential energy of this block. The gravitational potential energy of this block would have increased by
`\Delta \text{GPE} = 560\; {\rm J}`.

Note that the standard unit of energy, Joule, is equivalent to:

`1\; {\rm J} = 1\; {\rm N\cdot m} = 1\; {\rm (kg \cdot m\cdot s^(-2)) \cdot m}`.

It is given that
`m = 4.5\; {\rm kg}` while
`g = 9.8\; {\rm m\cdot s^(-2)}`. Rearrange the equation for
`\Delta \text{GPE}` to find the change in height
`\Delta h`:

`\begin{aligned} \Delta h &= \frac{\Delta \text{GPE}}{m\, g} \\ &= \frac{560\; {\rm J}}{(4.5\; {\rm kg})\, (9.8\; {\rm m\cdot s^(-2)})} && 1\; {\rm J} = 1\; {\rm (kg \cdot m\cdot s^(-2)) \cdot m}\\ &\approx 13\; {\rm m}\end{aligned}`.