Question

A sand mover at a quarry lifts 2,000 kg of sand per minute a vertical distance of 12 m. The sand is initially at rest and is discharged at the top of the sand mover with speed 5.0 m/s into a loading chute. What minimum power must be supplied to this machine?

Answer 1

The minimum power supplied to the sand mover is 3920 Watts.

Step-by-step explanation:

To find the minimum power supplied to the sand mover, we need to calculate the work done by the sand mover and divide it by the time it took to do the work. Work is given by the equation:

Work = Force x Distance

The force can be found using Newton's second law:

Force = Mass x Acceleration

In this case, the force is equal to the weight of the sand being lifted, so:

Force = Mass x Gravity

Substituting the values given in the problem, we get:

Force = 2000 kg x 9.8 m/s^2

= 19600 N

Now we can calculate the work:

Work = Force x Distance = 19600 N x 12 m

= 235200 J

Finally, to find the minimum power supplied, we divide the work by the time:

Power = Work / Time

Since the time is given as one minute (60 s), we have:

Power = 235200 J / 60 s

= 3920 W

Therefore, the minimum power that must be supplied to the sand mover is 3920 Watts.