Question

As you lift an 88 N box straight upward you produce a power of 72 W. What is the speed of the box?

Answer 1

The speed of the box is 0.818
`(m)/(s)`

Step-by-step explanation:

Power is defined as the speed with which a job is performed. That is, power is the amount of work done for a unit of time:

`Power=(work)/(time)`

Where P is the power developed by the force that performs the work and its unit of measure in the International System is the Watt or Watts (W), the unit of measure of work in the International System is July (J) and time during which the work is carried out, it has the unit of measure in the International System of seconds (s).

But work is defined as force multiplied by distance. Then:

`Power=(Work)/(Time) =(Force*Distance)/(Time)`

Considering that the speed is associated with the change of position of a body over time (that is,
`(distance)/(time)`) then:

`Power=(Work)/(Time) =(Force*Distance)/(Time)=Force*(Distance)/(Time)`

`Power=Force*Speed`

Then the speed can be calculated as:

`Speed=(Power)/(Force)`

where, in this case:

• Power= 72 W
• Force= 88 N

Then:

`Speed=(72 W)/(88 N)`

Speed= 0.818
`(m)/(s)`

Finally, the speed of the box is 0.818
`(m)/(s)`

Answer 2

F = force applied to lift the box = weight of the box = 88 N

P = power produced while lifting the box upward = 72 Watt

v = speed of the box = ?

Speed of the box is given as

v =
`(P)/(F)`

inserting the values

v =
`(72)/(88)`

v = 0.82 ms⁻¹