Final answer:
To find the required power to lift 10⁵ kg of coal from a 360m deep mine, apply the formula for power (P=W/t) using the given mass, gravitational acceleration, and height, and divide by the number of seconds in an hour.
Step-by-step explanation:
To calculate the power of an engine required to lift 10⁵kg of coal per hour from a mine 360m deep, we use the formula for power, P=W/t, where W is work done and t is time. The work done (W) to lift the coal is equal to the force due to gravity on the mass (mg) times the height (h), which in this case is W=mg*h. Given that g=10 m/s², the mass m=10⁵ kg, and the height h=360 m:
P = (10⁵ kg × 10 m/s² × 360 m) / 3600 s
This calculation would give us the power required to lift the coal in watts (W).