. A 475 kg pre-stressed concrete beam is to be raised 10.0 m in 24.0 s. How many kilowatts of power

is needed for the job?

power = work/time

work = weight * distance up
= 475*9.81*10
so
power = 475*9.81*10 / 24 Joules/second or Watts

divide by 1000 for kilowatts

1.9415625

To determine the power needed for this job, we can use the formula:

Power (P) = Work (W) / time (t)

To calculate the work, we need to find the gravitational potential energy of the concrete beam when it is raised 10.0 m.

The formula for gravitational potential energy is given by:

Potential Energy (PE) = mass (m) * gravity (g) * height (h)

Given:
Mass (m) = 475 kg
Height (h) = 10.0 m
Gravity (g) = 9.8 m/s^2

Potential Energy (PE) = 475 kg * 9.8 m/s^2 * 10.0 m
= 46,550 J

Now, we can substitute the values into the power formula:

Power (P) = Work (W) / time (t)
= Potential Energy (PE) / time (t)
= 46,550 J / 24.0 s

To convert joules (J) to kilowatts (kW), divide the result by 1000:

Power (P) = 46,550 J / 24.0 s / 1000
= 1.94 kW

Therefore, approximately 1.94 kilowatts of power is needed for the job.