Question

A science museum display about energy has a small engine that pulls on a rope to lift a block 1.00 m. The display indicates that 1.00 J

of work is done. What is the mass of the block?

Answer 1

0.102 kg

Step-by-step explanation:

Work is measured in Joules, an amount of energy. As the engine lifts the block, it will exert energy (doing work) to give that energy to the block in the form of gravitational potential energy.

Gravitational potential energy is given by the formula
`U=mgh`, where U is the gravitational potential energy, m is the mass of the object with the energy, g is the gravitational constant near the surface of the earth, and h is the height it was raised.

We can isolate "m" in the equation, substitute the known values into the equation, including g = 9.81 m/s^2, and calculate m.

`(U)/(gh)=m`

`((1.00[J]))/((9.81[(m)/(s^2)])(1.00[m]))=m`

Rewriting the units of Joules into its base SI units...

`((1.00[(kg \cdot m^2)/(s^2)]))/((9.81[(m)/(s^2)])(1.00[m]))=m`

Canceling units, and calculating...

`0.1019367991845[kg]=m`

Rounding to 3 sig figs...

`0.102[kg]=m`